Question

What is the speed of a satellite moving in a circular orbit at a height of 3800km above the
surface of the earth? (b) what is the period of the satellite in hours? The mass of the
earth is 5.97x10^24 kg. The radius of the earth is 6.38x10^6 m

Answer 1

(a) Determine the speed:

$$GMm/(R+H)^2=mv^2/(R+H),\\\space\\ v=\sqrt\frac{GM}{R+H}=6255\text{ m/s}.$$

(b) The period is

$$T=L/v=2\pi (R+H)/v=10226\text{ s, or 2 h 50 min}.$$