Editing SSC/Structure/BiPolytropes/Analytic1.53/Pt2 (section)

===Harrison's Approach===
Following {{ Harrison46full }}, we seek to solve this last expression in concert with solutions to a pair of additional key governing relations for spherically symmetric equilibrium configurations, namely,
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  <td align="center">{{Math/EQ_SShydrostaticBalance01}}</td>
  <td align="center">; &nbsp; &nbsp; &nbsp;</td>
  <td align="center">{{Math/EQ_SSmassConservation01}}</td>
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  <td align="center" colspan="3">
{{ Harrison46 }}, p. 196, Eq. (20)
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while adopting (see [[SR/IdealGas#Consequential_Ideal_Gas_Relations|related discussion]])

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<span id="IdealGas:FormA"><font color="#770000">'''Form A'''</font></span><br />
of the Ideal Gas Equation of State,

{{ Template:Math/EQ_EOSideal0A }}
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and adopting [https://en.wikipedia.org/wiki/Kramers'_opacity_law Kramers' opacity law], that is,
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  <td align="right"><math>\kappa_R ~~ \rightarrow ~~ \kappa_\mathrm{Kramers}</math></td>
  <td align="center"><math>=</math></td>
  <td align="left"><math>\kappa_0 \rho T^{-7 / 2} \, .</math></td>
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Dimensional Analysis:
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  <td align="right"><math>\biggl[ \frac{\kappa_0 L}{ca_\mathrm{rad}} \biggr]</math></td>
  <td align="center"><math>\sim</math></td>
  <td align="left"><math>
\frac{rT^{15/2}}{\rho^2} \sim m^{-2}\ell^7 ( {^\circ}K)^{15/2}
  </math></td>
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  <td align="right"><math>\frac{\mathfrak{R}}{\mu}</math></td>
  <td align="center"><math>\sim</math></td>
  <td align="left"><math>
t^{-2}\ell^2 ( {^\circ}K)^{-1}
  </math></td>
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----

We note as well that the leading coefficient in Kramers' opacity is,
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  <td align="right"><math>\kappa_0</math></td>
  <td align="center"><math>\approx</math></td>
  <td align="left"><math>
5 \times 10^{22} ~\mathrm{cm}^5~\mathrm{g}^{-2} ({^\circ}K)^{7 / 2} \, .
  </math></td>
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[<b>[[Appendix/References#Clayton68|<font color="red">Clayton68</font>]]</b>], &sect;3.3, Eq. (3-170)<br />
[<b>[[Appendix/References#KW94|<font color="red">KW94</font>]]</b>], &sect;17.2, Eq. (17.5)<br />
[<b>[[Appendix/References#HK94|<font color="red">HK94</font>]]</b>], &sect;4.4.2, Eq. (4.35)
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