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Redshift

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</style><div role="note" class="hatnote navigation-not-searchable">This article is about the astronomical phenomenon. For other uses, see <a href="Redshift_(disambiguation)" class="mw-disambig" title="Redshift (disambiguation)">Redshift (disambiguation)</a>.</div>

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</style><table class="sidebar sidebar-collapse nomobile nowraplinks plainlist"><tbody><tr><th class="sidebar-title"><a href="General_relativity" title="General relativity">General relativity</a></th></tr><tr><td class="sidebar-image"><div class="sidebar-caption" style="padding:0.5em 0.2em 0.6em;border-bottom:1px solid #aaa; display:block;margin-bottom:0.1em;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}">

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<annotation encoding="application/x-tex">{\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}</annotation>

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</math><img src="./124ab80fcb17e2733cc17ff6f93da5e52f355c77.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:19.468ex; height:2.843ex;" alt="{\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}" loading="lazy"></div></td></tr><tr><td class="sidebar-content" style="padding-bottom:0.75em;">

<ul><li><a href="Introduction_to_general_relativity" title="Introduction to general relativity">Introduction</a></li>

<li><div class="hlist"><ul><li><a href="History_of_general_relativity" title="History of general relativity">History</a></li><li><a href="Timeline_of_gravitational_physics_and_relativity" title="Timeline of gravitational physics and relativity">Timeline</a></li><li><a href="Tests_of_general_relativity" title="Tests of general relativity">Tests</a></li></ul></div></li>

<li><a href="Mathematics_of_general_relativity" title="Mathematics of general relativity">Mathematical formulation</a></li></ul></td>

</tr><tr><td class="sidebar-content">

<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf; text-align:center;;color: var(--color-base)"><div class="sidebar-list-title-c">Fundamental concepts</div></div><div class="sidebar-list-content mw-collapsible-content hlist">

<ul><li><a href="Equivalence_principle" title="Equivalence principle">Equivalence principle</a></li>

<li><a href="Special_relativity" title="Special relativity">Special relativity</a></li>

<li><a href="World_line" title="World line">World line</a></li>

<li><a href="Pseudo-Riemannian_manifold" title="Pseudo-Riemannian manifold">Pseudo-Riemannian manifold</a></li></ul></div></div></td>

</tr><tr><td class="sidebar-content">

<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf; text-align:center;;color: var(--color-base)"><div class="sidebar-list-title-c">Phenomena</div></div><div class="sidebar-list-content mw-collapsible-content hlist"><table class="sidebar nomobile nowraplinks" style="background-color: transparent; color: var( --color-base, #202122 ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tbody><tr><td class="sidebar-content">

<ul><li><a href="Two-body_problem_in_general_relativity" title="Two-body problem in general relativity">Kepler problem</a></li>

<li><a href="Gravitational_lens" title="Gravitational lens">Gravitational lensing</a></li>

<li><a href="Gravitational_redshift" title="Gravitational redshift">Gravitational redshift</a></li>

<li><a href="Gravitational_time_dilation" title="Gravitational time dilation">Gravitational time dilation</a></li>

<li><a href="Gravitational_wave" title="Gravitational wave">Gravitational waves</a></li>

<li><a href="Frame-dragging" title="Frame-dragging">Frame-dragging</a></li>

<li><a href="Geodetic_effect" title="Geodetic effect">Geodetic effect</a></li>

<li><a href="Event_horizon" title="Event horizon">Event horizon</a></li>

<li><a href="Gravitational_singularity" title="Gravitational singularity">Singularity</a></li>

<li><a href="Black_hole" title="Black hole">Black hole</a></li></ul></td>

</tr><tr><th class="sidebar-heading" style="background:#ececff; font-style:italic;font-weight:normal;">

<a href="Spacetime" title="Spacetime">Spacetime</a></th></tr><tr><td class="sidebar-content">

<ul><li><a href="Spacetime_diagram" title="Spacetime diagram">Spacetime diagrams</a></li>

<li><a href="Minkowski_space" title="Minkowski space">Minkowski spacetime</a></li>

<li><a href="Wormhole" title="Wormhole">Einstein–Rosen bridge</a></li></ul></td>

</tr></tbody></table></div></div></td>

</tr><tr><td class="sidebar-content">

<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf; text-align:center;;color: var(--color-base)"><div class="sidebar-list-title-c"><div class="hlist"><ul><li>Equations</li><li>Formalisms</li></ul></div></div></div><div class="sidebar-list-content mw-collapsible-content hlist"><table class="sidebar nomobile nowraplinks" style="background-color: transparent; color: var( --color-base, #202122 ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none;padding-bottom:0;margin-bottom:0;"><tbody><tr><th class="sidebar-heading" style="font-style:italic;font-weight:normal;padding-bottom:0;">

Equations</th></tr><tr><td class="sidebar-content" style="padding-top:0;">

<ul><li><a href="Linearized_gravity" title="Linearized gravity">Linearized gravity</a></li>

<li><a href="Einstein_field_equations" title="Einstein field equations">Einstein field equations</a></li>

<li><a href="Friedmann_equations" title="Friedmann equations">Friedmann</a></li>

<li><a href="Geodesics_in_general_relativity" title="Geodesics in general relativity">Geodesics</a></li>

<li><a href="Mathisson%E2%80%93Papapetrou%E2%80%93Dixon_equations" title="Mathisson–Papapetrou–Dixon equations">Mathisson–Papapetrou–Dixon</a></li>

<li><a href="Hamilton%E2%80%93Jacobi%E2%80%93Einstein_equation" title="Hamilton–Jacobi–Einstein equation">Hamilton–Jacobi–Einstein</a></li></ul></td>

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Formalisms</th></tr><tr><td class="sidebar-content" style="padding-top:0;">

<li><a href="Parameterized_post-Newtonian_formalism" title="Parameterized post-Newtonian formalism">Post-Newtonian</a></li></ul></td>

</tr><tr><th class="sidebar-heading" style="font-style:italic;font-weight:normal;padding-bottom:0;">

Advanced theory</th></tr><tr><td class="sidebar-content" style="padding-top:0;">

<ul><li><a href="Kaluza%E2%80%93Klein_theory" title="Kaluza–Klein theory">Kaluza–Klein theory</a></li>

<li><a href="Quantum_gravity" title="Quantum gravity">Quantum gravity</a></li></ul></td>

</tr></tbody></table></div></div></td>

</tr><tr><td class="sidebar-content">

<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf; text-align:center;;color: var(--color-base)"><div class="sidebar-list-title-c"><a href="Exact_solutions_in_general_relativity" title="Exact solutions in general relativity">Solutions</a></div></div><div class="sidebar-list-content mw-collapsible-content hlist">

<ul><li><a href="Schwarzschild_metric" title="Schwarzschild metric">Schwarzschild</a> (<a href="Interior_Schwarzschild_metric" title="Interior Schwarzschild metric">interior</a>)</li>

<li><a href="Reissner%E2%80%93Nordstr%C3%B6m_metric" title="Reissner–Nordström metric">Reissner–Nordström</a></li>

<li><a href="Einstein%E2%80%93Rosen_metric" title="Einstein–Rosen metric">Einstein–Rosen waves</a></li>

<li><a href="Wormhole" title="Wormhole">Wormhole</a></li>

<li><a href="G%C3%B6del_metric" title="Gödel metric">Gödel</a></li>

<li><a href="Kerr%E2%80%93Newman_metric" title="Kerr–Newman metric">Kerr–Newman</a></li>

<li><a href="Kerr%E2%80%93Newman%E2%80%93de%E2%80%93Sitter_metric" title="Kerr–Newman–de–Sitter metric">Kerr–Newman–de Sitter</a></li>

<li><a href="Kasner_metric" title="Kasner metric">Kasner</a></li>

<li><a href="Lema%C3%AEtre%E2%80%93Tolman_metric" title="Lemaître–Tolman metric">Lemaître–Tolman</a></li>

<li><a href="Milne_model" title="Milne model">Milne</a></li>

<li><a href="Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric" title="Friedmann–Lemaître–Robertson–Walker metric">Robertson–Walker</a></li>

<li><a href="Oppenheimer%E2%80%93Snyder_model" title="Oppenheimer–Snyder model">Oppenheimer–Snyder</a></li>

<li><a href="Van_Stockum_dust" title="Van Stockum dust">van Stockum dust</a></li>

<li><a href="Hartle%E2%80%93Thorne_metric" title="Hartle–Thorne metric">Hartle–Thorne</a></li>

<li><a href="Vaidya_metric" title="Vaidya metric">Vaidya</a></li>

<li><a href="Peres_metric" title="Peres metric">Peres</a></li>

<li><a href="De_Sitter%E2%80%93Schwarzschild_metric" title="De Sitter–Schwarzschild metric">De Sitter-Schwarzschild</a></li>

<li><a href="McVittie_metric" title="McVittie metric">McVittie</a></li>

<li><a href="Kerr%E2%80%93Newman%E2%80%93de%E2%80%93Sitter_metric" title="Kerr–Newman–de–Sitter metric">Kerr-Newman-de-Sitter</a></li></ul></div></div></td>

</tr><tr><td class="sidebar-content">

<ul><li><a href="Albert_Einstein" title="Albert Einstein">Einstein</a></li>

<li><a href="Hendrik_Lorentz" title="Hendrik Lorentz">Lorentz</a></li>

<li><a href="David_Hilbert" title="David Hilbert">Hilbert</a></li>

<li><a href="Henri_Poincar%C3%A9" title="Henri Poincaré">Poincaré</a></li>

<li><a href="Karl_Schwarzschild" title="Karl Schwarzschild">Schwarzschild</a></li>

<li><a href="Willem_de_Sitter" title="Willem de Sitter">de Sitter</a></li>

<li><a href="Hans_Reissner" title="Hans Reissner">Reissner</a></li>

<li><a href="Gunnar_Nordstr%C3%B6m" title="Gunnar Nordström">Nordström</a></li>

<li><a href="Arthur_Eddington" title="Arthur Eddington">Eddington</a></li>

<li><a href="Alexander_Friedmann" title="Alexander Friedmann">Friedmann</a></li>

<li><a href="Edward_Arthur_Milne" title="Edward Arthur Milne">Milne</a></li>

<li><a href="Fritz_Zwicky" title="Fritz Zwicky">Zwicky</a></li>

<li><a href="Georges_Lema%C3%AEtre" title="Georges Lemaître">Lemaître</a></li>

<li><a href="J._Robert_Oppenheimer" title="J. Robert Oppenheimer">Oppenheimer</a></li>

<li><a href="Kurt_G%C3%B6del" title="Kurt Gödel">Gödel</a></li>

<li><a href="John_Archibald_Wheeler" title="John Archibald Wheeler">Wheeler</a></li>

<li><a href="Howard_P._Robertson" title="Howard P. Robertson">Robertson</a></li>

<li><a href="James_M._Bardeen" title="James M. Bardeen">Bardeen</a></li>

<li><a href="Arthur_Geoffrey_Walker" title="Arthur Geoffrey Walker">Walker</a></li>

<li><a href="Subrahmanyan_Chandrasekhar" title="Subrahmanyan Chandrasekhar">Chandrasekhar</a></li>

<li><a href="J%C3%BCrgen_Ehlers" title="Jürgen Ehlers">Ehlers</a></li>

<li><a href="Roger_Penrose" title="Roger Penrose">Penrose</a></li>

<li><a href="Stephen_Hawking" title="Stephen Hawking">Hawking</a></li>

<li><a href="Amal_Kumar_Raychaudhuri" title="Amal Kumar Raychaudhuri">Raychaudhuri</a></li>

<li><a href="Joseph_Hooton_Taylor_Jr." title="Joseph Hooton Taylor Jr.">Taylor</a></li>

<li><a href="Russell_Alan_Hulse" title="Russell Alan Hulse">Hulse</a></li>

<li><a href="Willem_Jacob_van_Stockum" title="Willem Jacob van Stockum">van Stockum</a></li>

<li><a href="Ezra_T._Newman" title="Ezra T. Newman">Newman</a></li>

<li><a href="Kip_Thorne" title="Kip Thorne">Thorne</a></li>

<li><a href="List_of_contributors_to_general_relativity" title="List of contributors to general relativity">others</a></li></ul></div></div></td>

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<ul><li> <a href="Portal%3APhysics" title="Portal:Physics">Physics portal</a></li>

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</style><table class="sidebar sidebar-collapse nomobile nowraplinks plainlist physical-cosmology"><tbody><tr><td class="sidebar-pretitle">Part of a series on</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="Physical_cosmology" title="Physical cosmology">Physical cosmology</a></th></tr><tr><td class="sidebar-image"></td></tr><tr><td class="sidebar-above">

<ul><li><a href="Big_Bang" title="Big Bang">Big Bang</a> · <a href="Universe" title="Universe">Universe</a></li>

<li><a href="Age_of_the_universe" title="Age of the universe">Age of the universe</a></li>

<li><a href="Chronology_of_the_universe" title="Chronology of the universe">Chronology of the universe</a></li></ul></td></tr><tr><td class="sidebar-content-with-subgroup">

<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c">Early universe</div></div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar-subgroup"><tbody><tr><td class="sidebar-content">

<ul><li><a href="Cosmic_inflation" title="Cosmic inflation">Inflation</a> · <a href="Big_Bang_nucleosynthesis" title="Big Bang nucleosynthesis">Nucleosynthesis</a></li></ul></td>

</tr><tr><th class="sidebar-heading">

Backgrounds</th></tr><tr><td class="sidebar-content">

<ul><li><a href="Gravitational_wave_background" title="Gravitational wave background">Gravitational wave (GWB)</a></li>

<li><a href="Cosmic_microwave_background" title="Cosmic microwave background">Microwave (CMB)</a> · <a href="Cosmic_neutrino_background" title="Cosmic neutrino background">Neutrino (CNB)</a></li></ul></td>

</tr></tbody></table></div></div></td>

</tr><tr><td class="sidebar-content">

<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c">Expansion · Future</div></div><div class="sidebar-list-content mw-collapsible-content">

<ul><li><a href="Hubble's_law" title="Hubble's law">Hubble's law</a> · </li>

<li><a href="Expansion_of_the_universe" title="Expansion of the universe">Expansion of the universe</a></li>

<li><a href="Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric" title="Friedmann–Lemaître–Robertson–Walker metric">FLRW metric</a> · <a href="Friedmann_equations" title="Friedmann equations">Friedmann equations</a></li>

<li><a href="Lambda-CDM_model" title="Lambda-CDM model">Lambda-CDM model</a></li>

<li><a href="Future_of_an_expanding_universe" title="Future of an expanding universe">Future of an expanding universe</a></li>

<li><a href="Ultimate_fate_of_the_universe" title="Ultimate fate of the universe">Ultimate fate of the universe</a></li></ul></div></div></td>

</tr><tr><td class="sidebar-content-with-subgroup">

<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c">Components · Structure</div></div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar-subgroup"><tbody><tr><th class="sidebar-heading">

Components</th></tr><tr><td class="sidebar-content">

<ul><li><a href="Dark_energy" title="Dark energy">Dark energy</a> · <a href="Dark_matter" title="Dark matter">Dark matter</a></li>

<li><a href="Photon" title="Photon">Photons</a> · <a href="Baryon" title="Baryon">Baryons</a></li></ul></td>

</tr><tr><th class="sidebar-heading">

Structure</th></tr><tr><td class="sidebar-content">

<ul><li><a href="Shape_of_the_universe" title="Shape of the universe">Shape of the universe</a></li>

<li><a href="Galaxy_filament" title="Galaxy filament">Galaxy filament</a> · <a href="Galaxy_formation_and_evolution" title="Galaxy formation and evolution">Galaxy formation</a></li>

<li><a href="Large_quasar_group" title="Large quasar group">Large quasar group</a></li>

<li><a href="Observable_universe#Large-scale_structure" title="Observable universe">Large-scale structure</a></li>

<li><a href="Reionization" title="Reionization">Reionization</a> · <a href="Structure_formation" title="Structure formation">Structure formation</a></li></ul></td>

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<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c"><a href="Observational_cosmology" title="Observational cosmology">Experiments</a></div></div><div class="sidebar-list-content mw-collapsible-content">

<ul><li><a href="Black_Hole_Initiative" title="Black Hole Initiative">Black Hole Initiative (BHI)</a></li>

<li><a href="BOOMERanG_experiment" title="BOOMERanG experiment">BOOMERanG</a></li>

<li><a href="Cosmic_Background_Explorer" title="Cosmic Background Explorer">Cosmic Background Explorer (COBE)</a></li>

<li><a href="Dark_Energy_Survey" title="Dark Energy Survey">Dark Energy Survey</a></li>

<li><a href="Planck_(spacecraft)" title="Planck (spacecraft)">Planck space observatory</a></li>

<li><a href="Sloan_Digital_Sky_Survey" title="Sloan Digital Sky Survey">Sloan Digital Sky Survey (SDSS)</a></li>

<li><a href="2dF_Galaxy_Redshift_Survey" title="2dF Galaxy Redshift Survey">2dF Galaxy Redshift Survey ("2dF")</a></li>

<li><div style="display:inline-block; padding:0.2em 0.4em; line-height:1.2em;"><a href="Wilkinson_Microwave_Anisotropy_Probe" title="Wilkinson Microwave Anisotropy Probe">Wilkinson Microwave Anisotropy Probe (WMAP)</a></div></li></ul></div></div></td>

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<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c">Scientists</div></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist" style="padding:0 0.9em;">

<ul><li><a href="Marc_Aaronson" title="Marc Aaronson">Aaronson</a></li>

<li><a href="Hannes_Alfv%C3%A9n" title="Hannes Alfvén">Alfvén</a></li>

<li><a href="Ralph_Alpher" title="Ralph Alpher">Alpher</a></li>

<li><a href="Nicolaus_Copernicus" title="Nicolaus Copernicus">Copernicus</a></li>

<li><a href="Willem_de_Sitter" title="Willem de Sitter">de Sitter</a></li>

<li><a href="Robert_H._Dicke" title="Robert H. Dicke">Dicke</a></li>

<li><a href="J%C3%BCrgen_Ehlers" title="Jürgen Ehlers">Ehlers</a></li>

<li><a href="Albert_Einstein" title="Albert Einstein">Einstein</a></li>

<li><a href="George_F._R._Ellis" title="George F. R. Ellis">Ellis</a></li>

<li><a href="Alexander_Friedmann" title="Alexander Friedmann">Friedmann</a></li>

<li><a href="Galileo_Galilei" title="Galileo Galilei">Galileo</a></li>

<li><a href="George_Gamow" title="George Gamow">Gamow</a></li>

<li><a href="Stephen_Hawking" title="Stephen Hawking">Hawking</a></li>

<li><a href="Edwin_Hubble" title="Edwin Hubble">Hubble</a></li>

<li><a href="Christiaan_Huygens" title="Christiaan Huygens">Huygens</a></li>

<li><a href="Johannes_Kepler" title="Johannes Kepler">Kepler</a></li>

<li><a href="Georges_Lema%C3%AEtre" title="Georges Lemaître">Lemaître</a></li>

<li><a href="John_C._Mather" title="John C. Mather">Mather</a></li>

<li><a href="Isaac_Newton" title="Isaac Newton">Newton</a></li>

<li><a href="Roger_Penrose" title="Roger Penrose">Penrose</a></li>

<li><a href="Arno_Allan_Penzias" title="Arno Allan Penzias">Penzias</a></li>

<li><a href="Vera_Rubin" title="Vera Rubin">Rubin</a></li>

<li><a href="Brian_Schmidt" title="Brian Schmidt">Schmidt</a></li>

<li><a href="George_Smoot" title="George Smoot">Smoot</a></li>

<li><a href="Nicholas_B._Suntzeff" title="Nicholas B. Suntzeff">Suntzeff</a></li>

<li><a href="Rashid_Sunyaev" title="Rashid Sunyaev">Sunyaev</a></li>

<li><a href="Richard_C._Tolman" title="Richard C. Tolman">Tolman</a></li>

<li><a href="Robert_Woodrow_Wilson" title="Robert Woodrow Wilson">Wilson</a></li>

<li><a href="Yakov_Zeldovich" title="Yakov Zeldovich">Zeldovich</a></li></ul>

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<ul><li><a href="List_of_cosmologists" title="List of cosmologists">List of cosmologists</a></li></ul></div></div></td>

