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## Homework Statement

"Given a certain rocky material, estimate the greatest possible radius of a planet made up of said material"

## Homework Equations

##P = \frac{2}{3}\pi G\rho^2R^2##

##R = \frac{1}{\rho}\sqrt{\frac{3P}{2\pi G}}##

## The Attempt at a Solution

I'm not quite sure of the validity of my attempt at a solution, but here it is:

First I calculated the pressure at the center of a sphere of uniform density ρ and radius R under its own gravity, getting

##P = \frac{2}{3}\pi G\rho^2R^2##

which gives ##R = \frac{1}{\rho}\sqrt{\frac{3P}{2\pi G}}##.

Assuming the material was Iron, I plugged in its density ρ = 7874 kg/m

^{3}and for P i used its bulk modulus of 170 GPa. The result was 4.43 * 10

^{6}m.

Then I cheated and used the average density of the earth ρ = 5513 kg/m

^{3}and the same bulk modulus, which gave 6.32 * 10

^{6}m.

But both result are less than the radius of the Earth, so my solution is probably completely worthless. Any ideas on how to approach this problem differently?