Question

You observe an articial satellite orbiting the earth and estimate 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 force of gravity (Fg) right? So by combining the two laws I have Fg = ma. I solved for Fg, but I need some pointers on where to go from there.

Answer 1

mass is m (it will not matter in the end)

if height above earth is h

then radius of orbit = r = Rearth + h

then
Fg = G m Mearth/r^2

a = v^2/r
so Fg = m v2/r

so
G m Mearth/r^2 = m v^2/r
note m cancels, feather drifts right beside the space station

G Mearth/r = v^2
there you go
get v then it goes 2 pi r at v