1) The gravitational force F between the earth and the satellite is given by:
F = GMm / R²
where
G is the universal gravitational constant { = 6.67 x 10^-11 Nm²/kg² } ;
M is the mass of the Earth { = 5.97 x 10^24 kg } ;
m is the mass of the orbiting satellite ;
R is the distance between their centres of mass.
Force F provides the centripetal force needed to keep the satellite in a circular orbit.
Centripetal force = mω²R
where ω is the angular velocity. So we can write:
GMm / R² = mω²R
{m cancels out. Divide both sides by ω² and multiply by R² }
GM / ω² = R³
We are given that the satellite completes one orbit (= 2π radians) in 5700 seconds. So:
ω = (2π / 5700) = 1.10 x 10^-3 rad/s
R³ = (6.67 x 10^-11 * 5.97 x 10^24 / (1.10 x 10^-3 )² ) = 3.28 x 10^20
R = 6.89 x 10^6 m
2) Gravitational force = GMm / R²
= 6.67 x 10^-11 * 5.97 x 10^24 * 6000 / (6.89 x 10^6)²
= 5.03 x 10^4 newtons
3) Altitude = radius of orbit - radius of Earth
= 6.89 x 10^6 - 6.37 x 10^6
= 5.2 x 10^5 m