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<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c"><a href="Physical_cosmology#Subject_history" title="Physical cosmology">Subject history</a></div></div><div class="sidebar-list-content mw-collapsible-content">

<ul><li><div style="display:inline-block; padding:0.2em 0.4em; line-height:1.2em;"><a href="Discovery_of_cosmic_microwave_background_radiation" title="Discovery of cosmic microwave background radiation">Discovery of cosmic microwave background radiation</a></div></li>

<li><a href="History_of_the_Big_Bang_theory" title="History of the Big Bang theory">History of the Big Bang theory</a></li>

<li><a href="Timeline_of_cosmological_theories" title="Timeline of cosmological theories">Timeline of cosmological theories</a></li></ul></div></div></td>

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<ul><li> Category</li>

<li> <a href="Portal%3AAstronomy" title="Portal:Astronomy">Astronomy portal</a></li></ul></td></tr><tr><td class="sidebar-navbar"></td></tr></tbody></table>

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</style><table class="sidebar sidebar-collapse nomobile nowraplinks plainlist special-relativity-sidebar"><tbody><tr><th class="sidebar-title"><a href="Special_relativity" title="Special relativity">Special relativity</a></th></tr><tr><td class="sidebar-image"></td></tr><tr><td class="sidebar-content .special-relativity-sidebar-content1">

<div class="hlist"><ul><li><a href="Principle_of_relativity" title="Principle of relativity">Principle of relativity</a></li><li><a href="Theory_of_relativity" title="Theory of relativity">Theory of relativity</a></li><li><a href="Formulations_of_special_relativity" title="Formulations of special relativity">Formulations</a></li></ul></div></td>

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<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c">Foundations</div></div><div class="sidebar-list-content mw-collapsible-content">

<ul><li><a href="Postulates_of_special_relativity" title="Postulates of special relativity">Einstein's postulates</a></li>

<li><a href="Inertial_frame_of_reference" title="Inertial frame of reference">Inertial frame of reference</a></li>

<li><a href="Speed_of_light" title="Speed of light">Speed of light</a></li>

<li><a href="Maxwell's_equations" title="Maxwell's equations">Maxwell's equations</a></li>

<li><a href="Lorentz_transformation" title="Lorentz transformation">Lorentz transformation</a></li></ul></div></div></td>

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<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c">Consequences</div></div><div class="sidebar-list-content mw-collapsible-content">

<ul><li><a href="Time_dilation" title="Time dilation">Time dilation</a></li>

<li><a href="Length_contraction" title="Length contraction">Length contraction</a></li>

<li><a href="Mass_in_special_relativity" title="Mass in special relativity">Relativistic mass</a></li>

<li><a href="Mass%E2%80%93energy_equivalence" title="Mass–energy equivalence">Mass–energy equivalence</a></li>

<li><a href="Relativity_of_simultaneity" title="Relativity of simultaneity">Relativity of simultaneity</a></li>

<li><a href="Relativistic_Doppler_effect" title="Relativistic Doppler effect">Relativistic Doppler effect</a></li>

<li><a href="Thomas_precession" title="Thomas precession">Thomas precession</a></li>

<li><a href="Relativistic_disk" title="Relativistic disk">Relativistic disk</a></li>

<li><a href="Bell's_spaceship_paradox" title="Bell's spaceship paradox">Bell's spaceship paradox</a></li>

<li><a href="Ehrenfest_paradox" title="Ehrenfest paradox">Ehrenfest paradox</a></li></ul></div></div></td>

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<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c"><a href="Spacetime" title="Spacetime">Spacetime</a></div></div><div class="sidebar-list-content mw-collapsible-content">

<ul><li><a href="Minkowski_space" title="Minkowski space">Minkowski spacetime</a></li>

<li><a href="Minkowski_diagram" class="mw-redirect" title="Minkowski diagram">Spacetime diagram</a></li>

<li><a href="World_line" title="World line">World line</a></li>

<li><a href="Light_cone" title="Light cone">Light cone</a></li></ul></div></div></td>

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<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c"><a href="Dynamics_(mechanics)" title="Dynamics (mechanics)">Dynamics</a></div></div><div class="sidebar-list-content mw-collapsible-content">

<ul><li><a href="Proper_time" title="Proper time">Proper time</a></li>

<li><a href="Invariant_mass" title="Invariant mass">Proper mass</a></li>

<li><a href="Four-momentum" title="Four-momentum">Four-momentum</a></li></ul></div></div></td>

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<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c"><div class="hlist" style="font-size:110%;"><ul><li><a href="History_of_special_relativity" title="History of special relativity">History</a></li><li>Precursors</li></ul></div></div></div><div class="sidebar-list-content mw-collapsible-content">

<ul><li><a href="Galilean_invariance" title="Galilean invariance">Galilean relativity</a></li>

<li><a href="Galilean_transformation" title="Galilean transformation">Galilean transformation</a></li>

<li><a href="Aether_theories" title="Aether theories">Aether theories</a></li>

<li><a href="Hyperbolic_quaternion" title="Hyperbolic quaternion">Hyperbolic quaternions</a></li></ul></div></div></td>

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<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c">People</div></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist">

<ul><li><a href="Albert_Einstein" title="Albert Einstein">Einstein</a></li>

<li><a href="Arnold_Sommerfeld" title="Arnold Sommerfeld">Sommerfeld</a></li>

<li><a href="Albert_A._Michelson" title="Albert A. Michelson">Michelson</a></li>

<li><a href="Edward_W._Morley" title="Edward W. Morley">Morley</a></li>

<li><a href="George_Francis_FitzGerald" title="George Francis FitzGerald">FitzGerald</a></li>

<li><a href="Gustav_Herglotz" title="Gustav Herglotz">Herglotz</a></li>

<li><a href="Hendrik_Lorentz" title="Hendrik Lorentz">Lorentz</a></li>

<li><a href="Henri_Poincar%C3%A9" title="Henri Poincaré">Poincaré</a></li>

<li><a href="Hermann_Minkowski" title="Hermann Minkowski">Minkowski</a></li>

<li><a href="Hippolyte_Fizeau" title="Hippolyte Fizeau">Fizeau</a></li>

<li><a href="Max_Abraham" title="Max Abraham">Abraham</a></li>

<li><a href="Max_Planck" title="Max Planck">Planck</a></li>

<li><a href="Paul_Ehrenfest" title="Paul Ehrenfest">Ehrenfest</a></li>

<li><a href="Richard_C._Tolman" title="Richard C. Tolman">Tolman</a></li>

<li><a href="Paul_Dirac" title="Paul Dirac">Dirac</a></li></ul>

</div></div></div></td>

</tr><tr><td class="sidebar-below hlist">

<li> Category</li></ul></td></tr><tr><td class="sidebar-navbar"></td></tr></tbody></table>

In <a href="Physics" title="Physics">physics</a>, a redshift is an increase in the <a href="Wavelength" title="Wavelength">wavelength</a>, or equivalently, a decrease in the <a href="Frequency" title="Frequency">frequency</a> and <a href="Photon_energy" title="Photon energy">photon energy</a>, of <a href="Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic radiation</a> (such as <a href="Light" title="Light">light</a>). The opposite change, a decrease in wavelength and increase in frequency and energy, is known as a <a href="#Blueshift">blueshift</a>. The terms derive from the colours <a href="Red" title="Red">red</a> and <a href="Blue" title="Blue">blue</a> which form the extremes of the <a href="Visible_spectrum" title="Visible spectrum">visible light spectrum</a>.

Three forms of redshift occur in <a href="Astronomy" title="Astronomy">astronomy</a> and <a href="Cosmology" title="Cosmology">cosmology</a>: <a href="Doppler_effect" title="Doppler effect">Doppler</a> redshifts due to the relative motions of radiation sources, <a href="Gravitational_redshift" title="Gravitational redshift">gravitational redshift</a> as radiation escapes from gravitational potentials, and <a href="Cosmological_redshift" class="mw-redirect" title="Cosmological redshift">cosmological redshifts</a> caused by the <a href="Expansion_of_the_universe" title="Expansion of the universe">universe expanding</a>.

In astronomy, the value of a redshift is often denoted by the letter z, corresponding to the fractional change in wavelength (positive for redshifts, negative for blueshifts), and by the wavelength ratio 1 + z (which is greater than 1 for redshifts and less than 1 for blueshifts). Automated astronomical redshift surveys are an important tool for learning about the large scale structure of the universe.

Examples of strong redshifting are a <a href="Gamma_ray" title="Gamma ray">gamma ray</a> perceived as an <a href="X-ray" title="X-ray">X-ray</a>, or initially visible light perceived as <a href="Radio_wave" title="Radio wave">radio waves</a>. The initial heat from the <a href="Big_Bang" title="Big Bang">Big Bang</a> has redshifted far down to become the <a href="Cosmic_microwave_background" title="Cosmic microwave background">cosmic microwave background</a>. Subtler redshifts are seen in the <a href="Astronomical_spectroscopy" title="Astronomical spectroscopy">spectroscopic</a> observations of <a href="Astronomical" class="mw-redirect" title="Astronomical">astronomical</a> objects, and are used in terrestrial technologies such as <a href="Doppler_radar" title="Doppler radar">Doppler radar</a> and <a href="Radar_gun" class="mw-redirect" title="Radar gun">radar guns</a>.

<a href="Gravitational_wave" title="Gravitational wave">Gravitational waves</a>, which also travel at <a href="Speed_of_light" title="Speed of light">the speed of light</a>, are subject to the same redshift phenomena.<a href="#cite_note-1">[1]</a>

Other physical processes exist that can lead to a shift in the frequency of electromagnetic radiation, including <a href="Scattering" title="Scattering">scattering</a> and <a href="Physical_optics" title="Physical optics">optical effects</a>; however, the resulting changes are distinguishable from (astronomical) redshift and are not generally referred to as such (see section on <a href="#Effects_from_physical_optics_or_radiative_transfer">physical optics and radiative transfer</a>).

<div class="mw-heading mw-heading2"><h2 id="Concept">Concept</h2></div>

Using a telescope and a <a href="Spectrometer" title="Spectrometer">spectrometer</a>, the variation in intensity of star light with frequency can be measured. The resulting spectrum can be compared to the spectrum from hot gases expected in stars, such as <a href="Hydrogen" title="Hydrogen">hydrogen</a>, in a laboratory on Earth. As illustrated with the idealized spectrum in the top-right, to determine the redshift, features in the two spectra such as <a href="Spectral_line" title="Spectral line">absorption lines</a>, <a href="Spectral_line" title="Spectral line">emission lines</a>, or other variations in light intensity may be shifted.

Redshift (and blueshift) may be characterized by the relative difference between the observed and emitted wavelengths (or frequency) of an object. In astronomy, it is customary to refer to this change using a <a href="Dimensionless_quantity" title="Dimensionless quantity">dimensionless quantity</a> called z. If λ represents wavelength and f represents frequency (note, λf = c where c is the <a href="Speed_of_light" title="Speed of light">speed of light</a>), then z is defined by the equations:<a href="#cite_note-3">[3]</a>

<caption>Calculation of redshift, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z}">

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<annotation encoding="application/x-tex">{\displaystyle z}</annotation>

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</math><img src="./bf368e72c009decd9b6686ee84a375632e11de98.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.088ex; height:1.676ex;" alt="{\displaystyle z}" loading="lazy">

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<th>Based on wavelength</th>

<th>Based on frequency

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<annotation encoding="application/x-tex">{\displaystyle z={\frac {\lambda _{\mathrm {obsv} }-\lambda _{\mathrm {emit} }}{\lambda _{\mathrm {emit} }}}}</annotation>

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</math><img src="./6a999cd6480ab61dddeeb5372c8037c0d533f2c9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:17.486ex; height:5.843ex;" alt="{\displaystyle z={\frac {\lambda _{\mathrm {obsv} }-\lambda _{\mathrm {emit} }}{\lambda _{\mathrm {emit} }}}}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle z={\frac {f_{\mathrm {emit} }-f_{\mathrm {obsv} }}{f_{\mathrm {obsv} }}}}</annotation>

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</math><img src="./7cf28c6ce6fcc3087c62bf506432ce3381236738.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:17.054ex; height:5.843ex;" alt="{\displaystyle z={\frac {f_{\mathrm {emit} }-f_{\mathrm {obsv} }}{f_{\mathrm {obsv} }}}}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle 1+z={\frac {\lambda _{\mathrm {obsv} }}{\lambda _{\mathrm {emit} }}}}</annotation>

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</math><img src="./7f1dfb8b86273fadf1bd7cbe8b864da69b0915ba.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:13.865ex; height:5.843ex;" alt="{\displaystyle 1+z={\frac {\lambda _{\mathrm {obsv} }}{\lambda _{\mathrm {emit} }}}}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle 1+z={\frac {f_{\mathrm {emit} }}{f_{\mathrm {obsv} }}}}</annotation>

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</math><img src="./8747551886d0568e0d61ac980fdc9646872f67a6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:13.649ex; height:5.843ex;" alt="{\displaystyle 1+z={\frac {f_{\mathrm {emit} }}{f_{\mathrm {obsv} }}}}" loading="lazy">

</td></tr></tbody></table>

<a href="Doppler_effect" title="Doppler effect">Doppler effect</a> blueshifts (z < 0) are associated with objects approaching (moving closer to) the observer with the light shifting to greater <a href="Energy" title="Energy">energies</a>. Conversely, Doppler effect redshifts (z > 0) are associated with objects receding (moving away) from the observer with the light shifting to lower energies. Likewise, gravitational blueshifts are associated with light emitted from a source residing within a weaker <a href="Gravitational_field" title="Gravitational field">gravitational field</a> as observed from within a stronger gravitational field, while gravitational redshifting implies the opposite conditions.

<div class="mw-heading mw-heading2"><h2 id="History">History</h2></div>

The history of the subject began in the 19th century, with the development of classical <a href="Wave" title="Wave">wave</a> mechanics and the exploration of phenomena which are associated with the <a href="Doppler_effect" title="Doppler effect">Doppler effect</a>. The effect is named after the <a href="Austria" title="Austria">Austrian</a> mathematician <a href="Christian_Doppler" title="Christian Doppler">Christian Doppler</a>, who offered the first known physical explanation for the phenomenon in 1842.<a href="#cite_note-4">[4]</a><a href="#cite_note-Becker-2011-5">[5]</a>: 107 In 1845, the hypothesis was tested and confirmed for <a href="Sound_wave" class="mw-redirect" title="Sound wave">sound waves</a> by the <a href="Netherlands" title="Netherlands">Dutch</a> scientist <a href="C._H._D._Buys_Ballot" title="C. H. D. Buys Ballot">Christophorus Buys Ballot</a>.<a href="#cite_note-6">[6]</a> Doppler correctly predicted that the phenomenon would apply to all waves and, in particular, suggested that the varying <a href="Color" title="Color">colors</a> of <a href="Star" title="Star">stars</a> could be attributed to their motion with respect to the Earth.<a href="#cite_note-7">[7]</a>

Unaware of Doppler's work, French physicist <a href="Hippolyte_Fizeau" title="Hippolyte Fizeau">Hippolyte Fizeau</a> suggested in 1848 that a shift in <a href="Spectral_line" title="Spectral line">spectral lines</a> from stars might be used to measure their motion relative to Earth.<a href="#cite_note-Becker-2011-5">[5]</a>: 109 In 1850, <a href="Fran%C3%A7ois-Napol%C3%A9on-Marie_Moigno" title="François-Napoléon-Marie Moigno">François-Napoléon-Marie Moigno</a> analyzed both Doppler's and Fizeau's ideas in a publication read by both <a href="James_Clerk_Maxwell" title="James Clerk Maxwell">James Clerk Maxwell</a> and <a href="William_Huggins" title="William Huggins">William Huggins</a>, who initially stuck to the idea that the color of stars related to their chemistry, however by 1868, Huggins was the first to determine the velocity of a star moving away from the Earth by the analysis of spectral shifts.<a href="#cite_note-Huggins-8">[8]</a><a href="#cite_note-Becker-2011-5">[5]</a>: 111

In 1871, optical redshift was confirmed when the phenomenon was observed in <a href="Fraunhofer_lines" title="Fraunhofer lines">Fraunhofer lines</a>, using solar rotation, about 0.1 Å in the red.<a href="#cite_note-Nolte-9">[9]</a> In 1887, <a href="Hermann_Carl_Vogel" title="Hermann Carl Vogel">Hermann Carl Vogel</a> and <a href="Julius_Scheiner" title="Julius Scheiner">Julius Scheiner</a> discovered the "annual Doppler effect", the yearly change in the Doppler shift of stars located near the ecliptic, due to the orbital velocity of the Earth.<a href="#cite_note-10">[10]</a> In 1901, <a href="Aristarkh_Belopolsky" title="Aristarkh Belopolsky">Aristarkh Belopolsky</a> verified optical redshift in the laboratory using a system of rotating mirrors.<a href="#cite_note-11">[11]</a><a href="#cite_note-Nolte-9">[9]</a>

Beginning with observations in 1912, <a href="Vesto_Slipher" title="Vesto Slipher">Vesto Slipher</a> discovered that the <a href="Andromeda_Galaxy" title="Andromeda Galaxy">Andromeda Galaxy</a> had a blue shift, indicating that it was moving towards the Earth.<a href="#cite_note-SmithInKragh-2019-12">[12]</a> Slipher first reported his measurement in the inaugural volume of the <a href="Lowell_Observatory" title="Lowell Observatory">Lowell Observatory</a> Bulletin.<a href="#cite_note-13">[13]</a> Three years later, he wrote a review in the journal <a href="Popular_Astronomy_(US_magazine)" title="Popular Astronomy (US magazine)">Popular Astronomy</a>.<a href="#cite_note-Slipher-14">[14]</a> In it he stated that "the early discovery that the great Andromeda spiral had the quite exceptional velocity of –300 km[/s] showed the means then available, capable of investigating not only the spectra of the spirals but their velocities as well."<a href="#cite_note-Slipher-14">[14]</a> Slipher reported the velocities for 15 spiral nebulae spread across the entire <a href="Celestial_sphere" title="Celestial sphere">celestial sphere</a>, all but three having observable "positive" (that is recessional) velocities.<a href="#cite_note-SmithInKragh-2019-12">[12]</a>

Until 1923 the nature of the nebulae was unclear. By that year <a href="Edwin_Hubble" title="Edwin Hubble">Edwin Hubble</a> had established that these were <a href="Galaxies" class="mw-redirect" title="Galaxies">galaxies</a> and worked out a procedure to measure distance based on the period-luminosity relation of variable <a href="Cepheids" class="mw-redirect" title="Cepheids">Cepheids</a> stars. This made it possible to test a prediction by <a href="Willem_de_Sitter" title="Willem de Sitter">Willem de Sitter</a> in 1917 that redshift would be correlated with distance. In 1929 Hubble combined his distance estimates with redshift data from Slipher's reports and measurements by <a href="Milton_Humason" class="mw-redirect" title="Milton Humason">Milton Humason</a> to report an approximate relationship between the redshift and <a href="Distance" title="Distance">distance</a>, a result now called <a href="Hubble's_law" title="Hubble's law">Hubble's law</a>.<a href="#cite_note-SmithInKragh-2019-12">[12]</a>: 64 <a href="#cite_note-15">[15]</a><a href="#cite_note-16">[16]</a>

Theories relating to the redshift-distance relation also evolved during the 1920s. The solution to the equations of general relativity described by de Sitter contained no matter, but in 1922 <a href="Alexander_Friedmann" title="Alexander Friedmann">Alexander Friedmann</a> derived dynamic solutions, now called the <a href="Friedmann_equations" title="Friedmann equations">Friedmann equations</a>, based on frictionless fluid models.<a href="#cite_note-17">[17]</a> Independently <a href="Georges_Lema%C3%AEtre" title="Georges Lemaître">Georges Lemaître</a> derived similar equations in 1927 and his analysis became widely known around the time of Hubble's key publication.<a href="#cite_note-SmithInKragh-2019-12">[12]</a>: 77

By early 1930 the combination of the redshift measurements and theoretical models established a major breakthrough in the new science of cosmology: the universe had a history and its expansion could be investigated with physical models backed up with observational astronomy.<a href="#cite_note-SmithInKragh-2019-12">[12]</a>: 99

<a href="Arthur_Eddington" title="Arthur Eddington">Arthur Eddington</a> used the term "red shift" as early as 1923, which is the oldest example of the term reported by the <a href="Oxford_English_Dictionary" title="Oxford English Dictionary">Oxford English Dictionary</a>.<a href="#cite_note-18">[18]</a><a href="#cite_note-19">[19]</a> Willem de Sitter used the single-word version redshift in 1934.<a href="#cite_note-20">[20]</a>

In the 1960s the discovery of <a href="Quasars" class="mw-redirect" title="Quasars">quasars</a>, which appear as very blue point sources and thus were initially thought to be unusual stars, lead to the idea that they were as bright as they were because they were closer than their redshift data indicated. A flurry of theoretical and observational work concluded that these objects were very powerful but distant astronomical objects.<a href="#cite_note-SmithInKragh-2019-12">[12]</a>: 261

<div class="mw-heading mw-heading2"><h2 id="Physical_origins">Physical origins</h2></div>

Redshifts are differences between two wavelength measurements and wavelengths are a property of both the photons and the measuring equipment. Thus redshifts characterize differences between two measurement locations. These differences are

commonly organized in three groups, attributed to relative motion between the source and the observer, to the expansion of the universe, and to gravity.<a href="#cite_note-21">[21]</a> The following sections explain these groups.

