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	<id>https://selfgravitatingfluids.education/JETohline/index.php?action=history&amp;feed=atom&amp;title=SSC%2FStructure%2FBiPolytropes</id>
	<title>SSC/Structure/BiPolytropes - Revision history</title>
	<link rel="self" type="application/atom+xml" href="https://selfgravitatingfluids.education/JETohline/index.php?action=history&amp;feed=atom&amp;title=SSC%2FStructure%2FBiPolytropes"/>
	<link rel="alternate" type="text/html" href="https://selfgravitatingfluids.education/JETohline/index.php?title=SSC/Structure/BiPolytropes&amp;action=history"/>
	<updated>2026-04-23T05:55:11Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://selfgravitatingfluids.education/JETohline/index.php?title=SSC/Structure/BiPolytropes&amp;diff=2888&amp;oldid=prev</id>
		<title>Xxsrm: /* Solution Steps */</title>
		<link rel="alternate" type="text/html" href="https://selfgravitatingfluids.education/JETohline/index.php?title=SSC/Structure/BiPolytropes&amp;diff=2888&amp;oldid=prev"/>
		<updated>2025-01-24T00:14:00Z</updated>

		<summary type="html">&lt;p&gt;&lt;span class=&quot;autocomment&quot;&gt;Solution Steps&lt;/span&gt;&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 20:14, 23 January 2025&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-l722&quot;&gt;Line 722:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 722:&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;&amp;lt;/math&amp;gt;&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;&amp;lt;/math&amp;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;div&gt;&amp;lt;/div&amp;gt;&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;&amp;lt;/div&amp;gt;&lt;/div&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;These are two relations that Chandrasekhar found to be useful in his analysis of &quot;composite [polytropic] configurations&quot; &amp;amp;#8212; after setting &amp;lt;math&amp;gt;\mu_e=\mu_c&amp;lt;/math&amp;gt; they match, respectively, equations 486 &amp;amp;amp; 489 in &amp;amp;sect; 28 of [[&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;User:Tohline/&lt;/del&gt;Appendix/References#C67|[&amp;lt;b&amp;gt;&amp;lt;font color=&quot;red&quot;&amp;gt;C67&amp;lt;/font&amp;gt;&amp;lt;/b&amp;gt;]]].&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;These are two relations that Chandrasekhar found to be useful in his analysis of &quot;composite [polytropic] configurations&quot; &amp;amp;#8212; after setting &amp;lt;math&amp;gt;\mu_e=\mu_c&amp;lt;/math&amp;gt; they match, respectively, equations 486 &amp;amp;amp; 489 in &amp;amp;sect; 28 of [[Appendix/References#C67|[&amp;lt;b&amp;gt;&amp;lt;font color=&quot;red&quot;&amp;gt;C67&amp;lt;/font&amp;gt;&amp;lt;/b&amp;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;==Isothermal Core==&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;==Isothermal Core==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Xxsrm</name></author>
	</entry>
	<entry>
		<id>https://selfgravitatingfluids.education/JETohline/index.php?title=SSC/Structure/BiPolytropes&amp;diff=125&amp;oldid=prev</id>
		<title>Joel2: Created page with &quot;__FORCETOC__ =BiPolytropes= {| class=&quot;PGEclass&quot; style=&quot;float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black&quot; |-  ! style=&quot;height: 125px; width: 125px; background-color:#ffff99;&quot; | &lt;font size=&quot;-1&quot;&gt;&lt;b&gt;Composite&lt;br /&gt;Polytropes&lt;/b&gt;&lt;br /&gt;(Bipolytropes)&lt;/font&gt; |}  ==Background== While polytropic spheres can give us useful &#039;&#039;general&#039;&#039; insight into the internal s...&quot;</title>
		<link rel="alternate" type="text/html" href="https://selfgravitatingfluids.education/JETohline/index.php?title=SSC/Structure/BiPolytropes&amp;diff=125&amp;oldid=prev"/>
		<updated>2023-12-12T23:58:24Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;quot;__FORCETOC__ =BiPolytropes= {| class=&amp;quot;PGEclass&amp;quot; style=&amp;quot;float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black&amp;quot; |-  ! style=&amp;quot;height: 125px; width: 125px; background-color:#ffff99;&amp;quot; | &amp;lt;font size=&amp;quot;-1&amp;quot;&amp;gt;&lt;a href=&quot;/JETohline/index.php/H_BookTiledMenu#MoreModels&quot; title=&quot;H BookTiledMenu&quot;&gt;&amp;lt;b&amp;gt;Composite&amp;lt;br /&amp;gt;Polytropes&amp;lt;/b&amp;gt;&lt;/a&gt;&amp;lt;br /&amp;gt;(Bipolytropes)&amp;lt;/font&amp;gt; |}  ==Background== While &lt;a href=&quot;/JETohline/index.php/SSC/Structure/Polytropes#Polytropic_Spheres&quot; title=&quot;SSC/Structure/Polytropes&quot;&gt;polytropic spheres&lt;/a&gt; can give us useful &amp;#039;&amp;#039;general&amp;#039;&amp;#039; insight into the internal s...&amp;quot;&lt;/p&gt;
&lt;a href=&quot;https://selfgravitatingfluids.education/JETohline/index.php?title=SSC/Structure/BiPolytropes&amp;amp;diff=125&quot;&gt;Show changes&lt;/a&gt;</summary>
		<author><name>Joel2</name></author>
	</entry>
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