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## Homework Statement

Okay, so the question seems really simple so I don't know what I'm missing

A satellite orbits at a fixed point above the Earth's equator. Assuming the earth has uniform

density, radius R, and angular frequency of rotation, omega

Find an expression for eta, such that the orbital radius of the satellite is expressed as eta R

## Homework Equations

Below

## The Attempt at a Solution

Centripetal force= gravitational force

mr(omega)^2=GMm/r^2

r^3=GM/(omega)^2

But I honestly have no idea how to incorporate the Eaths radius. Every time I try it cancels.

Thanks in advance :)