= Homology scaling of central stellar pressure
{title2=$\rho_c\propto M/R^3,\ P_c\propto GM^2/R^4$}
= Homology scalings of central stellar pressure
{synonym}
In <stellar homology>, a fixed dimensionless density profile gives $\rho_c=C_\rho M/R^3$ through the mass integral. Integrating the <stellar hydrostatic equation> through the same profile gives $P_c=C_PGM^2/R^4$ when surface pressure is negligible. The constants depend on the shape, rather than the mass and radius. For an <ideal gas>, $T_c=(C_P/C_\rho)\mu GM/(\mathcal R R)$.
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