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	<title>Gauss&#039; Planetary Equations in a Non-Singular Potential - Revision history</title>
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	<updated>2026-07-22T20:46:24Z</updated>
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		<id>https://wiki.naturalphilosophy.org/index.php?title=Gauss%27_Planetary_Equations_in_a_Non-Singular_Potential&amp;diff=310201&amp;oldid=prev</id>
		<title>ClaudeBot: infobox: unlink bare volume/issue numbers (removes redlinks to numeric titles)</title>
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		<updated>2026-07-21T13:37:40Z</updated>

		<summary type="html">&lt;p&gt;infobox: unlink bare volume/issue numbers (removes redlinks to numeric titles)&lt;/p&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 09:37, 21 July 2026&lt;/td&gt;
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		<id>https://wiki.naturalphilosophy.org/index.php?title=Gauss%27_Planetary_Equations_in_a_Non-Singular_Potential&amp;diff=299840&amp;oldid=prev</id>
		<title>ClaudeBot: Remove stray backslash-escaped quotes (\&#039; and \&quot;) left by an old import escaping bug</title>
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		<updated>2026-07-20T03:41:23Z</updated>

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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 23:41, 19 July 2026&lt;/td&gt;
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	<entry>
		<id>https://wiki.naturalphilosophy.org/index.php?title=Gauss%27_Planetary_Equations_in_a_Non-Singular_Potential&amp;diff=23776&amp;oldid=prev</id>
		<title>Maintenance script: Imported from text file</title>
		<link rel="alternate" type="text/html" href="https://wiki.naturalphilosophy.org/index.php?title=Gauss%27_Planetary_Equations_in_a_Non-Singular_Potential&amp;diff=23776&amp;oldid=prev"/>
		<updated>2017-01-02T02:34:20Z</updated>

		<summary type="html">&lt;p&gt;Imported from text file&lt;/p&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 22:34, 1 January 2017&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l19&quot;&gt;Line 19:&lt;/td&gt;
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&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Scientific Paper|gauss &amp;#039; planetary equations non-singular potential]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Scientific Paper|gauss &amp;#039; planetary equations non-singular potential]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
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	<entry>
		<id>https://wiki.naturalphilosophy.org/index.php?title=Gauss%27_Planetary_Equations_in_a_Non-Singular_Potential&amp;diff=18373&amp;oldid=prev</id>
		<title>Maintenance script: Imported from text file</title>
		<link rel="alternate" type="text/html" href="https://wiki.naturalphilosophy.org/index.php?title=Gauss%27_Planetary_Equations_in_a_Non-Singular_Potential&amp;diff=18373&amp;oldid=prev"/>
		<updated>2017-01-01T17:27:49Z</updated>

		<summary type="html">&lt;p&gt;Imported from text file&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 13:27, 1 January 2017&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l15&quot;&gt;Line 15:&lt;/td&gt;
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&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Abstract==&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Abstract==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;We study the effects of a non-singular gravitational potential on satellite orbits calculating the corresponding changes of its orbital elements, using Gauss&#039; planetary equations. We derive two non-zero expressions for the changes of the argument of the perigee and the mean anomaly, and we compare them to those derived by the general theory relativity. Using the GRACE satellite system, we obtain numerical results from which we conclude that the effect of such a potential, on the perigee cannot be separated from that of general relativity. Furthermore we conclude that the effect on the mean anomaly can probably be observed by today&#039;s technology.[[Category:Scientific Paper]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;We study the effects of a non-singular gravitational potential on satellite orbits calculating the corresponding changes of its orbital elements, using Gauss&#039; planetary equations. We derive two non-zero expressions for the changes of the argument of the perigee and the mean anomaly, and we compare them to those derived by the general theory relativity. Using the GRACE satellite system, we obtain numerical results from which we conclude that the effect of such a potential, on the perigee cannot be separated from that of general relativity. Furthermore we conclude that the effect on the mean anomaly can probably be observed by today&#039;s technology.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Scientific Paper&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;|gauss &#039; planetary equations non-singular potential&lt;/ins&gt;]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Relativity]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Relativity]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Maintenance script</name></author>
	</entry>
	<entry>
		<id>https://wiki.naturalphilosophy.org/index.php?title=Gauss%27_Planetary_Equations_in_a_Non-Singular_Potential&amp;diff=11126&amp;oldid=prev</id>
		<title>Maintenance script: Imported from text file</title>
		<link rel="alternate" type="text/html" href="https://wiki.naturalphilosophy.org/index.php?title=Gauss%27_Planetary_Equations_in_a_Non-Singular_Potential&amp;diff=11126&amp;oldid=prev"/>
		<updated>2016-12-30T18:20:30Z</updated>

		<summary type="html">&lt;p&gt;Imported from text file&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;{{Infobox paper&lt;br /&gt;
| title = Gauss\&amp;#039; Planetary Equations in a Non-Singular Potential&lt;br /&gt;
| url = [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_5408.pdf Link to paper]&lt;br /&gt;
| author = [[Ioannis Iraklis Haranas]], [[Omiros Ragos]]&lt;br /&gt;
| keywords = [[Gauss&amp;#039; planetary equations]], [[non-singular potential]], [[Grace]]&lt;br /&gt;
| published = 2010&lt;br /&gt;
| journal = [[Proceedings of the NPA]]&lt;br /&gt;
| volume = [[7]]&lt;br /&gt;
| num_pages = 3&lt;br /&gt;
| pages = 199-201&lt;br /&gt;
}}&lt;br /&gt;
&lt;br /&gt;
&amp;#039;&amp;#039;&amp;#039;Read the full paper&amp;#039;&amp;#039;&amp;#039; [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_5408.pdf here]&lt;br /&gt;
&lt;br /&gt;
==Abstract==&lt;br /&gt;
&lt;br /&gt;
We study the effects of a non-singular gravitational potential on satellite orbits calculating the corresponding changes of its orbital elements, using Gauss&amp;#039; planetary equations. We derive two non-zero expressions for the changes of the argument of the perigee and the mean anomaly, and we compare them to those derived by the general theory relativity. Using the GRACE satellite system, we obtain numerical results from which we conclude that the effect of such a potential, on the perigee cannot be separated from that of general relativity. Furthermore we conclude that the effect on the mean anomaly can probably be observed by today&amp;#039;s technology.[[Category:Scientific Paper]]&lt;br /&gt;
&lt;br /&gt;
[[Category:Relativity]]&lt;/div&gt;</summary>
		<author><name>Maintenance script</name></author>
	</entry>
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