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</style><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><td class="sidebar-pretitle">Part of a series on</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="Astrodynamics" class="mw-redirect" title="Astrodynamics">Astrodynamics</a></th></tr><tr><td class="sidebar-image" style="padding-bottom:0.85em;"><span typeof="mw:File"></span></td></tr><tr><th class="sidebar-heading" style="padding-bottom:0.55em;">
<div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="Orbital_mechanics" title="Orbital mechanics"><span style="font-size:110%;">Orbital mechanics</span></a></div></th></tr><tr><td class="sidebar-content hlist">
<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="Orbital_elements" title="Orbital elements">Orbital elements</a></div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0;">
<ul><li><a href="Apsis" title="Apsis">Apsis</a></li>
<li><a href="Argument_of_periapsis" title="Argument of periapsis">Argument of periapsis</a></li>
<li><a href="Orbital_eccentricity" title="Orbital eccentricity">Eccentricity</a></li>
<li><a href="Orbital_inclination" title="Orbital inclination">Inclination</a></li>
<li><a href="Mean_anomaly" title="Mean anomaly">Mean anomaly</a></li>
<li><a href="Semi-major_and_semi-minor_axes" title="Semi-major and semi-minor axes">Semi-major axis</a></li>
<li><a href="True_anomaly" title="True anomaly">True anomaly</a></li></ul></div></div></td>
</tr><tr><td class="sidebar-content hlist">
<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Types of <a href="Two-body_problem" title="Two-body problem">two-body orbits</a> by <br>eccentricity</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0;">
<ul><li><a href="Circular_orbit" title="Circular orbit">Circular orbit</a></li>
<li><a href="Elliptic_orbit" title="Elliptic orbit">Elliptic orbit</a></li></ul>
<div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="Transfer_orbit" title="Transfer orbit">Transfer orbit</a> <div class="hlist" style="font-size:90%"><ul><li>(<a href="Hohmann_transfer_orbit" title="Hohmann transfer orbit">Hohmann transfer orbit</a></li><li><a href="Bi-elliptic_transfer" title="Bi-elliptic transfer">Bi-elliptic transfer orbit</a>)</li></ul></div></div>
<ul><li><a href="Parabolic_trajectory" title="Parabolic trajectory">Parabolic orbit</a></li>
<li><a href="Hyperbolic_trajectory" title="Hyperbolic trajectory">Hyperbolic orbit</a></li>
<li><a href="Radial_trajectory" title="Radial trajectory">Radial orbit</a></li>
<li><a href="Orbital_decay" title="Orbital decay">Decaying orbit</a></li></ul></div></div></td>
</tr><tr><td class="sidebar-content hlist">
<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Equations</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0;">
<ul><li><a href="Dynamical_friction" title="Dynamical friction">Dynamical friction</a></li>
<li><a href="Escape_velocity" title="Escape velocity">Escape velocity</a></li>
<li><a href="Kepler's_equation" title="Kepler's equation">Kepler's equation</a></li>
<li><a href="Kepler's_laws_of_planetary_motion" title="Kepler's laws of planetary motion">Kepler's laws of planetary motion</a></li>
<li><a href="Orbital_period" title="Orbital period">Orbital period</a></li>
<li><a href="Orbital_speed" title="Orbital speed">Orbital velocity</a></li>
<li><a href="Surface_gravity" title="Surface gravity">Surface gravity</a></li>
<li><a href="Specific_orbital_energy" title="Specific orbital energy">Specific orbital energy</a></li>
<li><a href="Vis-viva_equation" title="Vis-viva equation">Vis-viva equation</a></li></ul></div></div></td>
</tr><tr><th class="sidebar-heading" style="padding-bottom:0.55em;">
