A GPS satellite orbits at an altitude of 2.14×104 km above the surface of Earth. (Recall that RE = 6.37 × 106 m.)

Question

What is the speed of the satellite?

Answer 1

M = mass of earth (look it up in kg)

G = universal constant of gravitation (look it up in Nm²/kg²)

h = altitude of orbit (given, but convert to meters)

Assuming a circular orbit of radius r,

v² / r = GM / r²

v² = GM / r

v = √(GM/r) = √[GM / (R_e + h)]

Plug in the numbers (with h in meters) and get v in m/s.