PX158 - I5a - pressure at the centre of stars

most stars are in hydrostatic equilibrium (the pressure supports the fluid above it)
for a constant gravity, $g$ , and density, $ρ$ , at a depth, $h :$

p = ρ g h

for a star:
$h = R_{s}$
$g = \frac{G M_{s}}{R_{s}^{2}}$ (surface gravity, assumed to be constant)
$ρ = \bar{ρ} = \frac{M_{S}}{\frac{4}{3} π R_{s}^{3}}$ (bulk density, assumed to be constant)
$\begin{align*} p_{c} &= \rho \frac{GM_{s}}{R_{s}} \\ p_{c} &= \frac{3}{4\pi} \frac{GM_{s}^{2}}{R_{s}^{4}}$
eg: what is the central pressure for the sun?
- $M_{⊙} = 2 \times 10^{30} k g$ , $R_{⊙} = 7 \times 10^{8} k m$
$∴ p_{c ⊙} = 3 \times 10^{14} P a$
- cf. atmospheric pressure $= 10^{5} P a$
computer model:
$\sim \frac{1}{2} \times :$ due to realistic $g$ profile
$\sim 100 \times :$ due to realistic $ρ$ profile