Physics Problems: Altitude and period of Satellites...?

Question

A Satellite moves in a circular orbit around Earth at a speed of 5,000 m/s. Determine (a) the satellite’s altitude above the Earth’s surface and (b) the period of the satellite’s orbit.

I don’t understand this problem in my book. Please help me by explaining how to solve and what equations used to solve them. Thank You.

Answer 1

M=mass of the Earth, R=radius of the Earth~6367 km

m=mass of the satellite, r=satellite’s altitude above the Earth’s surface

At the Earth's surface mg=γmM/R² ==> γM=gR²

a) Centripetal force=Gravitational force

mv²/(R+r)=γmM/(R+r)²

v²=gR²/(R+r)

R+r=gR²/v²

r=gR²/v²-R

r=9.8*(6.367e06)²/5000²-6.367e06=9524 km

b) T=2π/ω=2π(R+r)/v=2πgR²/v³=19969s~5h 33m

Answer 2

Angular frequency is required .

Then v = w X r

w = angular frequency ( radians / second )

where r = altitude + earth radius

Now T = 2 X Pi X r / v

(complete the numerical substitutions yourself)