You observe an articial satellite orbiting the earth. You estimates it is at
an altitude h = [03] km above the earth's surface and has a mass
m = 3500 kg. You wish to calculate when the satellite will be back in the same position. From the second law of motion and the gravitational force law, calculate the following:
(a) What is the satellite's velocity? (m/s)
(b) What is the period of the satellite's motion?

The only force acting on the satellite is the gravitational force (Fg) right? So by combining the two laws, we would have that ma=Fg. I solved for the Fg, but I'm not sure where to go from there.

Sorry, that's supposed to be 736 km above the earth's surface.

You have to consider the centripetal force which prevents the satellite from crashing on the Earth.

F_c = \frac{mv^2}{r}

From that, you have Fc = Fg, then:

ma = \frac{mv^2}{r}

Solve for v.

Then, use v=r\omega

Find omega, which is 2pi/T.

Find T, the period of the satellite.

I hope it helped! :)