SSC/Structure/Lane1870 - Revision history

Joel2: /* Lane's 1870 Work */

2024-07-18T17:34:30Z

Lane's 1870 Work

← Older revision		Revision as of 13:34, 18 July 2024
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	=~~Lane's 1870 Work~~=		=Polytropic Spheres=

	<table border="1" align="center" width="100%" colspan="8">		<table border="1" align="center" width="100%" colspan="8">

Joel2: /* Lane's 1870 Work */

2024-07-18T17:31:28Z

Lane's 1870 Work

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 =Lane's 1870 Work=
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Joel2: /* SEGMENT III */

2024-07-17T22:37:26Z

SEGMENT III

← Older revision		Revision as of 18:37, 17 July 2024
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	In an effort to acknowledge the strikingly high precision with which Lane was able to determine the "curves of density" for this pair of models, the following table shows the values of <math>~x'</math> and <math>~\mu'</math> taken directly from Lane's publication (see the table cells with light green backgrounds) along with the corresponding values of the surface radius and total mass as has been calculated and published independently by [https://books.google.com/books?id=MiDQAAAAMAAJ&printsec=frontcover#v=onepage&q&f=true Emden (1907)] and by [~~http~~://~~adsabs~~.~~harvard~~.~~edu~~/~~abs~~/~~2004ASSL~~.~~.306.....H~~ Horedt (2004)]. (Additional details from the published tabulations of these two authors can be found in the subsections that follow.)		In an effort to acknowledge the strikingly high precision with which Lane was able to determine the "curves of density" for this pair of models, the following table shows the values of <math>~x'</math> and <math>~\mu'</math> taken directly from Lane's publication (see the table cells with light green backgrounds) along with the corresponding values of the surface radius and total mass as has been calculated and published independently by [https://books.google.com/books?id=MiDQAAAAMAAJ&printsec=frontcover#v=onepage&q&f=true Emden (1907)] and by [https://link.springer.com/book/10.1007/1-4020-2351-0 Horedt (2004)]. (Additional details from the published tabulations of these two authors can be found in the subsections that follow.)

Joel2 at 22:29, 17 July 2024

2024-07-17T22:29:27Z

← Older revision		Revision as of 18:29, 17 July 2024
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	<font size="-1">[[H_BookTiledMenu#Equilibrium_Structures\|<b>Lane</b>]]<br />(1870)</font>		<font size="-1">[[H_BookTiledMenu#Equilibrium_Structures\|<b>Lane</b>]]<br />(1870)</font>
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	In what follows, text presented in a dark green font (and/or, as indicated, each equation) has been copied ''verbatim'' from a scientifically impactful 1870 article by {{ Lane1870full }}. ~~Note~~ that we have ~~broken the article into separate '''segments''' in order to facilitate the insertion~~ of ~~interspersed comments~~. ~~Our~~ accompanying discussion of ''[[SSC/Structure/Polytropes#Polytropic_Spheres\|Polytropic Spheres]]'' ~~shows how this groundbreaking~~ physical/mathematical model ~~developed by Lane to probe the interior structure~~ of the ~~Sun — encapsulated~~ in ~~what~~ is ~~now~~ commonly referred to as the ''Lane-Emden'' equation ~~— provides a tool for understanding stars~~ that have ~~a wide range~~ of ~~structural properties~~.		In what follows, text presented in a dark green font (and/or, as indicated, each equation) has been copied ''verbatim'' from a scientifically impactful 1870 article by {{ Lane1870full }} which, when published, was intended to offer a physical/mathematical model of the interior of the sun. In practice, this groundbreaking work has provided a tool for understanding stars that have a wide variety of structural properties. (See, for example, our accompanying discussion of ''[[SSC/Structure/Polytropes#Polytropic_Spheres\|Polytropic Spheres]].'') Several decades later, {{ Emden07full }} independently developed essentially the same physical/mathematical model. The core element of the model is a 2<sup>nd</sup>-order ODE which, in the present era, is commonly referred to as the ''Lane-Emden'' equation. Note that we have broken this MediaWiki-based chapter into separate '''segments''' in order to facilitate the insertion of interspersed comments.
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Joel2: /* SEGMENT III */

2023-12-17T23:40:54Z

SEGMENT III

← Older revision		Revision as of 19:40, 17 December 2023
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	<table border="1" align="center" cellpadding="10" width="90%">		<table border="1" align="center" cellpadding="10" width="90%">
	~~<tr align="left">~~<tr><td align="~~left~~">		<tr><td align="center">
	[https://archive.org/details/mobot31753002152772/page/56 J. H. Lane (1870)], '''The American Journal of Science and Arts''', Vol. 50, pp. 57 - 74: ''On the Theoretical Temperature of the Sun under the Hypothesis of a Gaseous Mass Maintaining Its Volume by Its Internal Heat and Depending on the Laws of Gases Known to Terrestrial Experiment''		{{ Lane1870figure }}

