Originally posted by mtthw
True, that's exactly the simplication I used.

What does it do if you use a function? It makes it more complicated 🙂.

You need to integrate that function from 0 to r to get the gravitational force for r within the planet - you get something proportional to:

1/r^2 x Int{0 to r}(x^2 f(x) dx)

(which is proportional to r if f is constant)

You then need to integrate it again to get the potential energy difference.

Very interesting!

Does it differ a lot, do you think? I mean, the result using the simplyfied formula and using the density as a function?

Originally posted by FabianFnas
Very interesting!

Does it differ a lot, do you think? I mean, the result using the simplyfied formula and using the density as a function?

I leave that as an exercise for the reader 🙂

I might have a look later, if I get bored.