<div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="Celestial_mechanics" title="Celestial mechanics"><span style="font-size:110%;">Celestial mechanics</span></a></div></th></tr><tr><td class="sidebar-content hlist">
<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Gravitational influences</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0;">
<ul><li><a href="Barycenter" class="mw-redirect" title="Barycenter">Barycenter</a></li>
<li><a href="Hill_sphere" title="Hill sphere">Hill sphere</a></li>
<li><a href="Perturbation_(astronomy)" title="Perturbation (astronomy)">Perturbations</a></li>
<li><a href="Sphere_of_influence_(astrodynamics)" title="Sphere of influence (astrodynamics)">Sphere of influence</a></li></ul></div></div></td>
</tr><tr><td class="sidebar-content hlist">
<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="N-body_problem" title="N-body problem">N-body orbits</a></div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0;"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="Lagrange_point" title="Lagrange point">Lagrangian points</a> <div class="hlist" style="font-size:90%"><ul><li>(<a href="Halo_orbit" title="Halo orbit">Halo orbits</a>)</li></ul></div></div>
<ul><li><a href="Lissajous_orbit" title="Lissajous orbit">Lissajous orbits</a></li>
<li><a href="Lyapunov_stability" title="Lyapunov stability">Lyapunov orbits</a></li></ul></div></div></td>
</tr><tr><th class="sidebar-heading" style="padding-bottom:0.55em;">
<div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="Aerospace_engineering" title="Aerospace engineering"><span style="font-size:110%;">Engineering and efficiency</span></a></div></th></tr><tr><td class="sidebar-content hlist">
<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Preflight engineering</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0;">
<ul><li><a href="Mass_ratio" title="Mass ratio">Mass ratio</a></li>
<li><a href="Payload_fraction" title="Payload fraction">Payload fraction</a></li>
<li><a href="Propellant_mass_fraction" title="Propellant mass fraction">Propellant mass fraction</a></li>
<li><a href="Tsiolkovsky_rocket_equation" title="Tsiolkovsky rocket equation">Tsiolkovsky rocket equation</a></li></ul></div></div></td>
</tr><tr><td class="sidebar-content hlist">
<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Efficiency measures</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0;">
<ul><li><a href="Gravity_assist" title="Gravity assist">Gravity assist</a></li>
<li><a href="Oberth_effect" title="Oberth effect">Oberth effect</a></li></ul></div></div></td>
</tr><tr><td class="sidebar-content hlist">
<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Propulsive maneuvers</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0;">
<ul><li><a href="Orbital_maneuver" title="Orbital maneuver">Orbital maneuver</a></li>
<li><a href="Orbit_insertion" title="Orbit insertion">Orbit insertion</a></li></ul></div></div></td>
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<p>An <b>orbital node</b> is either of the two points where an <a href="Orbit" title="Orbit">orbit</a> <a href="Intersection_(Euclidean_geometry)" class="mw-redirect" title="Intersection (Euclidean geometry)">intersects</a> a <a href="Plane_of_reference" class="mw-redirect" title="Plane of reference">plane of reference</a> to which it is inclined.<sup id="cite_ref-col_1-0" class="reference"><a href="#cite_note-col-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> A <a href="Non-inclined_orbit" class="mw-redirect" title="Non-inclined orbit">non-inclined orbit</a>, which is <a href="Coplanarity" title="Coplanarity">contained</a> in the reference plane, has no nodes.