<div class="mw-heading mw-heading3"><h3 id="Doppler_effect">Doppler effect</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="Doppler_effect" title="Doppler effect">Doppler effect</a> and <a href="Relativistic_Doppler_effect" title="Relativistic Doppler effect">Relativistic Doppler effect</a></div>

If a source of the light is moving away from an observer, then redshift (z > 0) occurs; if the source moves towards the observer, then <a href="Blueshift" class="mw-redirect" title="Blueshift">blueshift</a> (z < 0) occurs. This is true for all electromagnetic waves and is explained by the <a href="Doppler_effect" title="Doppler effect">Doppler effect</a>. Consequently, this type of redshift is called the Doppler redshift. If the source moves away from the observer with <a href="Velocity" title="Velocity">velocity</a> v, which is much less than the speed of light (v ≪ c), the redshift is given by

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<annotation encoding="application/x-tex">{\displaystyle z\approx {\frac {v}{c}}}</annotation>

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</math><img src="./ebb477fa2d573b6c2c0629fe2d63adf8d871488d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:6.15ex; height:4.676ex;" alt="{\displaystyle z\approx {\frac {v}{c}}}" loading="lazy"> (since <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \gamma \approx 1}">

</mstyle>

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<annotation encoding="application/x-tex">{\displaystyle \gamma \approx 1}</annotation>

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</math><img src="./8fcbd0174b5d1b88845a6b75ee34893bda890f25.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.523ex; height:2.676ex;" alt="{\displaystyle \gamma \approx 1}" loading="lazy">)</dd></dl>

where c is the <a href="Speed_of_light" title="Speed of light">speed of light</a>. In the classical Doppler effect, the frequency of the source is not modified, but the recessional motion causes the illusion of a lower frequency.

A more complete treatment of the Doppler redshift requires considering relativistic effects associated with motion of sources close to the speed of light. A complete derivation of the effect can be found in the article on the <a href="Relativistic_Doppler_effect" title="Relativistic Doppler effect">relativistic Doppler effect</a>. In brief, objects moving close to the speed of light will experience deviations from the above formula due to the <a href="Time_dilation" title="Time dilation">time dilation</a> of <a href="Special_relativity" title="Special relativity">special relativity</a> which can be corrected for by introducing the <a href="Lorentz_factor" title="Lorentz factor">Lorentz factor</a> γ into the classical Doppler formula as follows (for motion solely in the line of sight):

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<annotation encoding="application/x-tex">{\displaystyle 1+z=\left(1+{\frac {v}{c}}\right)\gamma .}</annotation>

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</math><img src="./79c2489cb67179db42f3f7dbc3f60d08ac91a0c9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:19.228ex; height:4.843ex;" alt="{\displaystyle 1+z=\left(1+{\frac {v}{c}}\right)\gamma .}" loading="lazy"></dd></dl>

This phenomenon was first observed in a 1938 experiment performed by <a href="Herbert_E._Ives" title="Herbert E. Ives">Herbert E. Ives</a> and G. R. Stilwell, called the <a href="Ives%E2%80%93Stilwell_experiment" title="Ives–Stilwell experiment">Ives–Stilwell experiment</a>.<a href="#cite_note-22">[22]</a>

Since the Lorentz factor is dependent only on the <a href="Magnitude_(mathematics)" title="Magnitude (mathematics)">magnitude</a> of the velocity, this causes the redshift associated with the relativistic correction to be independent of the orientation of the source movement. In contrast, the classical part of the formula is dependent on the <a href="Scalar_resolute" class="mw-redirect" title="Scalar resolute">projection</a> of the movement of the source into the <a href="Line-of-sight_propagation" title="Line-of-sight propagation">line-of-sight</a> which yields different results for different orientations. If θ is the angle between the direction of relative motion and the direction of emission in the observer's frame<a href="#cite_note-23">[23]</a> (zero angle is directly away from the observer), the full form for the relativistic Doppler effect becomes:

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<annotation encoding="application/x-tex">{\displaystyle 1+z={\frac {1+v\cos(\theta )/c}{\sqrt {1-v^{2}/c^{2}}}}}</annotation>

</semantics>

</math><img src="./ead26fb14d65657facfb3a6860ee4308a186a98a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:22.723ex; height:7.009ex;" alt="{\displaystyle 1+z={\frac {1+v\cos(\theta )/c}{\sqrt {1-v^{2}/c^{2}}}}}" loading="lazy"></dd></dl>

and for motion solely in the line of sight (θ = 0°), this equation reduces to:

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<annotation encoding="application/x-tex">{\displaystyle 1+z={\sqrt {\frac {1+v/c}{1-v/c}}}}</annotation>

</semantics>

</math><img src="./c30334b803cfb927650f90f3f866836c50514e53.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:18.649ex; height:7.509ex;" alt="{\displaystyle 1+z={\sqrt {\frac {1+v/c}{1-v/c}}}}" loading="lazy"></dd></dl>

For the special case that the light is moving at <a href="Right_angle" title="Right angle">right angle</a> (θ = 90°) to the direction of relative motion in the observer's frame,<a href="#cite_note-24">[24]</a> the relativistic redshift is known as the <a href="Relativistic_Doppler_effect" title="Relativistic Doppler effect">transverse redshift</a>, and a redshift:

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<annotation encoding="application/x-tex">{\displaystyle 1+z={\frac {1}{\sqrt {1-v^{2}/c^{2}}}}}</annotation>

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</math><img src="./4e4094514c80479a19c599ddaeff025509cb6daf.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:20.758ex; height:6.509ex;" alt="{\displaystyle 1+z={\frac {1}{\sqrt {1-v^{2}/c^{2}}}}}" loading="lazy"></dd></dl>

is measured, even though the object is not moving away from the observer. Even when the source is moving towards the observer, if there is a transverse component to the motion then there is some speed at which the dilation just cancels the expected blueshift and at higher speed the approaching source will be redshifted.<a href="#cite_note-25">[25]</a>

<div class="mw-heading mw-heading3"><h3 id="Cosmological">Cosmological </h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Expansion_of_the_universe" title="Expansion of the universe">Expansion of the universe</a></div>

The observations of increasing redshifts from more and more distant galaxies can be modeled assuming a <a href="Cosmological_principle" title="Cosmological principle">homogeneous and isotropic universe</a> combined with <a href="General_relativity" title="General relativity">general relativity</a>. This cosmological redshift can be written as a function of a, the time-dependent cosmic <a href="Scale_factor_(cosmology)" title="Scale factor (cosmology)">scale factor</a>:<a href="#cite_note-26">[26]</a>: 72

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<annotation encoding="application/x-tex">{\displaystyle 1+z={\frac {a_{\mathrm {now} }}{a_{\mathrm {then} }}}={\frac {a_{0}}{a(t)}}}</annotation>

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</math><img src="./1a04ab79e8658c0c7cb8e30d746a4ca64cd14b6f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:21.499ex; height:5.509ex;" alt="{\displaystyle 1+z={\frac {a_{\mathrm {now} }}{a_{\mathrm {then} }}}={\frac {a_{0}}{a(t)}}}" loading="lazy"></dd></dl>

The scale factor is <a href="Monotonic_function" title="Monotonic function">monotonically increasing</a> as time passes. Thus z is positive, close to zero for local stars, and increasing for distant galaxies that appear redshifted.

Using a <a href="Friedmann%E2%80%93Robertson%E2%80%93Walker_model" class="mw-redirect" title="Friedmann–Robertson–Walker model">Friedmann–Robertson–Walker model</a> of the expansion of the universe, redshift can be related to the age of an observed object, the so-called <a href="Cosmic_time" title="Cosmic time">cosmic time</a>–redshift relation. Denote a density ratio as Ω0:

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<annotation encoding="application/x-tex">{\displaystyle \Omega _{0}={\frac {\rho }{\rho _{\text{crit}}}}\ ,}</annotation>

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</math><img src="./365f968094b2ae86425425b1f4b8ce2b174f97ff.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:11.8ex; height:5.343ex;" alt="{\displaystyle \Omega _{0}={\frac {\rho }{\rho _{\text{crit}}}}\ ,}" loading="lazy"></dd></dl>

with ρcrit the critical density demarcating a universe that eventually crunches from one that simply expands. This density is about three hydrogen atoms per cubic meter of space.<a href="#cite_note-Weinberg-27">[27]</a> At large redshifts, 1 + z > Ω0−1, one finds:

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<annotation encoding="application/x-tex">{\displaystyle t(z)\approx {\frac {2}{3H_{0}{\Omega _{0}}^{1/2}}}z^{-3/2}\ ,}</annotation>

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</math><img src="./b35f0563369c2ee1555ff73db0fdff6d4f4670b6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:23.545ex; height:6.343ex;" alt="{\displaystyle t(z)\approx {\frac {2}{3H_{0}{\Omega _{0}}^{1/2}}}z^{-3/2}\ ,}" loading="lazy"></dd></dl>

where H0 is the present-day <a href="Hubble_constant" class="mw-redirect" title="Hubble constant">Hubble constant</a>, and z is the redshift.<a href="#cite_note-Bergström-28">[28]</a><a href="#cite_note-Longair-29">[29]</a>

The cosmological redshift is commonly attributed to stretching of the wavelengths of photons due to the stretching of space. This interpretation can be misleading.

As required by <a href="General_relativity" title="General relativity">general relativity</a>, the cosmological expansion of space has no effect on local physics. There is no term related to expansion in <a href="Maxwell's_equations" title="Maxwell's equations">Maxwell's equations</a> that govern light propagation. The cosmological redshift can be interpreted as an accumulation of infinitesimal Doppler shifts along the trajectory of the light.<a href="#cite_note-Hogg-30">[30]</a>

There are several websites for calculating various times and distances from redshift, as the precise calculations require numerical integrals for most values of the parameters.<a href="#cite_note-UCLA-2018-31">[31]</a><a href="#cite_note-ICRAR-2022-32">[32]</a>

<div class="mw-heading mw-heading4"><h4 id="Distinguishing_between_cosmological_and_local_effects">Distinguishing between cosmological and local effects</h4></div>

The redshift of a galaxy includes both a component related to <a href="Recessional_velocity" title="Recessional velocity">recessional velocity</a> from expansion of the universe, and a component related to the <a href="Peculiar_motion" class="mw-redirect" title="Peculiar motion">peculiar motion</a> of the galaxy with respect to its local universe.<a href="#cite_note-33">[33]</a> The redshift due to expansion of the universe depends upon the recessional velocity in a fashion determined by the cosmological model chosen to describe the expansion of the universe, which is very different from how Doppler redshift depends upon local velocity.<a href="#cite_note-Harrison2-34">[34]</a> Describing the cosmological expansion origin of redshift, cosmologist <a href="Edward_Robert_Harrison" title="Edward Robert Harrison">Edward Robert Harrison</a> said, "Light leaves a galaxy, which is stationary in its local region of space, and is eventually received by observers who are stationary in their own local region of space. Between the galaxy and the observer, light travels through vast regions of expanding space. As a result, all wavelengths of the light are stretched by the expansion of space. It is as simple as that..."<a href="#cite_note-35">[35]</a> <a href="Steven_Weinberg" title="Steven Weinberg">Steven Weinberg</a> clarified, "The increase of wavelength from emission to absorption of light does not depend on the rate of change of a(t) [the <a href="Scale_factor_(cosmology)" title="Scale factor (cosmology)">scale factor</a>] at the times of emission or absorption, but on the increase of a(t) in the whole period from emission to absorption."<a href="#cite_note-Weinberg_Cosmology-36">[36]</a>

If the universe were contracting instead of expanding, we would see distant galaxies blueshifted by an amount proportional to their distance instead of redshifted.<a href="#cite_note-37">[37]</a>

<div class="mw-heading mw-heading3"><h3 id="Gravitational_redshift">Gravitational redshift</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Gravitational_redshift" title="Gravitational redshift">Gravitational redshift</a></div>

In the theory of <a href="General_relativity" title="General relativity">general relativity</a>, there is time dilation within a gravitational well. Light emitted within the well will appear to have fewer cycles per second when measured outside of the well, due to differences in the two clocks.<a href="#cite_note-38">[38]</a>: 284 This is known as the <a href="Gravitational_redshift" title="Gravitational redshift">gravitational redshift</a> or Einstein Shift.<a href="#cite_note-39">[39]</a> The theoretical derivation of this effect follows from the <a href="Schwarzschild_solution" class="mw-redirect" title="Schwarzschild solution">Schwarzschild solution</a> of the <a href="Einstein_field_equations" title="Einstein field equations">Einstein equations</a> which yields the following formula for redshift associated with a photon traveling in the <a href="Gravitational_field" title="Gravitational field">gravitational field</a> of an <a href="Electric_charge" title="Electric charge">uncharged</a>, <a href="Rotation" title="Rotation">nonrotating</a>, <a href="Spherical_symmetry" class="mw-redirect" title="Spherical symmetry">spherically symmetric</a> mass:

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<annotation encoding="application/x-tex">{\displaystyle 1+z={\frac {1}{\sqrt {1-{\frac {2GM}{rc^{2}}}}}},}</annotation>

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</math><img src="./32281ba5d64b16f8f2379257d6c1182af6c7481e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.671ex; width:20.676ex; height:8.009ex;" alt="{\displaystyle 1+z={\frac {1}{\sqrt {1-{\frac {2GM}{rc^{2}}}}}},}" loading="lazy"></dd></dl>

where

<ul><li>G is the <a href="Gravitational_constant" title="Gravitational constant">gravitational constant</a>,</li>

<li>M is the <a href="Mass" title="Mass">mass</a> of the object creating the gravitational field,</li>

<li>r is the radial coordinate of the source (which is analogous to the classical distance from the center of the object, but is actually a <a href="Schwarzschild_coordinates" title="Schwarzschild coordinates">Schwarzschild coordinate</a>), and</li>

<li>c is the <a href="Speed_of_light" title="Speed of light">speed of light</a>.</li></ul>

This gravitational redshift result can be derived from the assumptions of <a href="Special_relativity" title="Special relativity">special relativity</a> and the <a href="Equivalence_principle" title="Equivalence principle">equivalence principle</a>; the full theory of general relativity is not required.<a href="#cite_note-40">[40]</a>

The effect is very small but measurable on Earth using the <a href="M%C3%B6ssbauer_effect" title="Mössbauer effect">Mössbauer effect</a> and was first observed in the <a href="Pound%E2%80%93Rebka_experiment" title="Pound–Rebka experiment">Pound–Rebka experiment</a>.<a href="#cite_note-41">[41]</a> However, it is significant near a <a href="Black_hole" title="Black hole">black hole</a>, and as an object approaches the <a href="Event_horizon" title="Event horizon">event horizon</a> the red shift becomes infinite. It is also the dominant cause of large angular-scale temperature fluctuations in the <a href="Cosmic_microwave_background" title="Cosmic microwave background">cosmic microwave background</a> radiation (see <a href="Sachs%E2%80%93Wolfe_effect" title="Sachs–Wolfe effect">Sachs–Wolfe effect</a>).<a href="#cite_note-42">[42]</a>

<div class="mw-heading mw-heading3"><h3 id="Summary_table">Summary table</h3></div>

Several important special-case formulae for redshift in certain special spacetime geometries are summarized in the following table. In all cases the magnitude of the shift (the value of z) is independent of the wavelength.<a href="#cite_note-basicastronomy-43">[43]</a>

<caption>Redshift summary

</caption>

<th>Redshift type</th>

<th>Geometry</th>

<th>Formulae<a href="#cite_note-44">[44]</a>

</th></tr>

<tr>

<td><a href="Relativistic_Doppler_effect" title="Relativistic Doppler effect">Relativistic Doppler</a></td>

<td><a href="Minkowski_space" title="Minkowski space">Minkowski space</a> (flat spacetime)</td>

<td>

For motion completely in the radial or line-of-sight direction:

<mrow>

<mrow>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mrow>

<msqrt>

<mfrac>

<mrow>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

<mrow>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mfrac>

</msqrt>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 1+z=\gamma \left(1+{\frac {v_{\parallel }}{c}}\right)={\sqrt {\frac {1+{\frac {v_{\parallel }}{c}}}{1-{\frac {v_{\parallel }}{c}}}}}}</annotation>

</semantics>

</math><img src="./d13cfbc8e65189ef9324e78d38b21d02045b9e12.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.671ex; width:33.137ex; height:9.176ex;" alt="{\displaystyle 1+z=\gamma \left(1+{\frac {v_{\parallel }}{c}}\right)={\sqrt {\frac {1+{\frac {v_{\parallel }}{c}}}{1-{\frac {v_{\parallel }}{c}}}}}}" loading="lazy"></big></dd>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle z\approx {\frac {v_{\parallel }}{c}}}</annotation>

</semantics>

</math><img src="./95e407722c57dda3dd2e8a44cd590ddd13599d57.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.205ex; height:5.176ex;" alt="{\displaystyle z\approx {\frac {v_{\parallel }}{c}}}" loading="lazy"> for small <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\parallel }}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle v_{\parallel }}</annotation>

</semantics>

</math><img src="./7fdc28634f42e2cab943bba07f1b6b325a758ee9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:2.182ex; height:2.509ex;" alt="{\displaystyle v_{\parallel }}" loading="lazy"></dd></dl>

For motion completely in the transverse direction:

<mfrac>

<msqrt>

<mfrac>

</mrow>

</mrow>

</msubsup>

<msup>

</mrow>

</msup>

</mfrac>

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</msqrt>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 1+z={\frac {1}{\sqrt {1-{\frac {v_{\perp }^{2}}{c^{2}}}}}}}</annotation>

</semantics>

</math><img src="./e2090b5e3bc3d3397e2333b906efdc7de7be8eb7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.005ex; width:18.188ex; height:9.343ex;" alt="{\displaystyle 1+z={\frac {1}{\sqrt {1-{\frac {v_{\perp }^{2}}{c^{2}}}}}}}" loading="lazy"></dd>

<mfrac>

</mfrac>

</mrow>

<msup>

<mrow>

<mfrac>

<msub>

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</msub>

</mfrac>

</mrow>

</mrow>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle z\approx {\frac {1}{2}}\left({\frac {v_{\perp }}{c}}\right)^{2}}</annotation>

</semantics>

</math><img src="./6b575800fbc4e47bdab02803747483d261f78f26.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:13.489ex; height:5.176ex;" alt="{\displaystyle z\approx {\frac {1}{2}}\left({\frac {v_{\perp }}{c}}\right)^{2}}" loading="lazy"> for small <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\perp }}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle v_{\perp }}</annotation>

</semantics>

</math><img src="./f80a8cf80254aa3ef2640555e94986487d5cba0b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.638ex; height:2.009ex;" alt="{\displaystyle v_{\perp }}" loading="lazy"></dd></dl>

</td></tr>

<tr>

<td><a href="Cosmological_redshift" class="mw-redirect" title="Cosmological redshift">Cosmological redshift</a></td>

<td><a href="Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric" title="Friedmann–Lemaître–Robertson–Walker metric">FLRW spacetime</a> (expanding Big Bang universe)</td>

<td>

<mfrac>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 1+z={\frac {a_{\mathrm {now} }}{a_{\mathrm {then} }}}}</annotation>

