- #1

dlc_iii

## Homework Statement

"In a galaxy far far away, a planet composed of an incompressible liquid of uniform mass density ρ has mass

*m*

_{planet}and radius R. Determine the pressure midway between the surface and the center of the planet."I used M=mass of planet, m=mass of shell, R=radius of planet, r=radius of shell, V=volume of planet, dr=thickness of shell, ρ=density of planet

## Homework Equations

P=ρgh

g=Gm/r^2

Area of sphere = 4/3πr^3

## The Attempt at a Solution

I solved this problem by adding up all the pressures of thin shells from R/2 to R.

P=ρgh=∫(3GM

^{2}r)/(4πR

^{6})dr= (3GM

^{2})/(4πR

^{6})∫rdr from R/2 to R

final answer= (9GM

^{2})/(32πR

^{4})

This is the answer that I got and I found a few other places for a normal planet, but my textbook says it should be 45/64 instead of 9/32 in front of the (GM

^{2})/(πR

^{4}). Is it different for fluids or am I or my textbook wrong?