	~~<div align="center">'''SEGMENT III''' (pp. 60 - 64)</div>~~

			'''SEGMENT III''' (pp. 60 - 64)
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	<tr><td align="left">		<tr><td align="left">

Joel2: /* SEGMENT II */

2023-12-17T23:39:04Z

SEGMENT II

← Older revision		Revision as of 19:39, 17 December 2023
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	<table border="1" align="center" cellpadding="10" width="90%">		<table border="1" align="center" cellpadding="10" width="90%">
	~~<tr align="left">~~<tr><td align="~~left~~">		<tr><td align="center">
	[https://archive.org/details/mobot31753002152772/page/56 J. H. Lane (1870)], '''The American Journal of Science and Arts''', Vol. 50, pp. 57 - 74: ''On the Theoretical Temperature of the Sun under the Hypothesis of a Gaseous Mass Maintaining Its Volume by Its Internal Heat and Depending on the Laws of Gases Known to Terrestrial Experiment''		{{ Lane1870figure }}

	~~<div align="center">'''SEGMENT II''' (beginning on p. 59)</div>~~

			'''SEGMENT II''' (beginning on p. 59)
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Joel2: /* Lane's 1870 Work */

2023-12-17T23:36:37Z

Lane's 1870 Work

← Older revision		Revision as of 19:36, 17 December 2023
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	<font size="-1">[[H_BookTiledMenu#Equilibrium_Structures\|<b>Lane</b>]]<br />(1870)</font>		<font size="-1">[[H_BookTiledMenu#Equilibrium_Structures\|<b>Lane</b>]]<br />(1870)</font>
	\|}		\|}
	In what follows, text presented in a dark green font (and/or, as indicated, each equation) has been copied ''verbatim'' from a scientifically impactful 1870 article by ~~[https://en.wikipedia.org/wiki/Jonathan_Homer_Lane J. Homer Lane]~~. Note that we have broken the article into separate '''segments''' in order to facilitate the insertion of interspersed comments. Our accompanying discussion of ''[[SSC/Structure/Polytropes#Polytropic_Spheres\|Polytropic Spheres]]'' shows how this groundbreaking physical/mathematical model developed by Lane to probe the interior structure of the Sun — encapsulated in what is now commonly referred to as the ''Lane-Emden'' equation — provides a tool for understanding stars that have a wide range of structural properties.		In what follows, text presented in a dark green font (and/or, as indicated, each equation) has been copied ''verbatim'' from a scientifically impactful 1870 article by {{ Lane1870full }}. Note that we have broken the article into separate '''segments''' in order to facilitate the insertion of interspersed comments. Our accompanying discussion of ''[[SSC/Structure/Polytropes#Polytropic_Spheres\|Polytropic Spheres]]'' shows how this groundbreaking physical/mathematical model developed by Lane to probe the interior structure of the Sun — encapsulated in what is now commonly referred to as the ''Lane-Emden'' equation — provides a tool for understanding stars that have a wide range of structural properties.
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	<table border="1" align="center" cellpadding="10" width="90%">		<table border="1" align="center" cellpadding="10" width="90%">
	~~<tr align="left">~~<tr><td align="~~left~~">		<tr><td align="center">
	[https://archive.org/details/mobot31753002152772/page/56 J. H. Lane (1870)], '''The American Journal of Science and Arts''', Vol. 50, pp. 57 - 74: ''On the Theoretical Temperature of the Sun under the Hypothesis of a Gaseous Mass Maintaining Its Volume by Its Internal Heat and Depending on the Laws of Gases Known to Terrestrial Experiment''		{{ Lane1870figure }}

	~~<div align="center">'''SEGMENT I''' (beginning on p. 57)</div>~~

			'''SEGMENT I''' (beginning on p. 57)
	</td></tr>		</td></tr>
	<tr><td align="left">		<tr><td align="left">

Joel2: Created page with "FORCETOC =Lane's 1870 Work= {| class="PGEclass" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:#ffeeee;" | Lane
(1870) |} In what follows, text presented in a dark green font (and/or, as indicated, each equation) has been copied ''verbatim''..."

2023-12-17T23:20:09Z

Created page with "__FORCETOC__  =Lane's 1870 Work= {| class="PGEclass" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:#ffeeee;" | Lane (1870) |} In what follows, text presented in a dark green font (and/or, as indicated, each equation) has been copied ''verbatim''..."

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