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	<title>Appendix/Ramblings/51BiPolytropeStability/RethinkEnvelope - Revision history</title>
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	<updated>2026-05-03T00:27:04Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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		<title>Joel2: Created page with &quot;__FORCETOC__ =Rethink Handling of n = 1 Envelope=  ==Solution Steps== Drawing from an accompanying discussion &amp;hellip; * Step 1:  Choose &lt;math&gt;n_c&lt;/math&gt; and &lt;math&gt;n_e&lt;/math&gt;. * Step 2:  Adopt boundary conditions at the center of the core (&lt;math&gt;\theta = 1&lt;/math&gt; and &lt;math&gt;d\theta/d\xi = 0&lt;/math&gt; at &lt;math&gt;\xi=0&lt;/math&gt;), then solve the Lane-Emden equation to obtain the solution, &lt;math&gt;\theta(\xi)&lt;/math&gt;, and its first derivati...&quot;</title>
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		<updated>2024-07-16T00:08:49Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;quot;__FORCETOC__ =Rethink Handling of n = 1 Envelope=  ==Solution Steps== Drawing from an &lt;a href=&quot;/JETohline/index.php/SSC/Structure/BiPolytropes#Solution_Steps&quot; title=&quot;SSC/Structure/BiPolytropes&quot;&gt;accompanying discussion&lt;/a&gt; … * Step 1:  Choose &amp;lt;math&amp;gt;n_c&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;n_e&amp;lt;/math&amp;gt;. * Step 2:  Adopt boundary conditions at the center of the core (&amp;lt;math&amp;gt;\theta = 1&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;d\theta/d\xi = 0&amp;lt;/math&amp;gt; at &amp;lt;math&amp;gt;\xi=0&amp;lt;/math&amp;gt;), then solve the Lane-Emden equation to obtain the solution, &amp;lt;math&amp;gt;\theta(\xi)&amp;lt;/math&amp;gt;, and its first derivati...&amp;quot;&lt;/p&gt;
&lt;a href=&quot;https://selfgravitatingfluids.education/JETohline/index.php?title=Appendix/Ramblings/51BiPolytropeStability/RethinkEnvelope&amp;amp;diff=2297&quot;&gt;Show changes&lt;/a&gt;</summary>
		<author><name>Joel2</name></author>
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