</semantics>

</math><img src="./a8db63140bbbaa2b19965b212dd79898dde04acf.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:13.685ex; height:5.009ex;" alt="{\displaystyle 1+z={\frac {a_{\mathrm {now} }}{a_{\mathrm {then} }}}}" loading="lazy"></dd></dl>

<a href="Hubble's_law" title="Hubble's law">Hubble's law</a>:

<mfrac>

<mrow>

<msub>

</mrow>

</msub>

</mrow>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle z\approx {\frac {H_{0}D}{c}}}</annotation>

</semantics>

</math><img src="./b761c1207889db302fda9cd1bb5a9123792f368e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.932ex; height:5.343ex;" alt="{\displaystyle z\approx {\frac {H_{0}D}{c}}}" loading="lazy"> for <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D\ll {\frac {c}{H_{0}}}}">

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D\ll {\frac {c}{H_{0}}}}</annotation>

</semantics>

</math><img src="./dcda9d0b68d5d27ade4d4c2c59643b4a084193a2.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:9.36ex; height:5.176ex;" alt="{\displaystyle D\ll {\frac {c}{H_{0}}}}" loading="lazy"></dd></dl>

</td></tr>

<tr>

<td><a href="Gravitational_redshift" title="Gravitational redshift">Gravitational redshift</a></td>

<td>Any <a href="Stationary_spacetime" title="Stationary spacetime">stationary spacetime</a></td>

<td>

<msqrt>

<mfrac>

<mrow>

<msub>

</mrow>

</msub>

<mtext>receiver</mtext>

</mrow>

</mrow>

<mrow>

<msub>

</mrow>

</msub>

<mtext>source</mtext>

</mrow>

</mrow>

</mfrac>

</msqrt>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 1+z={\sqrt {\frac {g_{tt}({\text{receiver}})}{g_{tt}({\text{source}})}}}}</annotation>

</semantics>

</math><img src="./ebaa9033ebdaf13a0fadfae88aeb8d7e35b59a29.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:23.514ex; height:7.509ex;" alt="{\displaystyle 1+z={\sqrt {\frac {g_{tt}({\text{receiver}})}{g_{tt}({\text{source}})}}}}" loading="lazy"></dd></dl>

For the <a href="Schwarzschild_geometry" class="mw-redirect" title="Schwarzschild geometry">Schwarzschild geometry</a>:

<msqrt>

<mfrac>

<mrow>

<mfrac>

<msub>

</mrow>

</msub>

<msub>

<mtext>receiver</mtext>

</mrow>

</msub>

</mfrac>

</mrow>

<mrow>

<mfrac>

<msub>

</mrow>

</msub>

<msub>

<mtext>source</mtext>

</mrow>

</msub>

</mfrac>

</mrow>

</mfrac>

</msqrt>

</mrow>

<msqrt>

<mfrac>

<mrow>

<mfrac>

<mrow>

</mrow>

<mrow>

<msup>

</mrow>

</msup>

<msub>

<mtext>receiver</mtext>

</mrow>

</msub>

</mrow>

</mfrac>

</mrow>

<mrow>

<mfrac>

<mrow>

</mrow>

<mrow>

<msup>

</mrow>

</msup>

<msub>

<mtext>source</mtext>

</mrow>

</msub>

</mrow>

</mfrac>

</mrow>

</mfrac>

</msqrt>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 1+z={\sqrt {\frac {1-{\frac {r_{S}}{r_{\text{receiver}}}}}{1-{\frac {r_{S}}{r_{\text{source}}}}}}}={\sqrt {\frac {1-{\frac {2GM}{c^{2}r_{\text{receiver}}}}}{1-{\frac {2GM}{c^{2}r_{\text{source}}}}}}}}</annotation>

</semantics>

</math><img src="./961eb0e3a1c7c3c22eb1798bdc3d41b353cf34dc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:39.887ex; height:10.009ex;" alt="{\displaystyle 1+z={\sqrt {\frac {1-{\frac {r_{S}}{r_{\text{receiver}}}}}{1-{\frac {r_{S}}{r_{\text{source}}}}}}}={\sqrt {\frac {1-{\frac {2GM}{c^{2}r_{\text{receiver}}}}}{1-{\frac {2GM}{c^{2}r_{\text{source}}}}}}}}" loading="lazy"></big></dd></dl>

<mfrac>

</mfrac>

</mrow>

<mrow>

<mrow>

<mfrac>

<msub>

</mrow>

</msub>

<msub>

<mtext>source</mtext>

</mrow>

</msub>

</mfrac>

</mrow>

<mfrac>

<msub>

</mrow>

</msub>

<msub>

<mtext>receiver</mtext>

</mrow>

</msub>

</mfrac>

</mrow>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle z\approx {\frac {1}{2}}\left({\frac {r_{S}}{r_{\text{source}}}}-{\frac {r_{S}}{r_{\text{receiver}}}}\right)}</annotation>

</semantics>

</math><img src="./586969f3a4d4c16a054646159501b843c37544c1.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:27.091ex; height:6.176ex;" alt="{\displaystyle z\approx {\frac {1}{2}}\left({\frac {r_{S}}{r_{\text{source}}}}-{\frac {r_{S}}{r_{\text{receiver}}}}\right)}" loading="lazy"> for <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r\gg r_{S}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle r\gg r_{S}}</annotation>

</semantics>

</math><img src="./188b346af97604ae2105ff5dd3871833a4b731f2.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.004ex; height:2.176ex;" alt="{\displaystyle r\gg r_{S}}" loading="lazy"></big></dd></dl>

In terms of <a href="Escape_velocity" title="Escape velocity">escape velocity</a>:

<mfrac>

</mfrac>

</mrow>

<mrow>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mrow>

<mtext>source</mtext>

</mrow>

</mrow>

</msubsup>

<mfrac>

</mfrac>

</mrow>

<mrow>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mrow>

<mtext>receiver</mtext>

</mrow>

</mrow>

</msubsup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle z\approx {\frac {1}{2}}\left({\frac {v_{\text{e}}}{c}}\right)_{\text{source}}^{2}-{\frac {1}{2}}\left({\frac {v_{\text{e}}}{c}}\right)_{\text{receiver}}^{2}}</annotation>

</semantics>

</math><img src="./45e5e3f2277e29aa283a5239ed57475b6d16efbc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:32.915ex; height:5.343ex;" alt="{\displaystyle z\approx {\frac {1}{2}}\left({\frac {v_{\text{e}}}{c}}\right)_{\text{source}}^{2}-{\frac {1}{2}}\left({\frac {v_{\text{e}}}{c}}\right)_{\text{receiver}}^{2}}" loading="lazy"></dd></dl>

for <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\text{e}}\ll c}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle v_{\text{e}}\ll c}</annotation>

</semantics>

</math><img src="./4435035a4c2319b96d9bb16eb29311886acb28c0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.711ex; height:2.176ex;" alt="{\displaystyle v_{\text{e}}\ll c}" loading="lazy">

</td></tr></tbody></table>

<div class="mw-heading mw-heading2"><h2 id="Observations_in_astronomy">Observations in astronomy</h2></div>

The redshift observed in astronomy can be measured because the <a href="Emission_spectrum" title="Emission spectrum">emission</a> and <a href="Absorption_spectroscopy" title="Absorption spectroscopy">absorption</a> spectra for <a href="Atom" title="Atom">atoms</a> are distinctive and well known, calibrated from <a href="Spectroscopic" class="mw-redirect" title="Spectroscopic">spectroscopic</a> experiments in <a href="Laboratories" class="mw-redirect" title="Laboratories">laboratories</a> on Earth. When the redshifts of various absorption and emission lines from a single astronomical object are measured, z is found to be remarkably constant. Although distant objects may be slightly blurred and lines broadened, it is by no more than can be explained by <a href="Kinetic_theory_of_gases" title="Kinetic theory of gases">thermal</a> or mechanical <a href="Motion" title="Motion">motion</a> of the source. For these reasons and others, the consensus among astronomers is that the redshifts they observe are due to some combination of the three established forms of Doppler-like redshifts. Alternative hypotheses and explanations for redshift such as <a href="Tired_light" title="Tired light">tired light</a> are not generally considered plausible.<a href="#cite_note-reboul-46">[46]</a>

Spectroscopy, as a measurement, is considerably more difficult than simple <a href="Photometry_(astronomy)" title="Photometry (astronomy)">photometry</a>, which measures the <a href="Brightness" title="Brightness">brightness</a> of astronomical objects through certain <a href="Optical_filter" title="Optical filter">filters</a>.<a href="#cite_note-47">[47]</a> When photometric data is all that is available (for example, the <a href="Hubble_Deep_Field" title="Hubble Deep Field">Hubble Deep Field</a> and the <a href="Hubble_Ultra_Deep_Field" class="mw-redirect" title="Hubble Ultra Deep Field">Hubble Ultra Deep Field</a>), astronomers rely on a technique for measuring <a href="Photometric_redshift" title="Photometric redshift">photometric redshifts</a>.<a href="#cite_note-48">[48]</a> Due to the broad wavelength ranges in photometric filters and the necessary assumptions about the nature of the spectrum at the light-source, <a href="Observational_error" title="Observational error">errors</a> for these sorts of measurements can range up to δz = 0.5, and are much less reliable than spectroscopic determinations.<a href="#cite_note-49">[49]</a>

However, photometry does at least allow a qualitative characterization of a redshift. For example, if a Sun-like spectrum had a redshift of z = 1, it would be brightest in the <a href="Infrared" title="Infrared">infrared</a> (1000nm) rather than at the blue-green (500nm) color associated with the peak of its <a href="Black_body" title="Black body">blackbody</a> spectrum, and the light intensity will be reduced in the filter by a factor of four, (1 + z)2. Both the photon count rate and the photon energy are redshifted. (See <a href="K_correction" title="K correction">K correction</a> for more details on the photometric consequences of redshift.)<a href="#cite_note-50">[50]</a>

Determining the redshift of an object with spectroscopy requires the wavelength of the emitted light in the rest frame of the source. Astronomical applications rely on distinct spectral lines. Redshifts cannot be calculated by looking at unidentified features whose rest-frame frequency is unknown, or with a spectrum that is featureless or <a href="White_noise" title="White noise">white noise</a> (random fluctuations in a spectrum). Thus <a href="Gamma-ray_burst" title="Gamma-ray burst">gamma-ray bursts</a> themselves cannot be used for reliable redshift measurements, but optical afterglow associated with the burst can be analyzed for redshifts.<a href="#cite_note-51">[51]</a>

<div class="mw-heading mw-heading3"><h3 id="Local_observations">Local observations</h3></div>

In nearby objects (within our <a href="Milky_Way" title="Milky Way">Milky Way</a> galaxy) observed redshifts are almost always related to the <a href="Line-of-sight_propagation" title="Line-of-sight propagation">line-of-sight</a> velocities associated with the objects being observed. Observations of such redshifts and blueshifts enable astronomers to measure <a href="Velocity" title="Velocity">velocities</a> and parametrize the <a href="Mass" title="Mass">masses</a> of the <a href="Orbit" title="Orbit">orbiting</a> <a href="Star" title="Star">stars</a> in <a href="Spectroscopic_binaries" class="mw-redirect" title="Spectroscopic binaries">spectroscopic binaries</a>. Similarly, small redshifts and blueshifts detected in the spectroscopic measurements of individual stars are one way astronomers have been able to <a href="Methods_of_detecting_exoplanets#Radial_velocity" title="Methods of detecting exoplanets">diagnose and measure</a> the presence and characteristics of <a href="Exoplanet" title="Exoplanet">planetary systems</a> around other stars and have even made very <a href="Rossiter%E2%80%93McLaughlin_effect" title="Rossiter–McLaughlin effect">detailed differential measurements</a> of redshifts during <a href="Methods_of_detecting_exoplanets" title="Methods of detecting exoplanets">planetary transits</a> to determine precise orbital parameters. Some approaches are able to track the redshift variations in multiple objects at once.<a href="#cite_note-52">[52]</a>

Finely detailed measurements of redshifts are used in <a href="Helioseismology" title="Helioseismology">helioseismology</a> to determine the precise movements of the <a href="Photosphere" title="Photosphere">photosphere</a> of the <a href="Sun" title="Sun">Sun</a>.<a href="#cite_note-53">[53]</a> Redshifts have also been used to make the first measurements of the <a href="Rotation" title="Rotation">rotation</a> rates of <a href="Planet" title="Planet">planets</a>,<a href="#cite_note-54">[54]</a> velocities of <a href="Interstellar_cloud" title="Interstellar cloud">interstellar clouds</a>,<a href="#cite_note-55">[55]</a> the <a href="Galaxy_rotation_curve" title="Galaxy rotation curve">rotation of galaxies</a>,<a href="#cite_note-basicastronomy-43">[43]</a> and the <a href="Dynamics_(mechanics)" title="Dynamics (mechanics)">dynamics</a> of <a href="Accretion_disk" title="Accretion disk">accretion</a> onto <a href="Neutron_star" title="Neutron star">neutron stars</a> and <a href="Black_hole" title="Black hole">black holes</a> which exhibit both Doppler and gravitational redshifts.<a href="#cite_note-56">[56]</a> The <a href="Temperature" title="Temperature">temperatures</a> of various emitting and absorbing objects can be obtained by measuring <a href="Doppler_broadening" title="Doppler broadening">Doppler broadening</a>—effectively redshifts and blueshifts over a single emission or absorption line.<a href="#cite_note-57">[57]</a> By measuring the broadening and shifts of the 21-centimeter <a href="Hydrogen_line" title="Hydrogen line">hydrogen line</a> in different directions, astronomers have been able to measure the <a href="Recessional_velocity" title="Recessional velocity">recessional velocities</a> of <a href="Interstellar_gas" class="mw-redirect" title="Interstellar gas">interstellar gas</a>, which in turn reveals the <a href="Rotation_curve" class="mw-redirect" title="Rotation curve">rotation curve</a> of our Milky Way.<a href="#cite_note-basicastronomy-43">[43]</a> Similar measurements have been performed on other galaxies, such as <a href="Andromeda_Galaxy" title="Andromeda Galaxy">Andromeda</a>.<a href="#cite_note-basicastronomy-43">[43]</a>

<div class="mw-heading mw-heading3"><h3 id="Extragalactic_observations">Extragalactic observations</h3></div>

The most distant objects exhibit larger redshifts corresponding to the <a href="Hubble_flow" class="mw-redirect" title="Hubble flow">Hubble flow</a> of the <a href="Universe" title="Universe">universe</a>. The largest-observed redshift, corresponding to the greatest distance and furthest back in time, is that of the <a href="Cosmic_microwave_background" title="Cosmic microwave background">cosmic microwave background</a> radiation; the <a href="Hubble's_law#Redshift_velocity" title="Hubble's law">numerical value of its redshift</a> is about z = 1089 (z = 0 corresponds to present time), and it shows the state of the universe about 13.8 billion years ago,<a href="#cite_note-58">[58]</a> and 379,000 years after the initial moments of the <a href="Big_Bang" title="Big Bang">Big Bang</a>.<a href="#cite_note-59">[59]</a>

The luminous point-like cores of <a href="Quasar" title="Quasar">quasars</a> were the first "high-redshift" (z > 0.1) objects discovered before the improvement of telescopes allowed for the discovery of other high-redshift galaxies.<a href="#cite_note-Kellermann-60">[60]</a>

For galaxies more distant than the <a href="Local_Group" title="Local Group">Local Group</a> and the nearby <a href="Virgo_Cluster" title="Virgo Cluster">Virgo Cluster</a>, but within a thousand mega<a href="Parsec" title="Parsec">parsecs</a> or so, the redshift is approximately proportional to the galaxy's distance. This correlation was first observed by <a href="Edwin_Hubble" title="Edwin Hubble">Edwin Hubble</a> and has come to be known as <a href="Hubble's_law" title="Hubble's law">Hubble's law</a>. <a href="Vesto_Slipher" title="Vesto Slipher">Vesto Slipher</a> was the first to discover galactic redshifts, in about 1912, while Hubble correlated Slipher's measurements with distances he <a href="Cosmic_distance_ladder" title="Cosmic distance ladder">measured by other means</a> to formulate his law.<a href="#cite_note-FOOTNOTEPeebles199378–79-61">[61]</a> Because it is usually not known how <a href="Luminosity" title="Luminosity">luminous</a> objects are, measuring the redshift is easier than more direct distance measurements, so redshift is sometimes in practice converted to a crude distance measurement using Hubble's law.<a href="#cite_note-62">[62]</a>

<a href="Gravitation" class="mw-redirect" title="Gravitation">Gravitational</a> interactions of galaxies with each other and clusters cause a significant <a href="Variance" title="Variance">scatter</a> in the normal plot of the Hubble diagram. The <a href="Peculiar_velocity" title="Peculiar velocity">peculiar velocities</a> associated with galaxies superimpose a rough trace of the <a href="Mass" title="Mass">mass</a> of <a href="Virial_theorem" title="Virial theorem">virialized objects</a> in the universe. This effect leads to such phenomena as nearby galaxies (such as the <a href="Andromeda_Galaxy" title="Andromeda Galaxy">Andromeda Galaxy</a>) exhibiting blueshifts as we fall towards a common <a href="Barycenter" class="mw-redirect" title="Barycenter">barycenter</a>, and redshift maps of clusters showing a <a href="Fingers_of_god" class="mw-redirect" title="Fingers of god">fingers of god</a> effect due to the scatter of peculiar velocities in a roughly spherical distribution.<a href="#cite_note-FOOTNOTEPeebles199334-63">[63]</a> These "redshift-space distortions" can be used as a cosmological probe in their own right, providing information on how structure formed in the Universe,<a href="#cite_note-64">[64]</a> and how gravity behaves on large scales.<a href="#cite_note-65">[65]</a>

The Hubble law's linear relationship between distance and redshift assumes that the rate of expansion of the universe is constant. However, when the universe was much younger, the expansion rate, and thus the Hubble "constant", was larger than it is today. For more distant galaxies, then, whose light has been travelling to us for much longer times, the approximation of constant expansion rate fails, and the Hubble law becomes a non-linear integral relationship and dependent on the history of the expansion rate since the emission of the light from the galaxy in question. Observations of the redshift-distance relationship can be used, then, to determine the expansion history of the universe and thus the matter and energy content.<a href="#cite_note-66">[66]</a>

While it was long believed that the expansion rate has been continuously decreasing since the Big Bang, observations beginning in 1988 of the redshift-distance relationship using <a href="Type_Ia_supernova" title="Type Ia supernova">Type Ia supernovae</a> have suggested that in comparatively recent times the expansion rate of the universe has <a href="Accelerating_expansion_of_the_universe" title="Accelerating expansion of the universe">begun to accelerate</a>.<a href="#cite_note-67">[67]</a>

<div class="mw-heading mw-heading3"><h3 id="Highest_redshifts">Highest redshifts</h3></div>

<div role="note" class="hatnote navigation-not-searchable">See also: <a href="List_of_the_most_distant_astronomical_objects#List_of_most_distant_objects_by_type" title="List of the most distant astronomical objects">List of most distant objects by type</a></div>

The most reliable redshifts are from <a href="Spectroscopic" class="mw-redirect" title="Spectroscopic">spectroscopic</a> data,<a href="#cite_note-68">[68]</a> and the highest-confirmed spectroscopic redshift of a galaxy is that of <a href="JADES-GS-z14-0" title="JADES-GS-z14-0">JADES-GS-z14-0</a> with a redshift of z = 14.32, corresponding to 290 million years after the Big Bang.<a href="#cite_note-69">[69]</a> The previous record was held by <a href="GN-z11" title="GN-z11">GN-z11</a>,<a href="#cite_note-70">[70]</a> with a redshift of z = 11.1, corresponding to 400 million years after the Big Bang.

