Solve Circular Motion: Satellite Height, Speed, Location

[T71979]

At what height above the Earth's surface would a satellite have to orbit in order that it be stationary in reference to a point on the earth? What would be it's speed? How would you describe the general location of that point in relation to the Earth's surface?

Homework Equations

v=2PIr/T, ac=v^2/r, ac=4PI^2r/T^2
Fc=M v^2/r, Fc=M 4PI^2r/T^2, Fg=G m1m2/r^2


I know that the satellite would have to be moving faster than the Earth because if not the satellite could not stay stationary with that point on the earth. I have the radius and mass of the Earth so I can figure out everything as far as speed, force, acceleration, and the period for the Earth but because nothing is given for the satellite I do not know how I should figure out the speed of the satellite. I also know that to get the height you can use the equation (H = radius of Earth - radius of satellite), but am not sure how I am supposed to get the radius of the satellite because again no inoformation is given for the satellite. I have tried combining some of the above equations but have come up empty handed. Any help would be appreciated.

 

[MalachiK]

If the satellite is to remain above a fixed reference point on the Earth then it must have the same period of rotation as the Earth (i.e. the angular speed of the satellite must be the rotational speed of the Earth). You've got enough formulae to be able to link the period of the satellie's orbit to the force on the satellite (or the acceleration this is the same as the field strength at the height of the satellite's orbit). After that it's just a matter of putting in the values for the mass of the Earth and G and calculating.

You can check you've got the right answer quite easily as the altitude of a geo-stationary orbit around the Earth is easy to look up using any search engine.

 

[T71979]

Thanks for your help.