Calculating Satellite Height and Velocity for Geostationary Orbit

[Gauss177]

Homework Statement

Calculate at what height above the Earth's surface a satellite must be placed if it is to remain over the same geographical point on the equator of the earth. What is the velocity of such a satellite?

Homework Equations

v = sqrt(G*m / r)

The Attempt at a Solution

At first I thought the velocity of the satellite would have to be the same as the earth, but since r is different the velocity must also be different. I have 2 unknowns for the satellite, the velocity and r, and can't figure out what to do now.

Thanks for your help.

 

[Doc Al]

At first I thought the velocity of the satellite would have to be the same as the earth,

It must have the same angular velocity as the earth.

 

[Gauss177]

Hm..we haven't covered angular velocity yet. Is there another way to do it?

 

[Doc Al]

Whether you've explicitly covered angular velocity or not, there's no way around the fact that if the satellite is to "remain over the same geographical point" its angular speed must equal that of the earth. If you think in terms of both the Earth's surface and the satellite sweeping out equal angles in equal times, that might help you figure it out.