Slightly less reliable are <a href="Lyman-break_galaxy" title="Lyman-break galaxy">Lyman-break</a> redshifts, the highest of which is the lensed galaxy A1689-zD1 at a redshift z = 7.5<a href="#cite_note-71">[71]</a><a href="#cite_note-72">[72]</a> and the next highest being z = 7.0.<a href="#cite_note-73">[73]</a> The most distant-observed <a href="Gamma-ray_burst" title="Gamma-ray burst">gamma-ray burst</a> with a spectroscopic redshift measurement was <a href="GRB_090423" title="GRB 090423">GRB 090423</a>, which had a redshift of z = 8.2.<a href="#cite_note-74">[74]</a> The most distant-known quasar, <a href="ULAS_J1342%2B0928" title="ULAS J1342+0928">ULAS J1342+0928</a>, is at z = 7.54.<a href="#cite_note-75">[75]</a><a href="#cite_note-Nature-2018-01-76">[76]</a> The highest-known redshift radio galaxy (TGSS1530) is at a redshift z = 5.72<a href="#cite_note-77">[77]</a> and the highest-known redshift molecular material is the detection of emission from the CO molecule from the quasar SDSS J1148+5251 at z = 6.42.<a href="#cite_note-78">[78]</a>

Extremely red objects (EROs) are <a href="Radio_astronomy#Astronomical_sources" title="Radio astronomy">astronomical sources</a> of radiation that radiate energy in the red and near infrared part of the electromagnetic spectrum. These may be starburst galaxies that have a high redshift accompanied by reddening from intervening dust, or they could be highly redshifted elliptical galaxies with an older (and therefore redder) stellar population.<a href="#cite_note-79">[79]</a> Objects that are even redder than EROs are termed hyper extremely red objects (HEROs).<a href="#cite_note-80">[80]</a>

The <a href="Cosmic_microwave_background" title="Cosmic microwave background">cosmic microwave background</a> has a redshift of z = 1089, corresponding to an age of approximately 379,000 years after the Big Bang and a <a href="Comoving_and_proper_distances" title="Comoving and proper distances">proper distance</a> of more than 46 billion light-years.<a href="#cite_note-ly93-81">[81]</a> This redshift corresponds to a shift in average temperature from 3000K down to 3K.<a href="#cite_note-82">[82]</a>

The yet-to-be-observed first light from the oldest <a href="Population_III_stars" class="mw-redirect" title="Population III stars">Population III stars</a>, not long after atoms first formed and the CMB ceased to be absorbed almost completely, may have redshifts in the range of 20 < z < 100.<a href="#cite_note-83">[83]</a> Other high-redshift events predicted by physics but not presently observable are the <a href="Cosmic_neutrino_background" title="Cosmic neutrino background">cosmic neutrino background</a> from about two seconds after the Big Bang (and a redshift in excess of z > 1010)<a href="#cite_note-84">[84]</a> and the cosmic <a href="Gravitational_wave_background" title="Gravitational wave background">gravitational wave background</a> emitted directly from <a href="Inflation_(cosmology)" class="mw-redirect" title="Inflation (cosmology)">inflation</a> at a redshift in excess of z > 1025.<a href="#cite_note-85">[85]</a>

In June 2015, astronomers reported evidence for <a href="Stellar_population#Population_III_stars" title="Stellar population">Population III stars</a> in the <a href="Cosmos_Redshift_7" title="Cosmos Redshift 7">Cosmos Redshift 7</a> <a href="Galaxy" title="Galaxy">galaxy</a> at z = 6.60. Such stars are likely to have existed in the very early universe (i.e., at high redshift), and may have started the production of <a href="Chemical_element" title="Chemical element">chemical elements</a> heavier than <a href="Hydrogen" title="Hydrogen">hydrogen</a> that are needed for the later formation of <a href="Planet" title="Planet">planets</a> and <a href="Life" title="Life">life</a> as we know it.<a href="#cite_note-AJ-20150604-86">[86]</a><a href="#cite_note-NYT-20150617-87">[87]</a>

<div class="mw-heading mw-heading3"><h3 id="Redshift_surveys">Redshift surveys</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Redshift_survey" title="Redshift survey">Redshift survey</a></div>

With advent of automated <a href="Telescope" title="Telescope">telescopes</a> and improvements in <a href="Astronomical_spectroscopy" title="Astronomical spectroscopy">spectroscopes</a>, a number of collaborations have been made to map the universe in redshift space. By combining redshift with angular position data, a redshift survey maps the 3D distribution of matter within a field of the sky. These observations are used to measure properties of the <a href="Observable_universe" title="Observable universe">large-scale structure</a> of the universe. The <a href="CfA2_Great_Wall" title="CfA2 Great Wall">Great Wall</a>, a vast <a href="Supercluster" title="Supercluster">supercluster</a> of galaxies over 500 million <a href="Light-year" title="Light-year">light-years</a> wide, provides a dramatic example of a large-scale structure that redshift surveys can detect.<a href="#cite_note-88">[88]</a>

The first redshift survey was the <a href="CfA_Redshift_Survey" title="CfA Redshift Survey">CfA Redshift Survey</a>, started in 1977 with the initial data collection completed in 1982.<a href="#cite_note-89">[89]</a> More recently, the <a href="2dF_Galaxy_Redshift_Survey" title="2dF Galaxy Redshift Survey">2dF Galaxy Redshift Survey</a> determined the large-scale structure of one section of the universe, measuring redshifts for over 220,000 galaxies; data collection was completed in 2002, and the final <a href="Data_set" title="Data set">data set</a> was released 30 June 2003.<a href="#cite_note-90">[90]</a> The <a href="Sloan_Digital_Sky_Survey" title="Sloan Digital Sky Survey">Sloan Digital Sky Survey</a> (SDSS) began collecting data in 1998<a href="#cite_note-91">[91]</a> and published its eighteenth data release in 2023.<a href="#cite_note-92">[92]</a> SSDS has measured redshifts for galaxies as high as 0.8, and has recorded over 100,000 <a href="Quasar" title="Quasar">quasars</a> at z = 3 and beyond.<a href="#cite_note-93">[93]</a> The <a href="DEEP2_Redshift_Survey" title="DEEP2 Redshift Survey">DEEP2 Redshift Survey</a> used the <a href="Keck_telescopes" class="mw-redirect" title="Keck telescopes">Keck telescopes</a> with the "DEIMOS" <a href="Spectrograph" class="mw-redirect" title="Spectrograph">spectrograph</a>; a follow-up to the pilot program DEEP1, DEEP2 was designed to measure faint galaxies with redshifts 0.7 and above, and it recorded redshifts of over 38,000 objects by its conclusion in 2013.<a href="#cite_note-94">[94]</a><a href="#cite_note-95">[95]</a>

<div class="mw-heading mw-heading2"><h2 id="Effects_from_physical_optics_or_radiative_transfer">Effects from physical optics or radiative transfer</h2></div>

The interactions and phenomena summarized in the subjects of <a href="Radiative_transfer" title="Radiative transfer">radiative transfer</a> and <a href="Physical_optics" title="Physical optics">physical optics</a> can result in shifts in the wavelength and frequency of electromagnetic radiation. In such cases, the shifts correspond to a physical energy transfer to matter or other photons rather than being by a transformation between reference frames. Such shifts can be from such physical phenomena as <a href="Wolf_effect" title="Wolf effect">coherence effects</a> or the <a href="Scattering" title="Scattering">scattering</a> of <a href="Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic radiation</a> whether from <a href="Electric_charge" title="Electric charge">charged</a> <a href="Elementary_particle" title="Elementary particle">elementary particles</a>, from <a href="Particulates" class="mw-redirect" title="Particulates">particulates</a>, or from fluctuations of the <a href="Index_of_refraction" class="mw-redirect" title="Index of refraction">index of refraction</a> in a <a href="Dielectric" title="Dielectric">dielectric</a> medium as occurs in the radio phenomenon of <a href="Whistler_(radio)" title="Whistler (radio)">radio whistlers</a>.<a href="#cite_note-basicastronomy-43">[43]</a> While such phenomena are sometimes referred to as "redshifts" and "blueshifts", in astrophysics light-matter interactions that result in energy shifts in the radiation field are generally referred to as "reddening" rather than "redshifting" which, as a term, is normally reserved for the <a href="#Redshift_formulae">effects discussed above</a>.<a href="#cite_note-basicastronomy-43">[43]</a>

In many circumstances scattering causes radiation to redden because <a href="Entropy" title="Entropy">entropy</a> results in the predominance of many low-<a href="Energy" title="Energy">energy</a> photons over few high-energy ones (while <a href="Conservation_of_energy" title="Conservation of energy">conserving total energy</a>).<a href="#cite_note-basicastronomy-43">[43]</a> Except possibly under carefully controlled conditions, scattering does not produce the same relative change in wavelength across the whole spectrum; that is, any calculated z is generally a <a href="Function_(mathematics)" title="Function (mathematics)">function</a> of wavelength. Furthermore, scattering from <a href="Randomness" title="Randomness">random</a> <a href="Matter" title="Matter">media</a> generally occurs at many <a href="Angle" title="Angle">angles</a>, and z is a function of the scattering angle. If multiple scattering occurs, or the scattering particles have relative motion, then there is generally distortion of <a href="Spectral_line" title="Spectral line">spectral lines</a> as well.<a href="#cite_note-basicastronomy-43">[43]</a>

In <a href="Interstellar_medium" title="Interstellar medium">interstellar astronomy</a>, <a href="Visible_spectrum" title="Visible spectrum">visible spectra</a> can appear redder due to scattering processes in a phenomenon referred to as <a href="Interstellar_reddening" class="mw-redirect" title="Interstellar reddening">interstellar reddening</a><a href="#cite_note-basicastronomy-43">[43]</a>—similarly <a href="Rayleigh_scattering" title="Rayleigh scattering">Rayleigh scattering</a> causes the <a href="Atmosphere_of_Earth" title="Atmosphere of Earth">atmospheric</a> reddening of the Sun seen in the sunrise or sunset and causes the rest of the sky to have a blue color. This phenomenon is distinct from redshifting because the <a href="Spectroscopic" class="mw-redirect" title="Spectroscopic">spectroscopic</a> lines are not shifted to other wavelengths in reddened objects and there is an additional <a href="Extinction_(astronomy)" title="Extinction (astronomy)">dimming</a> and distortion associated with the phenomenon due to photons being scattered in and out of the <a href="Line-of-sight_propagation" title="Line-of-sight propagation">line of sight</a>.<a href="#cite_note-96">[96]</a>

<div class="mw-heading mw-heading2"><h2 id="Blueshift">Blueshift</h2></div>

<div role="note" class="hatnote navigation-not-searchable">"Blueshift" redirects here. For the term as used in photochemistry, see <a href="Hypsochromic_shift" title="Hypsochromic shift">hypsochromic shift</a>. For the political phenomenon, see <a href="Blue_shift_(politics)" title="Blue shift (politics)">blue shift (politics)</a>. For other uses of "blueshift" or "blue shift", see <a href="Blueshift_(disambiguation)" class="mw-disambig" title="Blueshift (disambiguation)">Blueshift (disambiguation)</a>.</div>

The opposite of a redshift is a blueshift. A blueshift is any decrease in <a href="Wavelength" title="Wavelength">wavelength</a> (increase in <a href="Energy" title="Energy">energy</a>), with a corresponding increase in frequency, of an <a href="Electromagnetic_wave" class="mw-redirect" title="Electromagnetic wave">electromagnetic wave</a>. In <a href="Light" title="Light">visible light</a>, this shifts a color towards the blue end of the spectrum.

<div class="mw-heading mw-heading3"><h3 id="Doppler_blueshift">Doppler blueshift</h3></div>

<a href="Doppler_effect" title="Doppler effect">Doppler</a> blueshift is caused by movement of a source towards the observer. The term applies to any decrease in wavelength and increase in frequency caused by relative motion, even outside the <a href="Visible_spectrum" title="Visible spectrum">visible spectrum</a>. Only objects moving at near-<a href="Relativistic_speed" title="Relativistic speed">relativistic speeds</a> toward the observer are noticeably bluer to the <a href="Naked_eye" title="Naked eye">naked eye</a>, but the wavelength of any reflected or emitted photon or other particle is shortened in the direction of travel.<a href="#cite_note-97">[97]</a>

Doppler blueshift is used in <a href="Astronomy" title="Astronomy">astronomy</a> to determine relative motion:

<ul><li>The <a href="Andromeda_Galaxy" title="Andromeda Galaxy">Andromeda Galaxy</a> is moving toward our own <a href="Milky_Way" title="Milky Way">Milky Way</a> <a href="Galaxy" title="Galaxy">galaxy</a> within the <a href="Local_Group" title="Local Group">Local Group</a>; thus, when observed from Earth, its light is undergoing a blueshift.<a href="#cite_note-98">[98]</a></li>

<li>Components of a <a href="Binary_star" title="Binary star">binary star</a> system will be blueshifted when moving towards Earth</li>

<li>When observing spiral galaxies, the side spinning toward us will have a slight blueshift relative to the side spinning away from us (see <a href="Tully%E2%80%93Fisher_relation" title="Tully–Fisher relation">Tully–Fisher relation</a>).</li>

<li><a href="Blazar" title="Blazar">Blazars</a> are known to propel <a href="Relativistic_jet" class="mw-redirect" title="Relativistic jet">relativistic jets</a> toward us, emitting <a href="Synchrotron_radiation" title="Synchrotron radiation">synchrotron radiation</a> and <a href="Bremsstrahlung" title="Bremsstrahlung">bremsstrahlung</a> that appears blueshifted.<a href="#cite_note-99">[99]</a></li>

<li>Nearby stars such as <a href="Barnard's_Star" title="Barnard's Star">Barnard's Star</a> are moving toward us, resulting in a very small blueshift.</li>

<li>Doppler blueshift of distant objects with a high z can be subtracted from the much larger <a href="Hubble's_law" title="Hubble's law">cosmological redshift</a> to determine relative motion in the <a href="Metric_expansion_of_space" class="mw-redirect" title="Metric expansion of space">expanding universe</a>.<a href="#cite_note-Aoki2005-100">[100]</a></li></ul>

<div class="mw-heading mw-heading3"><h3 id="Gravitational_blueshift">Gravitational blueshift</h3></div>

Unlike the relative Doppler blueshift, caused by movement of a source towards the observer and thus dependent on the received angle of the photon, gravitational blueshift is absolute and does not depend on the received angle of the photon:

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</style><blockquote class="templatequote">Photons climbing out of a gravitating object become less energetic. This loss of energy is known as a "redshifting", as photons in the visible spectrum would appear more red. Similarly, photons falling into a gravitational field become more energetic and exhibit a blueshifting. ... Note that the magnitude of the redshifting (blueshifting) effect is not a function of the emitted angle or the received angle of the photon—it depends only on how far radially the photon had to climb out of (fall into) the potential well.<a href="#cite_note-R.N_1-101">[101]</a><a href="#cite_note-R.N_2-102">[102]</a></blockquote>

It is a natural consequence of <a href="Conservation_of_energy" title="Conservation of energy">conservation of energy</a> and <a href="Mass%E2%80%93energy_equivalence" title="Mass–energy equivalence">mass–energy equivalence</a>, and was confirmed experimentally in 1959 with the <a href="Pound%E2%80%93Rebka_experiment" title="Pound–Rebka experiment">Pound–Rebka experiment</a>. Gravitational blueshift contributes to <a href="Cosmic_microwave_background" title="Cosmic microwave background">cosmic microwave background</a> (CMB) anisotropy via the <a href="Sachs%E2%80%93Wolfe_effect" title="Sachs–Wolfe effect">Sachs–Wolfe effect</a>: when a gravitational well evolves while a photon is passing, the amount of blueshift on approach will differ from the amount of <a href="Gravitational_redshift" title="Gravitational redshift">gravitational redshift</a> as it leaves the region.<a href="#cite_note-Bonometto2002-103">[103]</a>

<div class="mw-heading mw-heading4"><h4 id="Blue_outliers">Blue outliers</h4></div>

There are faraway <a href="Active_galaxies" class="mw-redirect" title="Active galaxies">active galaxies</a> that show a blueshift in their <a href="Doubly_ionized_oxygen" title="Doubly ionized oxygen">[O III]</a> emission <a href="Emission_spectrum" title="Emission spectrum">lines</a>. One of the largest blueshifts is found in the narrow-line <a href="Quasar" title="Quasar">quasar</a>, <a href="PG_1543%2B489" title="PG 1543+489">PG 1543+489</a>, which has a relative velocity of −1150 km/s.<a href="#cite_note-Aoki2005-100">[100]</a> These types of galaxies are called "blue outliers".<a href="#cite_note-Aoki2005-100">[100]</a>

<div class="mw-heading mw-heading3"><h3 id="Cosmological_blueshift">Cosmological blueshift</h3></div>

In a hypothetical universe undergoing a runaway <a href="Big_Crunch" title="Big Crunch">Big Crunch</a> contraction, a cosmological blueshift would be observed, with galaxies further away being increasingly blueshifted—the exact opposite of the actually observed <a href="Cosmological_redshift" class="mw-redirect" title="Cosmological redshift">cosmological redshift</a> in the present <a href="Expanding_universe" class="mw-redirect" title="Expanding universe">expanding universe</a>.<a href="#cite_note-104">[104]</a>

<ul><li><a href="Gravitational_potential" title="Gravitational potential">Gravitational potential</a></li>

<li><a href="Mattig_formula" title="Mattig formula">Mattig formula</a></li>

<li><a href="Relativistic_Doppler_effect" title="Relativistic Doppler effect">Relativistic Doppler effect</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFDing2021" class="citation journal cs1">Ding, Qianhang (August 2021). "Detectability of primordial black hole binaries at high redshift". Physical Review D. 104 (4). id. 043527. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/2011.13643">2011.13643</a>. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2021PhRvD.104d3527D">2021PhRvD.104d3527D</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevD.104.043527">10.1103/PhysRevD.104.043527</a>.</cite>

</li>

<li id="cite_note-2"><a href="#cite_ref-2">^</a> <cite class="citation news cs1"><a rel="nofollow" class="external text" href="https://esahubble.org/news/heic1219/">"Hubble census finds galaxies at redshifts 9 to 12"</a>. ESA/Hubble Press Release. Retrieved 13 December 2012.</cite>

</li>

<li id="cite_note-3"><a href="#cite_ref-3">^</a> For a tutorial on how to define and interpret large redshift measurements, see: <cite id="CITEREFHuchra" class="citation web cs1">Huchra, John. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20131222052715/http://ned.ipac.caltech.edu/help/zdef.html">"Extragalactic Redshifts"</a>. NASA/IPAC Extragalactic Database. Harvard-Smithsonian Center for Astrophysics. Archived from <a rel="nofollow" class="external text" href="http://ned.ipac.caltech.edu/help/zdef.html">the original</a> on 2013-12-22. Retrieved 2023-03-16.</cite>

</li>

<cite id="CITEREFDoppler1846" class="citation book cs1">Doppler, Christian (1846). Beiträge zur fixsternenkunde. Vol. 69. Prague: G. Haase Söhne. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1846befi.book.....D">1846befi.book.....D</a>.</cite>

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<cite id="CITEREFMaulik2005" class="citation book cs1">Maulik, Dev (2005). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=HedeGJms0n4C&q=%22Ballot%22&pg=PA3">"Doppler Sonography: A Brief History"</a>. In Maulik, Dev; Zalud, Ivica (eds.). <a rel="nofollow" class="external text" href="https://www.springer.com/west/home/medicine/gynecology?SGWID=4-10066-22-46625046-0">Doppler Ultrasound in Obstetrics And Gynecology</a>. Springer. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-540-23088-5</bdi>.</cite>

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<cite id="CITEREFO'ConnorRobertson1998" class="citation web cs1">O'Connor, John J.; Robertson, Edmund F. (1998). <a rel="nofollow" class="external text" href="http://www-history.mcs.st-andrews.ac.uk/Biographies/Doppler.html">"Christian Andreas Doppler"</a>. <a href="MacTutor_History_of_Mathematics_archive" class="mw-redirect" title="MacTutor History of Mathematics archive">MacTutor History of Mathematics archive</a>. <a href="University_of_St_Andrews" title="University of St Andrews">University of St Andrews</a>.</cite>

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<cite id="CITEREFHuggins1868" class="citation journal cs1">Huggins, William (1868). "Further Observations on the Spectra of Some of the Stars and Nebulae, with an Attempt to Determine Therefrom Whether These Bodies are Moving towards or from the Earth, Also Observations on the Spectra of the Sun and of Comet II". <a href="Philosophical_Transactions_of_the_Royal_Society_of_London" class="mw-redirect" title="Philosophical Transactions of the Royal Society of London">Philosophical Transactions of the Royal Society of London</a>. 158: 529–564. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1868RSPT..158..529H">1868RSPT..158..529H</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frstl.1868.0022">10.1098/rstl.1868.0022</a>.</cite>

