Period of Satellite's Orbital Motion Around Earth

[Asla]

Homework Statement

An artificial satellite is traveling in a circular orbit around the earth.The radius of the orbit from the Earth's center is r.Assume that the Earth is a uniform sphere of radius R.The magnitude of acceleration due to gravity at the surface is g.What is the period of the satellites orbital motion?
a)2pi r/sqrt(gR)
b)2pi R/sqrt(gr)
c)2pi r/R sqrt(r/g)
d)2pi R/r sqrt(R/g)

I am thinking that the problem is somehow related to uniform circular motion but I hit my first problem while trying to get the centripetal acceleration that is acting on the satellite because the give gravitational force is supposed to be on the surface of the earth.

 

[pbuk]

I hit my first problem while trying to get the centripetal acceleration that is acting on the satellite because the give gravitational force is supposed to be on the surface of the
earth.

How does the force of gravity change with distance?

So if the force of gravity on the surface of the earth, i.e. at distance R from the centre of the Earth is g, what is the force of gravity at distance r?

 

[Asla]

Yap I think that is the approach.Gravity acting on the satellite is R^2/r^2 (g) through which you get to (c) as the answer

 

[pbuk]

That's it