1. The problem statement, all variables and given/known data I have a sphere filled with unknown gas. I have to estimate the pressure inside of it. The tricky part is that density of the sphere changes as we go deeper inside of it with the given formula: ρ=ρo*(1-r/R), where R is radius of the sphere and is known: R=5*1010m, and r is a variable. Gas has mol mass m=2.7 g/mol. Mass of the whole sphere is M=3.3*1050 kg. Gas is ideal. 2. Relevant equations pV=nRT p=F/A 3. The attempt at a solution The force of gravity of an infinitesimal layer of thickness dr inside the sphere at some radius r caused by the inner sphere is: dF=GmM/r2 where m is the mass of the infinitesimal layer and M is the mass of inner part of the sphere. Mass m=V*ρ=4*PI*r2*ρo*(1-r/R)*dr Mass M=4/3*PI*r3*ρo*(1-r/R) so dF=G*16/3*PI2*r3*ρo2*(1-r/R)2*dr dp=dF/A dp=dF/4*PI*r2 dp=4/3*PI*G*ρo2*(1-r/R)2*r*dr so p(r)=4/3*PI*G*ρo2*[tex]\int[/tex](1-r/R)2*r*dr from r to R After making the calculations I will put p(r=0) and get the pressure inside the sphere. Is my method good?