How can I calculate the solar central density $\rho_C = 150 \textrm{g cm}^{-3}$ using one of the equations of stellar structure like the the mass distribution equation $\frac{dM(r)}{dr}=4 \pi r^2 \rho(r)$. This describes the mass M(r) contained within a radius r in terms of the mass density ρ (rho).]

Its not about the density at R=0, since the mass inside a sphere of radius R=0 is of course 0. But density is defined as mass per unit volume: So, you can imagine a small volume at the centre of the Sun, having mass.

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    $\begingroup$ You cannot calculate the central density of the Sun without making some assumptions or calculations about how the pressure varies with temperature and density and how the density varies with radius. Or by assuming the properties of a polytrope with some index. $\endgroup$
    – ProfRob
    Nov 23, 2022 at 16:56


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