</p>
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<div class="mw-heading mw-heading2"><h2 id="Planes_of_reference">Planes of reference</h2></div>
<p>Common <a href="Plane_of_reference" class="mw-redirect" title="Plane of reference">planes of reference</a> include the following:
</p>
<ul><li>For a <a href="Geocentric_orbit" title="Geocentric orbit">geocentric orbit</a>, <a href="Earth" title="Earth">Earth</a>'s <a href="Equatorial_plane" class="mw-redirect" title="Equatorial plane">equatorial plane</a>. In this case, non-inclined orbits are called <i>equatorial</i>.<sup id="cite_ref-darlinglon_2-0" class="reference"><a href="#cite_note-darlinglon-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></li>
<li>For a <a href="Heliocentric_orbit" title="Heliocentric orbit">heliocentric orbit</a>, the <a href="Ecliptic" title="Ecliptic">ecliptic</a> or <a href="Invariable_plane" title="Invariable plane">invariable plane</a>. In this case, non-inclined orbits are called <i>ecliptic</i>.<sup id="cite_ref-darlinglon_2-1" class="reference"><a href="#cite_note-darlinglon-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></li>
<li>For an orbit outside the <a href="Solar_System" title="Solar System">Solar System</a>, the plane through the <a href="Primary_(astronomy)" class="mw-redirect" title="Primary (astronomy)">primary</a> perpendicular to a line through the observer and the primary (called the <i><a href="Plane_of_the_sky" class="mw-redirect" title="Plane of the sky">plane of the sky</a></i>).<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></li></ul>
<div class="mw-heading mw-heading2"><h2 id="Node_distinction">Node distinction</h2></div>
<p>If a reference direction from one side of the plane of reference to the other is defined, the two nodes can be distinguished. For geocentric and heliocentric orbits, the <b>ascending node</b> (or <b>north node</b>) is where the orbiting object moves north through the plane of reference, and the <b>descending node</b> (or <b>south node</b>) is where it moves south through the plane.<sup id="cite_ref-darlingasc_4-0" class="reference"><a href="#cite_note-darlingasc-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> In the case of objects outside the Solar System, the ascending node is the node where the orbiting secondary passes away from the observer, and the descending node is the node where it moves towards the observer.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup>, p. 137.</sup>
</p><p>The position of the node may be used as one of a set of parameters, called <i><a href="Orbital_elements" title="Orbital elements">orbital elements</a></i>, which describe the orbit. This is done by specifying the <a href="Longitude_of_the_ascending_node" title="Longitude of the ascending node">longitude of the ascending node</a> (or, sometimes, the <a href="Longitude_of_the_node" class="mw-redirect" title="Longitude of the node">longitude of the node</a>).
</p><p>The <b>line of nodes</b> is the straight line resulting from the intersection of the object's orbital plane with the plane of reference; it passes through the two nodes.<sup id="cite_ref-darlinglon_2-2" class="reference"><a href="#cite_note-darlinglon-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading2"><h2 id="Symbols_and_nomenclature">Symbols and nomenclature</h2></div>
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<div class="side-box-text plainlist">Look up <i><b><a href="https://en.wiktionary.org/wiki/anabibazon" class="extiw external" title="wiktionary:anabibazon">anabibazon</a></b></i> in Wiktionary, the free dictionary.</div></div>
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<div class="side-box-text plainlist">Look up <i><b><a href="https://en.wiktionary.org/wiki/catabibazon" class="extiw external" title="wiktionary:catabibazon">catabibazon</a></b></i> in Wiktionary, the free dictionary.</div></div>
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<p>The symbol of the ascending node is <span typeof="mw:File"></span> (<a href="Unicode" title="Unicode">Unicode</a>: U+260A, ☊), and the symbol of the descending node is <span typeof="mw:File"></span> (<a href="Unicode" title="Unicode">Unicode</a>: U+260B, ☋).