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<li id="cite_note-Nolte-9">^ <a href="#cite_ref-Nolte_9-0">a</a> <a href="#cite_ref-Nolte_9-1">b</a> <cite id="CITEREFNolte2020" class="citation journal cs1">Nolte, David D. (1 March 2020). <a rel="nofollow" class="external text" href="https://doi.org/10.1063%2FPT.3.4429">"The fall and rise of the Doppler effect"</a>. Physics Today. 73 (3): 30–35. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2020PhT....73c..30N">2020PhT....73c..30N</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2FPT.3.4429">10.1063/PT.3.4429</a>.</cite>

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<cite id="CITEREFBélopolsky1901" class="citation journal cs1">Bélopolsky, A. (1901). <a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F140786">"On an Apparatus for the Laboratory Demonstration of the Doppler-Fizeau Principle"</a>. <a href="Astrophysical_Journal" class="mw-redirect" title="Astrophysical Journal">Astrophysical Journal</a>. 13: 15. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1901ApJ....13...15B">1901ApJ....13...15B</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F140786">10.1086/140786</a>.</cite>

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<li id="cite_note-SmithInKragh-2019-12">^ <a href="#cite_ref-SmithInKragh-2019_12-0">a</a> <a href="#cite_ref-SmithInKragh-2019_12-1">b</a> <a href="#cite_ref-SmithInKragh-2019_12-2">c</a> <a href="#cite_ref-SmithInKragh-2019_12-3">d</a> <a href="#cite_ref-SmithInKragh-2019_12-4">e</a> <a href="#cite_ref-SmithInKragh-2019_12-5">f</a> <cite id="CITEREFRobert2019" class="citation book cs1">Robert, Smith (2019). "Observations and the universe". In Kragh, Helge; Longair, Malcolm S. (eds.). The Oxford handbook of the history of modern cosmology. Oxford University Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-19-881766-6</bdi>. <a href="OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/1052868704">1052868704</a>.</cite>

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<cite id="CITEREFSlipher1912" class="citation journal cs1">Slipher, Vesto (1912). "The radial velocity of the Andromeda Nebula". <a href="Lowell_Observatory_Bulletin" class="mw-redirect" title="Lowell Observatory Bulletin">Lowell Observatory Bulletin</a>. 1 (8): 2.56 – 2.57. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1913LowOB...2...56S">1913LowOB...2...56S</a>. <q>The magnitude of this velocity, which is the greatest hitherto observed, raises the question whether the velocity-like displacement might not be due to some other cause, but I believe we have at present no other interpretation for it</q></cite>

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<cite id="CITEREFSlipher1915" class="citation journal cs1">Slipher, Vesto (1915). "Spectrographic Observations of Nebulae". <a href="Popular_Astronomy_(US_magazine)" title="Popular Astronomy (US magazine)">Popular Astronomy</a>. 23: 21–24. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1915PA.....23...21S">1915PA.....23...21S</a>.</cite>

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<cite id="CITEREFHubble1929" class="citation journal cs1">Hubble, Edwin (1929). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC522427">"A Relation between Distance and Radial Velocity among Extra-Galactic Nebulae"</a>. <a href="Proceedings_of_the_National_Academy_of_Sciences_of_the_United_States_of_America" title="Proceedings of the National Academy of Sciences of the United States of America">Proceedings of the National Academy of Sciences of the United States of America</a>. 15 (3): 168–173. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1929PNAS...15..168H">1929PNAS...15..168H</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1073%2Fpnas.15.3.168">10.1073/pnas.15.3.168</a>. <a href="PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC522427">522427</a>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/16577160">16577160</a>.</cite>

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<li id="cite_note-16"><a href="#cite_ref-16">^</a> <cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://imagine.gsfc.nasa.gov/educators/programs/cosmictimes/online_edition/1929/expanding.html">"Universe is Expanding"</a>. Goddard Space Flight Center. 2017-12-08. Retrieved 2023-09-06.</cite>

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<li id="cite_note-17"><a href="#cite_ref-17">^</a> <cite id="CITEREFFriedman1922" class="citation journal cs1">Friedman, A. A. (1922). "Über die Krümmung des Raumes". <a href="Zeitschrift_f%C3%BCr_Physik" title="Zeitschrift für Physik">Zeitschrift für Physik</a>. 10 (1): 377–386. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1922ZPhy...10..377F">1922ZPhy...10..377F</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01332580">10.1007/BF01332580</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:125190902">125190902</a>.</cite> English translation in <cite id="CITEREFFriedman1999" class="citation journal cs1">Friedman, A. (1999). "On the Curvature of Space". <a href="General_Relativity_and_Gravitation" title="General Relativity and Gravitation">General Relativity and Gravitation</a>. 31 (12): 1991–2000. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1999GReGr..31.1991F">1999GReGr..31.1991F</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1023%2FA%3A1026751225741">10.1023/A:1026751225741</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:122950995">122950995</a>.</cite>)

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<li id="cite_note-18"><a href="#cite_ref-18">^</a> <cite id="CITEREFEddington1923" class="citation book cs1"><a href="Arthur_Eddington" title="Arthur Eddington">Eddington, Arthur Stanley</a> (1923). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=errkj2WXGzIC&pg=PA164">The Mathematical Theory of Relativity</a>. The University Press. p. 164.</cite>

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<li id="cite_note-19"><a href="#cite_ref-19">^</a> <cite id="CITEREFReference-OED-redshift" class="citation encyclopaedia cs1"><a rel="nofollow" class="external text" href="https://www.oed.com/view/Entry/160477">"redshift"</a>. <a href="Oxford_English_Dictionary" title="Oxford English Dictionary">Oxford English Dictionary</a> (Online ed.). <a href="Oxford_University_Press" title="Oxford University Press">Oxford University Press</a>. Retrieved 2023-03-17.</cite> (Subscription or <a rel="nofollow" class="external text" href="https://www.oed.com/public/login/loggingin#withyourlibrary">participating institution membership</a> required.)

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<cite id="CITEREFde_Sitter1934" class="citation journal cs1">de Sitter, W. (1934). "On distance, magnitude, and related quantities in an expanding universe". <a href="Bulletin_of_the_Astronomical_Institutes_of_the_Netherlands" class="mw-redirect" title="Bulletin of the Astronomical Institutes of the Netherlands">Bulletin of the Astronomical Institutes of the Netherlands</a>. 7: 205. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1934BAN.....7..205D">1934BAN.....7..205D</a>. <q>It thus becomes urgent to investigate the effect of the redshift and of the metric of the universe on the apparent magnitude and observed numbers of nebulae of given magnitude</q></cite>

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<li id="cite_note-21"><a href="#cite_ref-21">^</a> <cite id="CITEREFLewis2016" class="citation journal cs1">Lewis, Geraint F. (2016). "On The Relativity of Redshifts: Does Space Really "Expand"?". Australian Physics. 53: 95. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/1605.08634">1605.08634</a>.</cite>

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<li id="cite_note-22"><a href="#cite_ref-22">^</a> <cite id="CITEREFIvesStilwell1938" class="citation journal cs1">Ives, H.; Stilwell, G. (1938). "An Experimental study of the rate of a moving atomic clock". Journal of the Optical Society of America. 28 (7): 215–226. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1938JOSA...28..215I">1938JOSA...28..215I</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1364%2Fjosa.28.000215">10.1364/josa.28.000215</a>.</cite>

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<li id="cite_note-23"><a href="#cite_ref-23">^</a> <cite id="CITEREFFreund2008" class="citation book cs1">Freund, Jurgen (2008). Special Relativity for Beginners. World Scientific. p. 120. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-981-277-160-5</bdi>.</cite>

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<li id="cite_note-24"><a href="#cite_ref-24">^</a> <cite id="CITEREFDitchburn1991" class="citation book cs1">Ditchburn, R. (1991). Light. Dover. p. 329. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-12-218101-6</bdi>.</cite>

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See "<a rel="nofollow" class="external text" href="http://www.physics.uq.edu.au/people/ross/phys2100/doppler.htm">Photons, Relativity, Doppler shift</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20060827063802/http://www.physics.uq.edu.au/people/ross/phys2100/doppler.htm">Archived</a> 2006-08-27 at the <a href="Wayback_Machine" title="Wayback Machine">Wayback Machine</a> " at the University of Queensland

</li>

<li id="cite_note-26"><a href="#cite_ref-26">^</a> <cite id="CITEREFPeacock1998" class="citation book cs1">Peacock, J. A. (1998-12-28). <a rel="nofollow" class="external text" href="https://www.cambridge.org/core/product/identifier/9780511804533/type/book">Cosmological Physics</a> (1 ed.). Cambridge University Press. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2Fcbo9780511804533">10.1017/cbo9780511804533</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-521-41072-4</bdi>.</cite>

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<li id="cite_note-Weinberg-27"><a href="#cite_ref-Weinberg_27-0">^</a> <cite id="CITEREFWeinberg1993" class="citation book cs1">Weinberg, Steven (1993). <a href="The_First_Three_Minutes%3A_A_Modern_View_of_the_Origin_of_the_Universe" class="mw-redirect" title="The First Three Minutes: A Modern View of the Origin of the Universe">The First Three Minutes: A Modern View of the Origin of the Universe</a> (2nd ed.). Basic Books. p. 34. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9780-465-02437-7</bdi>.</cite>

</li>

<li id="cite_note-Bergström-28"><a href="#cite_ref-Bergström_28-0">^</a> <cite id="CITEREFBergströmGoobar2006" class="citation book cs1"><a href="Lars_Bergstr%C3%B6m_(physicist)" title="Lars Bergström (physicist)">Bergström, Lars</a>; Goobar, Ariel (2006). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=CQYu_sutWAoC&pg=PA77">Cosmology and Particle Astrophysics</a> (2nd ed.). Springer. p. 77, Eq.4.79. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-540-32924-4</bdi>.</cite>

</li>

<li id="cite_note-Longair-29"><a href="#cite_ref-Longair_29-0">^</a> <cite id="CITEREFLongair1998" class="citation book cs1">Longair, M. S. (1998). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=2ARuLT-tk5EC&pg=PA161">Galaxy Formation</a>. Springer. p. 161. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-540-63785-1</bdi>.</cite>

</li>

<li id="cite_note-Hogg-30"><a href="#cite_ref-Hogg_30-0">^</a> <cite id="CITEREFBunnHogg2009" class="citation journal cs1">Bunn, E. F.; Hogg, D. W. (2009). "The kinematic origin of the cosmological redshift". American Journal of Physics. 77 (8): 688–694. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/0808.1081">0808.1081</a>. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2009AmJPh..77..688B">2009AmJPh..77..688B</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.3129103">10.1119/1.3129103</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:1365918">1365918</a>.</cite>

</li>

<li id="cite_note-UCLA-2018-31">^ <a href="#cite_ref-UCLA-2018_31-0">a</a> <a href="#cite_ref-UCLA-2018_31-1">b</a> <cite id="CITEREFWright2018" class="citation web cs1">Wright, Edward L. (2018). <a rel="nofollow" class="external text" href="http://www.astro.ucla.edu/~wright/ACC.html">"UCLA Cosmological Calculator"</a>. <a href="UCLA" class="mw-redirect" title="UCLA">UCLA</a>. Retrieved 6 August 2022.</cite> For parameter values as of 2018, H0=67.4 and OmegaM=0.315, see the table at <a href="Lambda-CDM_model#Parameters" title="Lambda-CDM model">Lambda-CDM model § Parameters</a>.

</li>

<li id="cite_note-ICRAR-2022-32">^ <a href="#cite_ref-ICRAR-2022_32-0">a</a> <a href="#cite_ref-ICRAR-2022_32-1">b</a> <cite id="CITEREFStaff2022" class="citation web cs1">Staff (2022). <a rel="nofollow" class="external text" href="https://cosmocalc.icrar.org/">"ICRAR Cosmology Calculator"</a>. <a href="International_Centre_for_Radio_Astronomy_Research" title="International Centre for Radio Astronomy Research">International Centre for Radio Astronomy Research</a>. Retrieved 6 August 2022.</cite>

</li>

<li id="cite_note-33"><a href="#cite_ref-33">^</a> <cite id="CITEREFBedran2002" class="citation journal cs1">Bedran, M. L. (2002). <a rel="nofollow" class="external text" href="http://www.df.uba.ar/users/sgil/physics_paper_doc/papers_phys/cosmo/doppler_redshift.pdf">"A comparison between the Doppler and cosmological redshifts"</a> (PDF). American Journal of Physics. 70 (4): 406–408. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2002AmJPh..70..406B">2002AmJPh..70..406B</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.1446856">10.1119/1.1446856</a>. Retrieved 2023-03-16.</cite>

</li>

<li id="cite_note-Harrison2-34"><a href="#cite_ref-Harrison2_34-0">^</a> <cite id="CITEREFHarrison1992" class="citation journal cs1">Harrison, Edward (1992). <a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F172179">"The redshift-distance and velocity-distance laws"</a>. Astrophysical Journal, Part 1. 403: 28–31. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1993ApJ...403...28H">1993ApJ...403...28H</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F172179">10.1086/172179</a>.</cite>. A pdf file can be found here <a rel="nofollow" class="external autonumber" href="http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1993ApJ...403...28H&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf">[1]</a>.

</li>

<li id="cite_note-35"><a href="#cite_ref-35">^</a> <a href="#CITEREFHarrison2000">Harrison 2000</a>, p. 302.

</li>

<li id="cite_note-Weinberg_Cosmology-36"><a href="#cite_ref-Weinberg_Cosmology_36-0">^</a> <cite id="CITEREFWeinberg2008" class="citation book cs1">Weinberg, Steven (2008). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=48C-ym2EmZkC&pg=PA11">Cosmology</a>. Oxford University Press. p. 11. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-19-852682-7</bdi>.</cite>

</li>

<li id="cite_note-37"><a href="#cite_ref-37">^</a> This is only true in a universe where there are no <a href="Peculiar_velocity" title="Peculiar velocity">peculiar velocities</a>. Otherwise, redshifts combine as

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<annotation encoding="application/x-tex">{\displaystyle 1+z=(1+z_{\mathrm {Doppler} })(1+z_{\mathrm {expansion} })}</annotation>

</semantics>

</math><img src="./4fe0c8de8ae09afbfdfc8822be962e2508baa28e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:35.267ex; height:3.009ex;" alt="{\displaystyle 1+z=(1+z_{\mathrm {Doppler} })(1+z_{\mathrm {expansion} })}" loading="lazy"></dd></dl>

which yields solutions where certain objects that "recede" are blueshifted and other objects that "approach" are redshifted. For more on this bizarre result see: <cite id="CITEREFDavisLineweaverWebb2003" class="citation journal cs1">Davis, T. M.; Lineweaver, C. H.; Webb, J. K. (April 2003). "Solutions to the tethered galaxy problem in an expanding universe and the observation of receding blueshifted objects". American Journal of Physics. 71 (4): 358–364. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/0104349">astro-ph/0104349</a>. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2003AmJPh..71..358D">2003AmJPh..71..358D</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.1528916">10.1119/1.1528916</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:3219383">3219383</a>.</cite>

</li>

<li id="cite_note-38"><a href="#cite_ref-38">^</a> <cite id="CITEREFZee2013" class="citation book cs1">Zee, Anthony (2013). Einstein Gravity in a Nutshell. In a Nutshell Series (1st ed.). Princeton: Princeton University Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-691-14558-7</bdi>.</cite>

</li>

<li id="cite_note-39"><a href="#cite_ref-39">^</a> <cite id="CITEREFChant1930" class="citation journal cs1">Chant, C. A. (1930). "Notes and Queries (Telescopes and Observatory Equipment – The Einstein Shift of Solar Lines)". <a href="Journal_of_the_Royal_Astronomical_Society_of_Canada" title="Journal of the Royal Astronomical Society of Canada">Journal of the Royal Astronomical Society of Canada</a>. 24: 390. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1930JRASC..24..390C">1930JRASC..24..390C</a>.</cite>

</li>

<li id="cite_note-40"><a href="#cite_ref-40">^</a> <cite id="CITEREFEinstein1907" class="citation journal cs1"><a href="Albert_Einstein" title="Albert Einstein">Einstein, A.</a> (1907). "Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen". Jahrbuch der Radioaktivität und Elektronik. 4: 411–462. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1908JRE.....4..411E">1908JRE.....4..411E</a>.</cite> See p. 458 The influence of a gravitational field on clocks

</li>

<li id="cite_note-41"><a href="#cite_ref-41">^</a> <cite id="CITEREFPoundRebka1960" class="citation journal cs1">Pound, R.; Rebka, G. (1960). <a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.4.337">"Apparent Weight of Photons"</a>. Physical Review Letters. 4 (7): 337–341. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1960PhRvL...4..337P">1960PhRvL...4..337P</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.4.337">10.1103/PhysRevLett.4.337</a>.</cite>. This paper was the first measurement.

</li>

<li id="cite_note-42"><a href="#cite_ref-42">^</a> <cite id="CITEREFSachsWolfe1967" class="citation journal cs1"><a href="Rainer_K._Sachs" title="Rainer K. Sachs">Sachs, R. K.</a>; <a href="Arthur_M._Wolfe" title="Arthur M. Wolfe">Wolfe, A. M.</a> (1967). "Perturbations of a cosmological model and angular variations of the cosmic microwave background". Astrophysical Journal. 147 (73): 73. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1967ApJ...147...73S">1967ApJ...147...73S</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F148982">10.1086/148982</a>.</cite>

</li>

<li id="cite_note-basicastronomy-43">^ <a href="#cite_ref-basicastronomy_43-0">a</a> <a href="#cite_ref-basicastronomy_43-1">b</a> <a href="#cite_ref-basicastronomy_43-2">c</a> <a href="#cite_ref-basicastronomy_43-3">d</a> <a href="#cite_ref-basicastronomy_43-4">e</a> <a href="#cite_ref-basicastronomy_43-5">f</a> <a href="#cite_ref-basicastronomy_43-6">g</a> <a href="#cite_ref-basicastronomy_43-7">h</a> <a href="#cite_ref-basicastronomy_43-8">i</a> See Binney and Merrifeld (1998), Carroll and Ostlie (1996), Kutner (2003) for applications in astronomy.

</li>

<li id="cite_note-44"><a href="#cite_ref-44">^</a> Where z = redshift; v|| = <a href="Velocity" title="Velocity">velocity</a> parallel to line-of-sight (positive if moving away from receiver); c = <a href="Speed_of_light" title="Speed of light">speed of light</a>; γ = <a href="Lorentz_factor" title="Lorentz factor">Lorentz factor</a>; a = <a href="Scale_factor_(Universe)" class="mw-redirect" title="Scale factor (Universe)">scale factor</a>; G = <a href="Gravitational_constant" title="Gravitational constant">gravitational constant</a>; M = object <a href="Mass" title="Mass">mass</a>; r = <a href="Schwarzschild_coordinates" title="Schwarzschild coordinates">radial Schwarzschild coordinate</a>, gtt = t,t component of the <a href="Metric_tensor" title="Metric tensor">metric tensor</a>

</li>

<li id="cite_note-Pilipenko-45"><a href="#cite_ref-Pilipenko_45-0">^</a> <cite id="CITEREFPilipenko2013" class="citation arxiv cs1">Pilipenko, Sergey V. (2013). "Paper-and-pencil cosmological calculator". <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/1303.5961">1303.5961</a> [<a rel="nofollow" class="external text" href="https://arxiv.org/archive/astro-ph.CO">astro-ph.CO</a>].</cite> Including <a rel="nofollow" class="external text" href="https://code.google.com/archive/p/cosmonom/downloads">Fortran-90 code</a> upon which the citing charts and formulae are based.

