Editing SSC/PerspectiveReconciliation (section)

==Step 2:==
As we have shown in a 
[[SSCpt2/SolutionStrategies#Technique_1|separate discussion of how to construct equilibrium, spherically symmetric configurations]], the Poisson equation can be integrated once to give an expression for the gravitational acceleration (see, also, Rosseland's equation 2.16) of the form,
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<math>~g \equiv \frac{d\Phi}{dr}</math>
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<math>~=</math>
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<math>~\frac{GM_r}{r^2} \, .</math>
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As is quite customary in this field of research, Rosseland substitutes <math>~g</math> for the radial gradient of the gravitational potential in the Euler equation &#8212; that is, he writes,
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<math>~\frac{dv_r}{dt}</math>
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<math>~=</math>
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<math>~- \frac{1}{\rho} \frac{\partial P}{\partial r} - g \, ,</math>
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(see his equation 2.14 with nonadiabatic terms set to zero) &#8212; and, in so doing, considers that the Poisson equation has been solved.  This reduces the number of governing equations (as well as the number of unknown structural variables) to three.  Then Rosseland proceeds to point out that, when the radial pulsation of a spherically symmetric configuration is viewed from a Lagrangian perspective &#8212; that is, while riding along with a fluid element &#8212; the mass enclosed inside the radial position of each fluid element, <math>~M_r</math>, does not change with time.  Hence, the ''Lagrangian'' time-derivative of the gravitational acceleration is (see Rosseland's equation 2.17),
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<math>~\frac{dg}{dt}</math>
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<math>~=</math>
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<math>~GM_r \frac{d}{dt}\biggl(\frac{1}{r^2}\biggr) = - \frac{2GM_r}{r^3} \frac{dr}{dt} = - \frac{2gv_r}{r} \, .</math>
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