The satellite is in circular motion, and the only force acting on it is the gravity exerted from the Earth:
[tex]F=G \frac{Mm}{r^2} [/tex]
where [tex]G=6.67 \cdot 10^{-11}m^3 kg^{-1}s^{-2}[/tex] is the gravitational constant, [tex]M=5.97 \cdot 10^{24}kg[/tex] 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, [tex]m \frac{v^2}{r} [/tex]:
[tex]m \frac{v^2}{r} =G \frac{Mm}{r^2} [/tex]
where v is the satellite's speed.
But the speed is also equal to the distance covered in one revolution (which is the circumference: [tex]2 \pi r[/tex]) divided by the time needed to cover one revolution (which is the period T=6560 s):
[tex]v= \frac{2 \pi r}{T} [/tex]
By replacing this into the previous formula and simplifying ,we get
[tex]\frac{4 \pi^2 r}{T^2} = \frac{GM}{r^2} [/tex]
And re-arranging and substituting the values, we find the radius of the orbit:
[tex]r= \sqrt[3]{ \frac{T^2 G M}{4 \pi^2} } = 7.57 \cdot 10^7 m=7570 km[/tex]
