SSC/Structure/Polytropes - Revision history

Joel2: /* Isolated Polytropes */

2023-12-24T02:56:57Z

Isolated Polytropes

← Older revision		Revision as of 22:56, 23 December 2023
Line 39:		Line 39:
	</div>		</div>

	In his effort to model the Sun's interior, ~~[https://archive.org/details/mobot31753002152772/page/56 J. Homer Lane (1870)]~~ was the first to couch an examination of stellar structure in the context of, what is now usually referred to as, "polytropic structures." He examined the structural properties of spherically symmetric models having, effectively, indexes of <math>~n = \tfrac{3}{2}</math> and <math>~n = \tfrac{5}{2}</math>. In an [[SSC/Structure/Lane1870#Lane.27s_1870_Work\|accompanying chapter]], we review this early groundbreaking work highlighting the quantitative care with which Lane carried out his analysis. A much more expansive study of polytropic (and isothermal) structures was subsequently published by ~~[https://books.google.com/books?id=MiDQAAAAMAAJ&printsec=frontcover#v=onepage&q&f=true Emden (1907)]~~, who was aware of Lane's work — see, for example, the footnote on p. 462 of his book. It is largely Emden's notation — especially as employed by [[Appendix/References#C67\|[<font color="red">C67</font>] ]] — that is adopted in current discussions of polytropic structures, including our discussion which follows.		In his effort to model the Sun's interior, {{ Lane1870full }} was the first to couch an examination of stellar structure in the context of, what is now usually referred to as, "polytropic structures." He examined the structural properties of spherically symmetric models having, effectively, indexes of <math>n = \tfrac{3}{2}</math> and <math>n = \tfrac{5}{2}</math>. In an [[SSC/Structure/Lane1870#Lane.27s_1870_Work\|accompanying chapter]], we review this early groundbreaking work highlighting the quantitative care with which Lane carried out his analysis. A much more expansive study of polytropic (and isothermal) structures was subsequently published by {{ Emden07full }}, who was aware of Lane's work — see, for example, the footnote on p. 462 of his book. It is largely Emden's notation — especially as employed by [[Appendix/References#C67\|[<font color="red">C67</font>] ]] — that is adopted in current discussions of polytropic structures, including our discussion which follows.

	==Governing Relations==		==Governing Relations==

Joel2: /* Polytropic Spheres */

2023-12-18T18:25:01Z

Polytropic Spheres

← Older revision		Revision as of 14:25, 18 December 2023
Line 4:		Line 4:
	<table border="1" align="center" width="100%" colspan="8">		<table border="1" align="center" width="100%" colspan="8">
	<tr>		<tr>
	<td align="center" bgcolor="lightblue" width="25%"><br />[[SSC/Structure/Lane1870\|Lane (~~1980~~)]]		<td align="center" bgcolor="lightblue" width="25%"><br />[[SSC/Structure/Lane1870\|Lane (1870)]]

	</td>		</td>

Joel2: /* Polytropic Spheres */

2023-12-18T18:10:52Z

Polytropic Spheres

@@ Line 2: / Line 2: @@
 <!-- __NOTOC__ will force TOC off -->
 =Polytropic Spheres=
 {| class="PGEclass" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black"

Joel2: /* Known Analytic Solutions */

2023-12-18T17:40:19Z

Known Analytic Solutions

Show changes

Joel2: /* Numerical Solutions */

2023-12-18T17:36:39Z

Numerical Solutions

← Older revision		Revision as of 13:36, 18 December 2023
Line 1,959:		Line 1,959:

	==Numerical Solutions==		==Numerical Solutions==
			Go [[SSC/Structure/Polytropes/Numerical\|here]]

	=Related Discussions=		=Related Discussions=

Joel2: /* Numerical Solutions */

2023-12-18T17:35:38Z

Numerical Solutions

Show changes

Joel2: Created page with "FORCETOC =Polytropic Spheres= {| class="PGEclass" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:#ffff99;" | Isolated
Polytropes |} Here we will supplement the SSCpt1/PGE|simplified set of..."

2023-12-13T00:11:23Z

Created page with "__FORCETOC__  =Polytropic Spheres= {| class="PGEclass" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:#ffff99;" | Isolated Polytropes |}  Here we will supplement the SSCpt1/PGE|simplified set of..."

Show changes