</p><p>In medieval and early modern times, the ascending and descending nodes of the Moon in the ecliptic plane were called the "dragon's head" (<a href="Latin_language" class="mw-redirect" title="Latin language">Latin</a>: <i lang="la">caput draconis</i>, <a href="Arabic_language" class="mw-redirect" title="Arabic language">Arabic</a>: <span lang="ar" dir="rtl"><a href="Gochihr_(Zoroastrianism)" title="Gochihr (Zoroastrianism)">رأس الجوزهر</a></span>) and "dragon's tail" (<a href="Latin_language" class="mw-redirect" title="Latin language">Latin</a>: <i lang="la">cauda draconis</i>), respectively.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: p.141,">: p.141, </span></sup><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: p.245">: p.245 </span></sup> These terms originally referred to the times when the <a href="Moon" title="Moon">Moon</a> crossed the apparent path of the sun in the sky (as in a <a href="Solar_eclipse" title="Solar eclipse">solar eclipse</a>). Also, corruptions of the Arabic term such as <i>ganzaar</i>, <i>genzahar</i>, <i>geuzaar</i> and <i>zeuzahar</i> were used in the medieval West to denote either of the nodes.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: pp.196–197,">: pp.196–197, </span></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: p.65,">: p.65, </span></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: pp.95–96">: pp.95–96 </span></sup>
</p><p>The <a href="Koine_Greek" title="Koine Greek">Koine Greek</a> terms <span title="Ancient Greek (to 1453)-language text"><span lang="grc">αναβιβάζων</span></span> and <span title="Ancient Greek (to 1453)-language text"><span lang="grc">καταβιβάζων</span></span> were also used for the ascending and descending nodes, giving rise to the English terms <i>anabibazon</i> and <i>catabibazon</i>.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: ¶27">: ¶27 </span></sup>
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<div class="mw-heading mw-heading2"><h2 id="Lunar_nodes">Lunar nodes</h2></div>
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</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Lunar_node" title="Lunar node">Lunar node</a></div>
<p>For the <a href="Orbit_of_the_Moon" title="Orbit of the Moon">orbit of the Moon</a> around <a href="Earth" title="Earth">Earth</a>, the <a href="Plane_of_reference" class="mw-redirect" title="Plane of reference">plane</a> is taken to be the <a href="Ecliptic" title="Ecliptic">ecliptic</a>, not the <a href="Celestial_equator" title="Celestial equator">equatorial plane</a>. The <a href="Gravity" title="Gravity">gravitational</a> pull of the <a href="Sun" title="Sun">Sun</a> upon the Moon causes <a href="Lunar_node" title="Lunar node">its nodes</a> to gradually <a href="Lunar_precession" title="Lunar precession">precess</a> westward, completing a cycle in approximately 18.6 years.<sup id="cite_ref-col_1-1" class="reference"><a href="#cite_note-col-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="Use_in_astrology">Use in astrology</h3></div>
<p>The image of the ascending and descending orbital nodes as the head and tail of a dragon, 180 degrees apart in the sky, goes back to the Chaldeans; it was used by the Zoroastrians, and then by Arabic astronomers and astrologers. In Middle Persian, its head and tail were respectively called <span title="Middle Persian-language text"><i lang="pal">gōzihr sar</i></span> and <span title="Middle Persian-language text"><i lang="pal">gōzihr dumb</i></span>; in Arabic, <span title="Arabic-language text"><i lang="ar">al-ra's al-jawzihr</i></span> and <span title="Arabic-language text"><i lang="ar">al-dhanab al-jawzihr</i></span> — or in the case of the Moon, ___ <span title="Arabic-language text"><i lang="ar">al-tennin</i></span>.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Among the arguments against astrologers made by <a href="Ibn_Qayyim_al-Jawziyya" title="Ibn Qayyim al-Jawziyya">Ibn Qayyim al-Jawziyya</a> (1292–1350), in his <i>Miftah Dar al-SaCadah:</i> "Why is it that you have given an influence to <span title="Arabic-language text"><i lang="ar">al-Ra's</i></span> [the head] and <span title="Arabic-language text"><i lang="ar">al-Dhanab</i></span> [the tail], which are two imaginary points [ascending and descending nodes]?"<sup id="cite_ref-Livingston_15-0" class="reference"><a href="#cite_note-Livingston-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div>
<ul><li><a href="Eclipse" title="Eclipse">Eclipse</a></li>
<li><a href="Euler_angles" title="Euler angles">Euler angles</a></li>
<li><a href="Longitude_of_the_ascending_node" title="Longitude of the ascending node">Longitude of the ascending node</a></li></ul>
<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>
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