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<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Zenithal Hourly Rate</span></h1>
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<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="de" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="de" dir="ltr"><p>Die <b>Zenithal Hourly Rate</b> (<b>ZHR</b>, <a href="Deutsche_Sprache" title="Deutsche Sprache">deutsch</a> etwa <i>zenitale stündliche Rate</i>) eines <a href="Meteorstrom" title="Meteorstrom">Meteorstroms</a> ist die Anzahl der <a href="Meteor" title="Meteor">Meteore</a>, die ein <i>einzelner</i> <a href="Beobachtung" title="Beobachtung">Beobachter</a> innerhalb einer Stunde unter einem Himmel mit der visuellen <a href="Grenzhelligkeit" class="mw-redirect" title="Grenzhelligkeit">Grenzhelligkeit</a> 6,5<a href="Scheinbare_Helligkeit" title="Scheinbare Helligkeit"><sup>m</sup></a> sieht, wenn der <a href="Radiant_(Astronomie)" title="Radiant (Astronomie)">Radiant</a> des Stroms genau im <a href="Zenit_(Richtungsangabe)" class="mw-redirect" title="Zenit (Richtungsangabe)">Zenit</a> steht und sich kein Hindernis im Blickfeld befindet.
</p><p>Da diese Idealsituation nicht exakt vorkommen kann, ist die wahre, beobachtete Rate <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {N}{t}}}">
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<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
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<mi>N</mi>
<mi>t</mi>
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<annotation encoding="application/x-tex">{\displaystyle {\tfrac {N}{t}}}</annotation>
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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b757a4c7767ee6c900379fa226be2ffa7d6b2553.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:2.295ex; height:3.509ex;" alt="{\displaystyle {\tfrac {N}{t}}}" loading="lazy"></span> immer niedriger als die theoretische <i>Zenithal Hourly Rate</i>:
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ZHR>{\frac {N}{t}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>Z</mi>
<mi>H</mi>
<mi>R</mi>
<mo>></mo>
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<mfrac>
<mi>N</mi>
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<annotation encoding="application/x-tex">{\displaystyle ZHR>{\frac {N}{t}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/bcbfc5cf690589a829c41018a521a956cbba0669.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:11.506ex; height:5.176ex;" alt="{\displaystyle ZHR>{\frac {N}{t}}}" loading="lazy"></span></dd></dl>
<p>mit
</p>
<ul><li><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>N</mi>
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<annotation encoding="application/x-tex">{\displaystyle N}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f5e3890c981ae85503089652feb48b191b57aae3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}" loading="lazy"></span>: Anzahl der beobachteten Meteore</li>
<li><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>t</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle t}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/65658b7b223af9e1acc877d848888ecdb4466560.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}" loading="lazy"></span>: Beobachtungszeit in Stunden.</li></ul>
<p>Mittels der folgenden Formel lässt sich die beobachtete Rate näherungsweise in die <i>Zenithal Hourly Rate</i> umrechnen:
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ZHR\approx {\frac {N}{t}}\cdot {\frac {r^{6,5-m_{gr}}}{\sin h}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>Z</mi>
<mi>H</mi>
<mi>R</mi>
<mo>≈<!-- ≈ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>N</mi>
<mi>t</mi>
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<mo>⋅<!-- ⋅ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<msup>
<mi>r</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>6</mn>
<mo>,</mo>
<mn>5</mn>
<mo>−<!-- − --></mo>
<msub>
<mi>m</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>g</mi>
<mi>r</mi>
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<mi>sin</mi>
<mo><!-- --></mo>
<mi>h</mi>
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<annotation encoding="application/x-tex">{\displaystyle ZHR\approx {\frac {N}{t}}\cdot {\frac {r^{6,5-m_{gr}}}{\sin h}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/eeb62c5d7a2210aa2e59cbc4168514869417c833.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:21.532ex; height:5.843ex;" alt="{\displaystyle ZHR\approx {\frac {N}{t}}\cdot {\frac {r^{6,5-m_{gr}}}{\sin h}}}" loading="lazy"></span></dd></dl>
<p>mit
</p>
<ul><li><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>r</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle r}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/0d1ecb613aa2984f0576f70f86650b7c2a132538.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}" loading="lazy"></span> (>1): <a href="Populationsindex" title="Populationsindex">Populationsindex</a>, d. h. Helligkeitsverteilung des beobachteten Meteorstroms</li>
<li><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{gr}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>m</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>g</mi>
<mi>r</mi>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle m_{gr}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/eb26e02902e09b46c616f7434ad0b0b219781de9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.803ex; height:2.343ex;" alt="{\displaystyle m_{gr}}" loading="lazy"></span>: <a href="Grenzhelligkeit" class="mw-redirect" title="Grenzhelligkeit">Grenzhelligkeit</a> der schwächsten, mit bloßem Auge beobachtbaren <a href="Stern" title="Stern">Sterne</a> bei der aktuellen Beobachtung</li>
<li><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>h</mi>
</mstyle>
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<annotation encoding="application/x-tex">{\displaystyle h}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b26be3e694314bc90c3215047e4a2010c6ee184a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.339ex; height:2.176ex;" alt="{\displaystyle h}" loading="lazy"></span>: <a href="H%C3%B6henwinkel" class="mw-redirect" title="Höhenwinkel">Höhenwinkel</a> des Radianten des beobachteten Meteorstroms über dem <a href="Horizont" title="Horizont">Horizont</a>, gemessen zur Mitte des Beobachtungszeitraums.</li></ul>
<p>Da die aktuelle Grenzgröße <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{gr}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>m</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>g</mi>
<mi>r</mi>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle m_{gr}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/eb26e02902e09b46c616f7434ad0b0b219781de9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.803ex; height:2.343ex;" alt="{\displaystyle m_{gr}}" loading="lazy"></span> oft unterhalb der sehr optimistischen 6,5 <a href="Scheinbare_Helligkeit" title="Scheinbare Helligkeit">Magnituden</a> liegen wird, die für die ZHR selbst gelten, ergibt sich in o. g. Formel ein <a href="Potenz_(Mathematik)" title="Potenz (Mathematik)">Exponent</a> > 0 für den Populationsindex <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>r</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle r}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/0d1ecb613aa2984f0576f70f86650b7c2a132538.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}" loading="lazy"></span>.
</p>
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