</li>

<li id="cite_note-reboul-46"><a href="#cite_ref-reboul_46-0">^</a> When cosmological redshifts were first discovered, <a href="Fritz_Zwicky" title="Fritz Zwicky">Fritz Zwicky</a> proposed an effect known as tired light. While usually considered for historical interests, it is sometimes, along with <a href="Intrinsic_redshift" class="mw-redirect" title="Intrinsic redshift">intrinsic redshift</a> suggestions, utilized by <a href="Nonstandard_cosmologies" class="mw-redirect" title="Nonstandard cosmologies">nonstandard cosmologies</a>. In 1981, H. J. Reboul summarised many <a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1981A%26AS...45..129R&db_key=AST&data_type=HTML&format=&high=42ca922c9c23806">alternative redshift mechanisms</a> that had been discussed in the literature since the 1930s. In 2001, <a href="Geoffrey_Burbidge" title="Geoffrey Burbidge">Geoffrey Burbidge</a> remarked in a <a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2001PASP..113..899B&db_key=AST&data_type=HTML">review</a> that the wider astronomical community has marginalized such discussions since the 1960s. Burbidge and <a href="Halton_Arp" title="Halton Arp">Halton Arp</a>, while investigating the mystery of <a href="Quasar#History_of_observation_and_interpretation" title="Quasar">the nature of quasars</a>, tried to develop alternative redshift mechanisms, and very few of their fellow scientists acknowledged let alone accepted their work. Moreover, <cite id="CITEREFGoldhaberGroomKimAldering2001" class="citation journal cs1">Goldhaber, G.; et al. (2001). <a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F322460">"Timescale Stretch Parameterization of Type Ia Supernova B-Band Lightcurves"</a>. Astrophysical Journal. 558 (1): 359–386. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/0104382">astro-ph/0104382</a>. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2001ApJ...558..359G">2001ApJ...558..359G</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F322460">10.1086/322460</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:17237531">17237531</a>.</cite> pointed out that alternative theories are unable to account for timescale stretch observed in <a href="Type_Ia_supernovae" class="mw-redirect" title="Type Ia supernovae">type Ia supernovae</a>

</li>

<li id="cite_note-47"><a href="#cite_ref-47">^</a> For a review of the subject of photometry, consider: <cite id="CITEREFBudding1993" class="citation book cs1">Budding, E. (September 24, 1993). Introduction to Astronomical Photometry. Cambridge University Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-521-41867-4</bdi>.</cite>

</li>

<li id="cite_note-48"><a href="#cite_ref-48">^</a> The technique was first described by: <cite id="CITEREFBaum1962" class="citation conference cs1">Baum, W. A. (1962). McVittie, G. C. (ed.). Problems of extra-galactic research. IAU Symposium No. 15. p. 390.</cite>

</li>

<li id="cite_note-49"><a href="#cite_ref-49">^</a> <cite id="CITEREFBolzonellaMirallesPelló2000" class="citation journal cs1">Bolzonella, M.; Miralles, J.-M.; Pelló, R. (2000). "Photometric redshifts based on standard SED fitting procedures". Astronomy and Astrophysics. 363: 476–492. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/0003380">astro-ph/0003380</a>. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2000A&A...363..476B">2000A&A...363..476B</a>.</cite>

</li>

<li id="cite_note-50"><a href="#cite_ref-50">^</a> A pedagogical overview of the K-correction by David Hogg and other members of the <a href="Sloan_Digital_Sky_Survey" title="Sloan Digital Sky Survey">SDSS</a> collaboration can be found at: <cite id="CITEREFHoggBaldryBlantonEisenstein2002" class="citation arxiv cs1">Hogg, David W.; et al. (October 2002). "The K correction". <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/0210394">astro-ph/0210394</a>.</cite>

</li>

<li id="cite_note-51"><a href="#cite_ref-51">^</a> <cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://swift.gsfc.nasa.gov/about_swift/redshift.html">"Swift: About Swift"</a>. swift.gsfc.nasa.gov. Retrieved 2025-04-07.</cite>

</li>

<li id="cite_note-52"><a href="#cite_ref-52">^</a> <cite id="CITEREFGeVan_EykenMahadevanDewitt2006" class="citation journal cs1">Ge, Jian; Van Eyken, Julian; <a href="Suvrath_Mahadevan" title="Suvrath Mahadevan">Mahadevan, Suvrath</a>; Dewitt, Curtis; et al. (2006). "The First Extrasolar Planet Discovered with a New-Generation High-Throughput Doppler Instrument". The Astrophysical Journal. 648 (1): 683–695. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/0605247">astro-ph/0605247</a>. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2006ApJ...648..683G">2006ApJ...648..683G</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F505699">10.1086/505699</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:13879217">13879217</a>.</cite>

</li>

<li id="cite_note-53"><a href="#cite_ref-53">^</a> <cite id="CITEREFLibbrecht1988" class="citation journal cs1">Libbrecht, Keng (1988). <a rel="nofollow" class="external text" href="https://authors.library.caltech.edu/104214/1/1988SSRv___47__275L.pdf">"Solar and stellar seismology"</a> (PDF). Space Science Reviews. 47 (3–4): 275–301. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1988SSRv...47..275L">1988SSRv...47..275L</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF00243557">10.1007/BF00243557</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:120897051">120897051</a>.</cite>

</li>

<li id="cite_note-54"><a href="#cite_ref-54">^</a> In 1871 <a href="Hermann_Carl_Vogel" title="Hermann Carl Vogel">Hermann Carl Vogel</a> measured the rotation rate of <a href="Venus" title="Venus">Venus</a>. <a href="Vesto_Slipher" title="Vesto Slipher">Vesto Slipher</a> was working on such measurements when he turned his attention to spiral nebulae.

</li>

<li id="cite_note-55"><a href="#cite_ref-55">^</a> An early review by <a href="Jan_Hendrik_Oort" class="mw-redirect" title="Jan Hendrik Oort">Oort, J. H.</a> on the subject: <cite id="CITEREFOort1970" class="citation journal cs1">Oort, J. H. (1970). "The formation of galaxies and the origin of the high-velocity hydrogen". <a href="Astronomy_and_Astrophysics" class="mw-redirect" title="Astronomy and Astrophysics">Astronomy and Astrophysics</a>. 7: 381. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1970A&A.....7..381O">1970A&A.....7..381O</a>.</cite>

</li>

<li id="cite_note-56"><a href="#cite_ref-56">^</a> <cite id="CITEREFAsaoka1989" class="citation journal cs1">Asaoka, Ikuko (1989). "X-ray spectra at infinity from a relativistic accretion disk around a Kerr black hole". Publications of the Astronomical Society of Japan. 41 (4): 763–778. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1989PASJ...41..763A">1989PASJ...41..763A</a>.</cite>

</li>

<li id="cite_note-57"><a href="#cite_ref-57">^</a> <cite id="CITEREFRybickiLightman1979" class="citation book cs1">Rybicki, G. B.; Lightman, A. R. (1979). Radiative Processes in Astrophysics. John Wiley & Sons. p. 288. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-471-82759-2</bdi>.</cite>

</li>

<li id="cite_note-58"><a href="#cite_ref-58">^</a> <cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.esa.int/Our_Activities/Space_Science/Cosmic_detectives">"Cosmic Detectives"</a>. The European Space Agency (ESA). 2013-04-02. Retrieved 2013-04-25.</cite>

</li>

<li id="cite_note-59"><a href="#cite_ref-59">^</a> An accurate measurement of the cosmic microwave background was achieved by the <a href="Cosmic_Background_Explorer" title="Cosmic Background Explorer">COBE</a> experiment. The final published temperature of 2.73 K was reported in this paper: <cite id="CITEREFFixsenChengCottinghamEplee1994" class="citation journal cs1">Fixsen, D. J.; Cheng, E. S.; Cottingham, D. A.; Eplee, R. E. Jr.; Isaacman, R. B.; Mather, J. C.; Meyer, S. S.; Noerdlinger, P. D.; Shafer, R. A.; Weiss, R.; Wright, E. L.; Bennett, C. L.; <a href="Nancy_Boggess" title="Nancy Boggess">Boggess, N. W.</a>; Kelsall, T.; Moseley, S. H.; Silverberg, R. F.; Smoot, G. F.; Wilkinson, D. T. (January 1994). "Cosmic microwave background dipole spectrum measured by the COBE FIRAS instrument". Astrophysical Journal. 420: 445. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1994ApJ...420..445F">1994ApJ...420..445F</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F173575">10.1086/173575</a>.</cite>. The most accurate measurement as of 2006 was achieved by the <a href="Wilkinson_Microwave_Anisotropy_Probe" title="Wilkinson Microwave Anisotropy Probe">WMAP</a> experiment.

</li>

<li id="cite_note-Kellermann-60"><a href="#cite_ref-Kellermann_60-0">^</a> <cite id="CITEREFKellermann2014" class="citation journal cs1">Kellermann, K.I. (2014). "The Discovery of Quasars and its Aftermath". Journal of Astronomical History and Heritage. 17 (3): 267–282. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/1304.3627">1304.3627</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.3724%2FSP.J.1440-2807.2014.03.03">10.3724/SP.J.1440-2807.2014.03.03</a>.</cite>

</li>

<li id="cite_note-FOOTNOTEPeebles199378–79-61"><a href="#cite_ref-FOOTNOTEPeebles199378–79_61-0">^</a> <a href="#CITEREFPeebles1993">Peebles 1993</a>, pp. 78–79.

</li>

<li id="cite_note-62"><a href="#cite_ref-62">^</a> <cite id="CITEREFHalstead2021" class="citation web cs1">Halstead, Evan (2021-08-16). <a rel="nofollow" class="external text" href="https://phys.libretexts.org/Courses/Skidmore_College/Introduction_to_General_Relativity/07:_Cosmology/7.03:_Redshift">"Introduction to General Relativity: 7.3: Redshift"</a>. Physics LibreTexts. Retrieved 2025-03-06.</cite>

</li>

<li id="cite_note-FOOTNOTEPeebles199334-63"><a href="#cite_ref-FOOTNOTEPeebles199334_63-0">^</a> <a href="#CITEREFPeebles1993">Peebles 1993</a>, p. 34.

</li>

<li id="cite_note-64"><a href="#cite_ref-64">^</a> <cite id="CITEREFPercivalWhite2009" class="citation journal cs1">Percival, Will J.; White, Martin (11 February 2009). <a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fj.1365-2966.2008.14211.x">"Testing cosmological structure formation using redshift-space distortions"</a>. Monthly Notices of the Royal Astronomical Society. 393 (1): 297–308. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/0808.0003">0808.0003</a>. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2009MNRAS.393..297P">2009MNRAS.393..297P</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fj.1365-2966.2008.14211.x">10.1111/j.1365-2966.2008.14211.x</a>.</cite>

</li>

<li id="cite_note-65"><a href="#cite_ref-65">^</a> <cite id="CITEREFRaccanelliBertaccaPietrobonSchmidt2013" class="citation journal cs1">Raccanelli, A.; Bertacca, D.; Pietrobon, D.; Schmidt, F.; Samushia, L.; Bartolo, N.; Dore, O.; Matarrese, S.; Percival, W. J. (25 September 2013). <a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fmnras%2Fstt1517">"Testing gravity using large-scale redshift-space distortions"</a>. Monthly Notices of the Royal Astronomical Society. 436 (1): 89–100. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/1207.0500">1207.0500</a>. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2013MNRAS.436...89R">2013MNRAS.436...89R</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fmnras%2Fstt1517">10.1093/mnras/stt1517</a>.</cite>

</li>

<li id="cite_note-66"><a href="#cite_ref-66">^</a> <cite id="CITEREFKnox2016" class="citation web cs1">Knox, Lloyd (2016-12-22). <a rel="nofollow" class="external text" href="https://phys.libretexts.org/Courses/University_of_California_Davis/Physics_156:_A_Cosmology_Workbook/01:_Workbook/1.07:_The_Distance-Redshift_Relation">"Physics 156: A Cosmology Workbook: 1.7: The Distance-Redshift Relation"</a>. Physics LibreTexts. Retrieved 2025-03-06.</cite>

</li>

<li id="cite_note-67"><a href="#cite_ref-67">^</a> <cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.nobelprize.org/uploads/2019/05/popular-physicsprize2011.pdf">"The Nobel Prize in Physics 2011: Information for the Public"</a> (PDF). nobelprize.org. Retrieved 2023-06-13.</cite>

</li>

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<li id="cite_note-88"><a href="#cite_ref-88">^</a> <cite id="CITEREFGellerHuchra1989" class="citation journal cs1">Geller, M. J.; Huchra, J. P. (1989). "Mapping the Universe". Science. 246 (4932): 897–903. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1989Sci...246..897G">1989Sci...246..897G</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fscience.246.4932.897">10.1126/science.246.4932.897</a>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/17812575">17812575</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:31328798">31328798</a>.</cite>

</li>

<li id="cite_note-89"><a href="#cite_ref-89">^</a> See the CfA website for more details: <cite id="CITEREFHuchra" class="citation web cs1"><a href="John_Huchra" title="John Huchra">Huchra, John P.</a> <a rel="nofollow" class="external text" href="https://lweb.cfa.harvard.edu/~dfabricant/huchra/zcat/">"The CfA Redshift Survey"</a>. Harvard & Smithsonian Center for Astrophysics. Retrieved 2023-03-20.</cite>

</li>

<li id="cite_note-90"><a href="#cite_ref-90">^</a> <cite id="CITEREFColePercivalPeacockNorberg2005" class="citation journal cs1"><a href="Shaun_Cole" title="Shaun Cole">Cole, Shaun</a>; Percival, Will J.; Peacock, John A.; Norberg, Peder; et al. (2005). <a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fj.1365-2966.2005.09318.x">"The 2dF galaxy redshift survey: Power-spectrum analysis of the final dataset and cosmological implications"</a>. Monthly Notices of the Royal Astronomical Society. 362 (2): 505–34. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/0501174">astro-ph/0501174</a>. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2005MNRAS.362..505C">2005MNRAS.362..505C</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fj.1365-2966.2005.09318.x">10.1111/j.1365-2966.2005.09318.x</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:6906627">6906627</a>.</cite> <a rel="nofollow" class="external text" href="http://msowww.anu.edu.au/2dFGRS/">2dF Galaxy Redshift Survey homepage</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070205010241/http://msowww.anu.edu.au/2dFGRS/">Archived</a> 2007-02-05 at the <a href="Wayback_Machine" title="Wayback Machine">Wayback Machine</a>

</li>

<li id="cite_note-91"><a href="#cite_ref-91">^</a> <cite id="CITEREFGunnSiegmundManneryOwen2006" class="citation journal cs1">Gunn, James E.; Siegmund, Walter A.; Mannery, Edward J.; Owen, Russell E.; Hull, Charles L.; Leger, R. French; et al. (April 2006). <a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F500975">"The 2.5 m Telescope of the Sloan Digital Sky Survey"</a>. The Astronomical Journal. 131 (4): 2332–2359. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/0602326">astro-ph/0602326</a>. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2006AJ....131.2332G">2006AJ....131.2332G</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F500975">10.1086/500975</a>.</cite>

</li>

<li id="cite_note-92"><a href="#cite_ref-92">^</a> <cite id="CITEREFAlmeida2023" class="citation journal cs1">Almeida, Andrés; et al. (2023). <a rel="nofollow" class="external text" href="https://doi.org/10.3847%2F1538-4365%2Facda98">"The Eighteenth Data Release of the Sloan Digital Sky Surveys: Targeting and First Spectra from SDSS-V"</a>. The Astrophysical Journal Supplement Series. 267 (2): 44. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/2301.07688">2301.07688</a>. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2023ApJS..267...44A">2023ApJS..267...44A</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.3847%2F1538-4365%2Facda98">10.3847/1538-4365/acda98</a>.</cite>

</li>

<li id="cite_note-93"><a href="#cite_ref-93">^</a> <cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.sdss4.org/science/">"Science Results"</a>. SSDS. Retrieved 2025-05-20.</cite>

</li>

<li id="cite_note-94"><a href="#cite_ref-94">^</a> <cite id="CITEREFDavis2002" class="citation conference cs1">Davis, Marc; et al. (DEEP2 collaboration) (2002). Science objectives and early results of the DEEP2 redshift survey. Conference on Astronomical Telescopes and Instrumentation, Waikoloa, Hawaii, 22–28 Aug 2002. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/0209419">astro-ph/0209419</a>. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2003SPIE.4834..161D">2003SPIE.4834..161D</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1117%2F12.457897">10.1117/12.457897</a>.</cite>

</li>

<li id="cite_note-95"><a href="#cite_ref-95">^</a> <cite id="CITEREFNewman2013" class="citation journal cs1">Newman, Jeffrey A.; et al. (2013). "The DEEP2 Galaxy Redshift Survey: Design, Observations, Data Reduction, and Redshifts". The Astrophysical Journal Supplement Series. 208 (1): 5. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/1203.3192">1203.3192</a>. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2013ApJS..208....5N">2013ApJS..208....5N</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F0067-0049%2F208%2F1%2F5">10.1088/0067-0049/208/1/5</a>.</cite>

</li>

<li id="cite_note-96"><a href="#cite_ref-96">^</a> <cite id="CITEREFImpey" class="citation web cs1">Impey, Chris. Gay, Pamela (ed.). <a rel="nofollow" class="external text" href="https://www.teachastronomy.com/textbook/The-Milky-Way/Dust-Extinction-and-Reddening/">"Dust Extinction and Reddening"</a>. Teach Astronomy - Dust Extinction and Reddening. Teach Astronomy. Retrieved 2025-03-06.</cite>

</li>

<li id="cite_note-97"><a href="#cite_ref-97">^</a> <cite id="CITEREFKuhnKoupelis2004" class="citation book cs1">Kuhn, Karl F.; Koupelis, Theo (2004). In Quest of the Universe. <a href="Jones_%26_Bartlett_Publishers" class="mw-redirect" title="Jones & Bartlett Publishers">Jones & Bartlett Publishers</a>. pp. 122–3. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-7637-0810-8</bdi>.</cite>

</li>

<li id="cite_note-98"><a href="#cite_ref-98">^</a> <cite id="CITEREFWoodhouse2017" class="citation book cs1">Woodhouse, Chris (2017-12-04). "M31 (Andromeda Galaxy)". The Astrophotography Manual (2nd ed.). Routledge. pp. 308–313. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.4324%2F9781315159225-42">10.4324/9781315159225-42</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-315-15922-5</bdi>.</cite>

</li>

<li id="cite_note-99"><a href="#cite_ref-99">^</a> <cite id="CITEREFMaria_Raiteri2024" class="citation book cs1">Maria Raiteri, Claudia (2024). "Monitoring Blazar Variability to Understand Extragalactic Jets". Publications of the Astronomical Observatory of Belgrade. Vol. 104. pp. 29–38. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/2412.11565">2412.11565</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.69646%2Faob104p029">10.69646/aob104p029</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-86-82296-11-9</bdi>.</cite>

</li>

<li id="cite_note-Aoki2005-100">^ <a href="#cite_ref-Aoki2005_100-0">a</a> <a href="#cite_ref-Aoki2005_100-1">b</a> <a href="#cite_ref-Aoki2005_100-2">c</a> <cite id="CITEREFAokiKawaguchiOhta2005" class="citation journal cs1">Aoki, Kentaro; Kawaguchi, Toshihiro; Ohta, Kouji (January 2005). "The Largest Blueshifts of the [O III] Emission Line in Two Narrow-Line Quasars". Astrophysical Journal. 618 (2): 601–608. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/0409546">astro-ph/0409546</a>. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2005ApJ...618..601A">2005ApJ...618..601A</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F426075">10.1086/426075</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:17680991">17680991</a>.</cite>

</li>

<li id="cite_note-R.N_1-101"><a href="#cite_ref-R.N_1_101-0">^</a> <cite id="CITEREFNemiroff1993" class="citation web cs1">Nemiroff, R. J. (1993). <a rel="nofollow" class="external text" href="https://antwrp.gsfc.nasa.gov/htmltest/gifcity/nslens_math.html">"Gravitational Principles and Mathematics"</a>. <a href="NASA" title="NASA">NASA</a>.</cite>

</li>

<li id="cite_note-R.N_2-102"><a href="#cite_ref-R.N_2_102-0">^</a> <cite id="CITEREFNemiroff1993" class="citation journal cs1">Nemiroff, R. J. (1993). "Visual distortions near a neutron star and black hole". American Journal of Physics. 61 (7): 619–632. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/9312003v1">astro-ph/9312003v1</a>. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1993AmJPh..61..619N">1993AmJPh..61..619N</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.17224">10.1119/1.17224</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:16640860">16640860</a>.</cite>

</li>

<li id="cite_note-Bonometto2002-103"><a href="#cite_ref-Bonometto2002_103-0">^</a> <cite id="CITEREFBonomettoGoriniMoschella2002" class="citation book cs1">Bonometto, Silvio; Gorini, Vittorio; Moschella, Ugo (2002). Modern Cosmology. <a href="CRC_Press" title="CRC Press">CRC Press</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-7503-0810-6</bdi>.</cite>

