Geostationary Orbit?

Question

My friends and I have way too much time on our hands and have found this problem we want to solve... but we're all stuck. Any help would be lovely!

Assume the planet of Junto is a spherical planet with a diameter of 1600 km with a uniform density of 5200 kilograms per cubic metre. If it's moon "Pheron" is in a geostationary orbit around Junto, and assuming a Juntonian sidereal day is exactly 24 hours, how far is that geostationary orbit above the surface of Junto?

Answer 1

This mathmatical problem was time consuming, but I got 59455.86km for an answer. I'm almost positive that my answer is correct. Is this question for a neopets contest? I'm a member and there is a contest involving a question similar to yours. Good luck!

Answer 2

You can calculate the mass of Junto.  Pheron's orbit doesn't depend on its mass.  For a geostationary orbit, you want a circular orbit, so its eccentricity is zero.  That's a degenerate case of an ellipse, but it's simpler.  You can just look through information about orbits to find equations to answer your question.  Or you could understand how orbits work and derive the answer.  Note that the radius of the lunar orbit isn't the answer.  You want height above the planet's surface.

PS: This is a very good use for all this time on your hands!

Answer 3

The actual text of the contest puzzle is as follows:

"Assume the world of Neopia is a spherical planet with a diameter of 1600 km with a uniform density of 5200 kilograms per cubic metre. If the moon of Kreludor is in a geostationary orbit around Neopia, and assuming a Neopian sidereal day is exactly 24 hours, how far is that geostationary orbit above the surface of Neopia?"

To get the prize-winning answer value, follow the instructions here:

http://lennyconundrumsolutions.blogspot....