The satellite is in circular motion, and the only force acting on it is the gravity exerted from the Earth:
where
is the gravitational constant,
is the Earth's mass, m is the mass of the satellite and r is the radius of the circular orbit.
Since it is a circular motion, this force acts as centripetal force,
:
where v is the satellite's speed.
But the speed is also equal to the distance covered in one revolution (which is the circumference:
) divided by the time needed to cover one revolution (which is the period T=6560 s):
By replacing this into the previous formula and simplifying ,we get
And re-arranging and substituting the values, we find the radius of the orbit: