1. The problem statement, all variables and given/known data Find the pressure at the center of a planet 2. Relevant equations dP/dr = -ρg (Hydrostatic Equilibrium) g = GM/r2 (acceleration due to gravity) 3. The attempt at a solution dP/dr = -ρg Assume that density is constant. subsitute GM/r2 for g in the pressure gradient formula dP/dr = -ρGM/r2 Now we need Mass as a function of radius. Divide the planet up into differential concentric rings then the differential mass element is related to the surface area. dM = 4πr2ρdr or dM/dr = 4πr2ρ (conservation of mass) Then integrating both sides of the the above equation gives. ∫dM = ∫4πr2ρdr M(r) = ∫4πr2ρdr With limits of integration from 0 to r and since density is constant M(r) = 4/3πr3ρ so the pressure gradient with a constant density gives dP/dr = (-ρg/r2)(4/3πr3ρ) Solving the differential equation for P gives ∫dP = ∫-(4πGρ2rdr)/3 with limits of integration from r1 to r2 (radius) and P1 to P2 (pressure) gives: P2-P1 = (-4Gπρ2/3)(r22-r12/2) Solving for P1 gives P1 = P2+(-2Gπρ2/3)(r22-r12/2) Setting the boundry condition as r2 = R1 and P2=0 gives the final equation for Pressure as a function of radius inside the planet with density ρ, planetary radius R and varying radius r as P(r) = (2πGρ2R2/3)(1-r2/R2) Is this correct? Does this mean that inserting 0 for r will give you (1-0) or just 1 and then the pressure at the center of the planet is dependent on just the density of the planet and the radius of the planet?