Help me find the geostationary orbit of an unknown planet?

Question

I need to figure out the geostationary orbit of an unknown planet using only the unknown planets density and diameter. The unknown planet is on a sidereal day.

I've searched the internet and cannot find the equation for calculating geostationary orbit.

I've tried to figure out the equation by looking at Earth's measurements, but I still can't quite get it. Here's what I found to help save some time.

density of Earth: 5,515 kg/m^3

diameter of Earth: 12,753 km

Anyone able to help? Thanks.

Answer 1

The density and diameter allow you to determine the gravitational constant of the planet, which you can then feed into the equation found here: http://en.wikipedia.org/wiki/Geosynchron...

Answer 2

You need to calculate the orbital distance that has the same orbital period as the rotation period of the planet.

You can use Newton's form of Kepler's third law, and the fact that you know the mass of the Earth from its density and radius.