</li>

<li id="cite_note-104"><a href="#cite_ref-104">^</a> <cite id="CITEREFMiller" class="citation web cs1">Miller, Cole. <a rel="nofollow" class="external text" href="https://www.astro.umd.edu/~miller/teaching/questions/cosmology.html">"Cosmology"</a>. www.astro.umd.edu. Retrieved 2025-03-06.</cite>

</li>

</ol></div>

<div class="mw-heading mw-heading2"><h2 id="Sources">Sources</h2></div>

<div class="mw-heading mw-heading3"><h3 id="Articles">Articles</h3></div>

<ul><li>Odenwald, S. & Fienberg, RT. 1993; "Galaxy Redshifts Reconsidered" in Sky & Telescope Feb. 2003; pp31–35 (This article is useful further reading in distinguishing between the 3 types of redshift and their causes.)</li>

<li>Lineweaver, Charles H. and Tamara M. Davis, "<a rel="nofollow" class="external text" href="https://web.archive.org/web/20070715030354/http://www.sciam.com/article.cfm?chanID=sa006&colID=1&articleID=0009F0CA-C523-1213-852383414B7F0147">Misconceptions about the Big Bang</a>", <a href="Scientific_American" title="Scientific American">Scientific American</a>, March 2005. (This article is useful for explaining the cosmological redshift mechanism as well as clearing up misconceptions regarding the physics of the expansion of space.)</li></ul>

<div class="mw-heading mw-heading3"><h3 id="Books">Books</h3></div>

<ul><li><cite id="CITEREFNussbaumerLydia_Bieri2009" class="citation book cs1">Nussbaumer, Harry; <a href="Lydia_Bieri" title="Lydia Bieri">Lydia Bieri</a> (2009). Discovering the Expanding Universe. Cambridge University Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-521-51484-2</bdi>.</cite></li>

<li><cite id="CITEREFBinneyMichael_Merrifeld1998" class="citation book cs1">Binney, James; Michael Merrifeld (1998). Galactic Astronomy. Princeton University Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-691-02565-0</bdi>.</cite></li>

<li><cite id="CITEREFCarroll,_Bradley_W.Dale_A._Ostlie1996" class="citation book cs1">Carroll, Bradley W. & Dale A. Ostlie (1996). An Introduction to Modern Astrophysics. Addison-Wesley Publishing Company, Inc. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-201-54730-6</bdi>.</cite></li>

<li><cite id="CITEREFFeynman,_RichardLeighton,_RobertSands,_Matthew1989" class="citation book cs1">Feynman, Richard; Leighton, Robert; Sands, Matthew (1989). <a href="The_Feynman_Lectures_on_Physics" title="The Feynman Lectures on Physics">Feynman Lectures on Physics. Vol. 1</a>. Addison-Wesley. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-201-51003-4</bdi>.</cite></li>

<li><cite id="CITEREFGrønHervik,_Sigbjørn2007" class="citation book cs1"><a href="%C3%98yvind_Gr%C3%B8n" title="Øyvind Grøn">Grøn, Øyvind</a>; Hervik, Sigbjørn (2007). Einstein's General Theory of Relativity. New York: Springer. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-387-69199-2</bdi>.</cite></li>

<li><cite id="CITEREFHarrison2000" class="citation book cs1">Harrison, Edward (2000). Cosmology: The Science of the Universe (2nd ed.). Cambridge University Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-521-66148-5</bdi>.</cite></li>

<li><cite id="CITEREFKutner,_Marc2003" class="citation book cs1">Kutner, Marc (2003). <a rel="nofollow" class="external text" href="https://archive.org/details/astronomyphysica00kutn">Astronomy: A Physical Perspective</a>. Cambridge University Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-521-52927-3</bdi>.</cite></li>

<li><cite id="CITEREFMisnerThorne,_Kip_S.Wheeler,_John_Archibald1973" class="citation book cs1">Misner, Charles; Thorne, Kip S.; Wheeler, John Archibald (1973). Gravitation. San Francisco: W. H. Freeman. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-7167-0344-0</bdi>.</cite></li>

<li><cite id="CITEREFPeebles1993" class="citation book cs1">Peebles, P. J. E. (1993). <a rel="nofollow" class="external text" href="https://archive.org/details/principlesofphys00pjep">Principles of Physical Cosmology</a>. Princeton University Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-691-01933-8</bdi>.</cite></li>

<li><cite id="CITEREFTaylorWheeler1992" class="citation book cs1">Taylor, Edwin F.; <a href="John_Archibald_Wheeler" title="John Archibald Wheeler">Wheeler, John Archibald</a> (1992). <a rel="nofollow" class="external text" href="https://archive.org/details/spacetimephysics00edwi_0">Spacetime Physics: Introduction to Special Relativity</a> (2nd ed.). W.H. Freeman. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-7167-2327-1</bdi>.</cite></li>

<li><cite id="CITEREFWeinberg1971" class="citation book cs1">Weinberg, Steven (1971). <a rel="nofollow" class="external text" href="https://archive.org/details/gravitationcosmo00stev_0">Gravitation and Cosmology</a>. John Wiley. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-471-92567-5</bdi>.</cite></li>

<li>See also <a href="Physical_cosmology#Textbooks" title="Physical cosmology">physical cosmology textbooks</a> for applications of the cosmological and gravitational redshifts.</li></ul>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

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<div class="side-box-text plainlist">Wikimedia Commons has media related to <a href="https://commons.wikimedia.org/wiki/Redshift" class="extiw external" title="commons:Redshift">Redshift</a>.</div></div>

</div>

<div class="side-box-text plainlist">Look up <a href="https://en.wiktionary.org/wiki/Special:Search/redshift" class="extiw external" title="wiktionary:Special:Search/redshift">redshift</a> in Wiktionary, the free dictionary.</div></div>

</div>

<ul><li><a rel="nofollow" class="external text" href="http://www.astro.ucla.edu/~wright/doppler.htm">Ned Wright's Cosmology tutorial</a></li>

<li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20051203093117/http://coolcosmos.ipac.caltech.edu/cosmic_classroom/cosmic_reference/redshift.html">Cosmic reference guide entry on redshift</a></li>

<li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20051121214031/http://www.asterism.org/tutorials/tut29-1.htm">Mike Luciuk's Astronomical Redshift tutorial</a></li>

<li><a rel="nofollow" class="external text" href="http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/Images/hu_animexp.gif">Animated GIF of Cosmological Redshift</a> by Wayne Hu</li>

<li><cite id="CITEREFMerrifieldHill2009" class="citation web cs1">Merrifield, Michael; Hill, Richard (2009). <a rel="nofollow" class="external text" href="http://www.sixtysymbols.com/videos/redshift.htm">"Z Redshift"</a>. SIXTψ SYMBΦLS. <a href="Brady_Haran" title="Brady Haran">Brady Haran</a> for the <a href="University_of_Nottingham" title="University of Nottingham">University of Nottingham</a>.</cite></li></ul>

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</style></div><div role="navigation" class="navbox authority-control" aria-labelledby="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q76250#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata1084" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q76250#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata1084" style="font-size:114%;margin:0 4em">Authority control databases </div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4178556-3">Germany</a></li><li><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85112092">United States</a></li><li><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/00575344">Japan</a></li><li><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph311253&CON_LNG=ENG">Czech Republic</a></li><li><a rel="nofollow" class="external text" href="https://www.nli.org.il/en/authorities/987007565862105171">Israel</a></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><a rel="nofollow" class="external text" href="https://lux.collections.yale.edu/view/concept/8d45e768-ca6f-44ca-aef1-cf161ef28e37">Yale LUX</a></li></ul></div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Gravitational-wave_astronomy227" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Gravitational-wave_astronomy227" style="font-size:114%;margin:0 4em"><a href="Gravitational-wave_astronomy" title="Gravitational-wave astronomy">Gravitational-wave astronomy</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div>

<ul><li><a href="Gravitational_wave" title="Gravitational wave">Gravitational wave</a></li>

<li><a href="Gravitational-wave_observatory" title="Gravitational-wave observatory">Gravitational-wave observatory</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Gravitational-wave_observatory" title="Gravitational-wave observatory">Detectors</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Gravitational-wave_observatory#Weber_bars" title="Gravitational-wave observatory">Resonant mass antennas</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Active</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li>NAUTILUS (IGEC)</li>

<li><a href="AURIGA" title="AURIGA">AURIGA</a> (IGEC)</li>

<li><a href="MiniGrail" title="MiniGrail">MiniGRAIL</a></li>

<li><a href="Mario_Schenberg_(Gravitational_Wave_Detector)" title="Mario Schenberg (Gravitational Wave Detector)">Mario Schenberg</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Past</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li>EXPLORER (IGEC)</li>

<li><a href="Allegro_gravitational-wave_detector" title="Allegro gravitational-wave detector">ALLEGRO</a> (IGEC)</li>

<li><a href="NIOBE" title="NIOBE">NIOBE</a> (IGEC)</li>

<li>Stanford gravitational wave detector</li>

<li>ALTAIR</li>

<li>GEOGRAV</li>

<li>AGATA</li>

<li><a href="Weber_bar" title="Weber bar">Weber bar</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Proposed</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Past proposals</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="MiniGrail" title="MiniGrail">GRAIL</a> (downsized to <a href="MiniGrail" title="MiniGrail">MiniGRAIL</a>)</li>

<li>SFERA</li>

<li><a href="Mario_Schenberg_(Gravitational_Wave_Detector)" title="Mario Schenberg (Gravitational Wave Detector)">Graviton</a> (downsized to <a href="Mario_Schenberg_(Gravitational_Wave_Detector)" title="Mario Schenberg (Gravitational Wave Detector)">Mario Schenberg</a>)</li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Ground-based_interferometric_gravitational-wave_search" title="Ground-based interferometric gravitational-wave search"> Ground-based interferometers</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Active</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="AIGO" title="AIGO">AIGO</a> (<a href="ACIGA" title="ACIGA">ACIGA</a>)</li>

<li><a href="Holometer" title="Holometer">Fermilab holometer</a></li>

<li><a href="LIGO" title="LIGO">Advanced LIGO</a> (<a href="LIGO_Scientific_Collaboration" title="LIGO Scientific Collaboration">LIGO Scientific Collaboration</a>)</li>

<li><a href="KAGRA" title="KAGRA">KAGRA</a></li>

<li><a href="Virgo_interferometer" title="Virgo interferometer">Advanced Virgo</a> (<a href="European_Gravitational_Observatory" title="European Gravitational Observatory">European Gravitational Observatory</a>)</li></ul>

<li><a href="TAMA_300" title="TAMA 300">TAMA 20, later known as LISM</a></li>

<li>TENKO-100</li>

<li><a href="LIGO#Background" title="LIGO">Caltech 40m interferometer</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Planned</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Indian_Initiative_in_Gravitational-wave_Observations" title="Indian Initiative in Gravitational-wave Observations">INDIGO (LIGO-India)</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Proposed</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Cosmic_Explorer_(gravitational_wave_observatory)" title="Cosmic Explorer (gravitational wave observatory)">Cosmic Explorer</a></li>

<li><a href="Einstein_Telescope" title="Einstein Telescope">Einstein Telescope</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Past proposals</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="LIGO-Australia" class="mw-redirect" title="LIGO-Australia">LIGO-Australia</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Space-based interferometers</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Planned</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Big_Bang_Observer" title="Big Bang Observer">Big Bang Observer</a></li>

<li><a href="Deci-hertz_Interferometer_Gravitational_wave_Observatory" title="Deci-hertz Interferometer Gravitational wave Observatory">DECIGO</a></li>

<li><a href="TianQin" title="TianQin">TianQin</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Pulsar_timing_array" title="Pulsar timing array">Pulsar timing arrays</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="North_American_Nanohertz_Observatory_for_Gravitational_Waves" title="North American Nanohertz Observatory for Gravitational Waves">NANOGrav</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Data analysis</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Einstein%40Home" title="Einstein@Home">Einstein@Home</a></li>

<li><a href="PyCBC" title="PyCBC">PyCBC</a></li>

<li><a href="Zooniverse" title="Zooniverse">Zooniverse</a>: Gravity Spy</li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Observations</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Events</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="List_of_gravitational_wave_observations" title="List of gravitational wave observations">List of observations</a></li>

<li><a href="First_observation_of_gravitational_waves" title="First observation of gravitational waves">First observation (GW150914)</a></li>

<li><a href="GW170817" title="GW170817">GW170817</a> (first <a href="Neutron_star_merger" title="Neutron star merger">neutron star merger</a>)</li>

<li><a href="GW190521" title="GW190521">GW190521</a> (first-ever possible light from bh-bh merger)</li>

<li><a href="GW190814" title="GW190814">GW190814</a> (first-ever "mass gap" collision)</li>

<li>GW200105 (first black hole - neutron star merger)</li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Methods</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li>Direct detection

<ul><li><a href="Interferometric_gravitational-wave_detector" class="mw-redirect" title="Interferometric gravitational-wave detector">Laser interferometers</a></li>

<li>Resonant mass detectors</li>

<li>Proposed: <a href="Atom_interferometer" title="Atom interferometer">Atom interferometers</a></li></ul></li>

<li>Indirect detection

<ul><li><a href="Cosmic_microwave_background#B-modes" title="Cosmic microwave background">B-modes</a> of <a href="Cosmic_microwave_background" title="Cosmic microwave background">CMB</a></li>

<li><a href="Pulsar_timing_array" title="Pulsar timing array">Pulsar timing array</a></li>

<li><a href="Binary_pulsar" title="Binary pulsar">Binary pulsar</a></li></ul></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theory</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="General_relativity" title="General relativity">General relativity</a></li>

<li><a href="Tests_of_general_relativity" title="Tests of general relativity">Tests of general relativity</a></li>

<li><a href="Alternatives_to_general_relativity" title="Alternatives to general relativity">Metric theories</a></li>

<li><a href="Graviton" title="Graviton">Graviton</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Effects / properties</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Gravitational_wave#Effects_of_passing" title="Gravitational wave">Polarization</a></li>

<li>Travel with <a href="Speed_of_light" title="Speed of light">speed of light</a></li>

<li>h strain</li>

<li>Chirp signal (<a href="Chirp_mass" title="Chirp mass">chirp mass</a>)</li>

<li>Carried <a href="Energy" title="Energy">energy</a></li>

<li><a href="Gravitational_wave_background" title="Gravitational wave background">Gravitational wave background</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Types / sources</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Stochastic" title="Stochastic">Stochastic</a>

<ul><li><a href="Cosmic_inflation" title="Cosmic inflation">Cosmic inflation</a>-<a href="Quantum_fluctuation" title="Quantum fluctuation">quantum fluctuation</a></li>

<li><a href="Phase_transition" title="Phase transition">Phase transition</a></li></ul></li>

<li>Binary inspiral

<ul><li><a href="Supermassive_black_hole" title="Supermassive black hole">Supermassive black holes</a></li>

<li><a href="Stellar_black_hole" title="Stellar black hole">Stellar black holes</a></li>

<li><a href="Neutron_star" title="Neutron star">Neutron stars</a></li>

<li>Continuous

<ul><li>Rotating neutron star</li></ul></li>

<li>Burst

<ul><li><a href="Supernova" title="Supernova">Supernova</a> or from unknown sources</li></ul></li>

<li>Hypothesis

<ul><li>Colliding <a href="Cosmic_string" title="Cosmic string">cosmic string</a> and other unknown sources</li></ul></li></ul>

</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Cosmology278" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2" style="text-align:center;"><div id="Cosmology278" style="font-size:114%;margin:0 4em"><a href="Cosmology" title="Cosmology">Cosmology</a></div></th></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Background</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Age_of_the_universe" title="Age of the universe">Age of the universe</a></li>

<li><a href="Chronology_of_the_universe" title="Chronology of the universe">Chronology of the universe</a></li>

<li><a href="Timeline_of_the_universe" class="mw-redirect" title="Timeline of the universe">Timeline of the universe</a></li>

<li><a href="Universe" title="Universe">Universe</a></li>

<li><a href="Observable_universe" title="Observable universe">Observable universe</a></li>

<li><a href="Cosmic_distance_ladder" title="Cosmic distance ladder">Cosmic distance ladder</a></li>

<li><a href="Cosmogony" title="Cosmogony">Cosmogony</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">History of cosmological theories</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Cosmological_principle" title="Cosmological principle">Cosmological principle</a></li>

<li><a href="Copernican_principle" title="Copernican principle">Copernican principle</a></li>

<li><a href="Discovery_of_cosmic_microwave_background_radiation" title="Discovery of cosmic microwave background radiation">Discovery of cosmic microwave background</a></li>

<li><a href="History_of_the_Big_Bang_theory" title="History of the Big Bang theory">History of the Big Bang theory</a></li>

<li><a href="Religious_interpretations_of_the_Big_Bang_theory" title="Religious interpretations of the Big Bang theory">Religious interpretations of the Big Bang</a></li>

<li><a href="Timeline_of_cosmological_theories" title="Timeline of cosmological theories">Timeline of cosmological theories</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Past universe</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Cosmic_background_radiation" title="Cosmic background radiation">Cosmic background radiation</a></li>

<li><a href="Cosmic_microwave_background" title="Cosmic microwave background">Cosmic microwave background</a></li>

<li><a href="Cosmic_neutrino_background" title="Cosmic neutrino background">Cosmic neutrino background</a></li>

<li><a href="Gravitational_wave_background" title="Gravitational wave background">Gravitational wave background</a></li>

<li><a href="Inflation_(cosmology)" class="mw-redirect" title="Inflation (cosmology)">Inflation</a></li>

<li><a href="Big_Bang_nucleosynthesis" title="Big Bang nucleosynthesis">Nucleosynthesis</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Present universe</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric" title="Friedmann–Lemaître–Robertson–Walker metric">FLRW metric</a></li>

<li><a href="Friedmann_equations" title="Friedmann equations">Friedmann equations</a></li>

<li><a href="Hubble's_law" title="Hubble's law">Hubble's law</a></li>

<li><a href="Expansion_of_the_universe" title="Expansion of the universe">Expansion of the universe</a></li>

<li><a href="Accelerating_expansion_of_the_universe" title="Accelerating expansion of the universe">Accelerating expansion</a></li>

</ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Future universe</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Future_of_an_expanding_universe" title="Future of an expanding universe">Future of an expanding universe</a></li>

<li><a href="Ultimate_fate_of_the_universe" title="Ultimate fate of the universe">Ultimate fate of the universe</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Components</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Dark_energy" title="Dark energy">Dark energy</a></li>

<li><a href="Dark_fluid" title="Dark fluid">Dark fluid</a></li>

<li><a href="Dark_matter" title="Dark matter">Dark matter</a></li>

<li><a href="Quintessence_(physics)" title="Quintessence (physics)">Quintessence</a></li>

<li><a href="Lambda-CDM_model" title="Lambda-CDM model">Lambda-CDM model</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Structure formation</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Galaxy_filament" title="Galaxy filament">Galaxy filament</a></li>

<li><a href="Galaxy_formation_and_evolution" title="Galaxy formation and evolution">Galaxy formation</a></li>

<li><a href="Large_quasar_group" title="Large quasar group">Large quasar group</a></li>

<li><a href="Large-scale_structure_of_the_cosmos" class="mw-redirect" title="Large-scale structure of the cosmos">Large-scale structure</a></li>

<li><a href="Reionization" title="Reionization">Reionization</a></li>

<li><a href="Shape_of_the_universe" title="Shape of the universe">Shape of the universe</a></li>

<li><a href="Structure_formation" title="Structure formation">Structure formation</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Experiments</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="BOOMERanG_experiment" title="BOOMERanG experiment">BOOMERanG</a></li>

<li><a href="Illustris_project" title="Illustris project">Illustris project</a></li>

<li><a href="Observational_cosmology" title="Observational cosmology">Observational cosmology</a></li>

<li><a href="Planck_(spacecraft)" title="Planck (spacecraft)">Planck</a></li>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="2" style="text-align:center;"><div> <a href="Portal%3AAstronomy" title="Portal:Astronomy">astronomy portal</a></div></td></tr></tbody></table></div></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2025-08-01" href="https://en.wikipedia.org/wiki/?title=Redshift&oldid=1303614183">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

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