# Geophysics: Dynamic form factor and Equipotential surfaces

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1. Apr 27, 2015

### NaturalSymphony

I've got the following problem which I need help with. I'm used to calculating coefficients when the problem is about ellipsoids and first order approximations. But when it comes to spheres and coefficients $J_n$ I really don't know how to approach the problem. Can somebody help me out?

Consider a spherical planet of radius $a$. This planet has two spherical holes inside of radius $a/4$, both situated on the $X_3$ axis (vertical) at a distance of $3a/4$ from the center of the planet. If the planet were homogeneous, it's mass would me $M$.

a) Find a general expression for coefficients $J_n$.

b) Draw approximately the equipotential surface that goes through the planet's pole, when we consider only a first order approximation, and we don't consider the rotation.

data: $G=6.67\times 10^{-11} \ m/kg \ s^2$; $M=5.973\times 10^{24} \ kg$

2. May 2, 2015

### Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?