Question

What linear speed must an earth satellite have to be in a circular orbit at an altitude of 159 km?

Answer 1

Gravitational acceleration, g = GM/r^2. Additionally, for a satellite in a circular orbit, g = v^2/r

Where, G = Gravitational constant, M = Mass of earth, r = distance from the center of the earth to the satellite, v = linear speed of the satellite.

Equating the two expressions;
v^2/r = GM/r^2
v = Sqrt (GM/r);
But GM = Constant = 398600.5 km^3/sec^2
r = Altitude+Radius of the earth = 159+6371 = 6530 km

Substituting;
v = Sqrt (398600.5/6530) = 7.81 km/sec = 781 m/s