Question

A satellite of mass 290 kg is orbiting in a circular orbit of radius 1150 km (measured from the center of the planet). The mass of the planet is 5.78×10²⁴ kg.

Part A

What is the angular momentum of the satellite with respect to the point at the center of the planet?

Answer 1

Gravitational constant = G = 6.67 x 10^-11 N.m²/kg²

Mass of the planet = M = 5.78 x 10²⁴ kg

Mass of the satellite = m = 290 kg

Radius of orbit = R = 1150 km = 1150 x 10³ m = 1.15 x 10⁶ m

Orbital speed of the satellite = V

The gravitational force between the planet and the satellite provides the necessary centripetal force for the circular motion of the satellite.

V = 1.831 x 10⁴ m/s

Angular momentum of the satellite with respect to the point at the center of the planet = L

L = mVR

L = (290)(1.831x10⁴)(1.15x10⁶)

L = 6.106 x 10¹² kg.m²/s

A) Angular momentum of the satellite with respect to the point at the center of the planet = 6.106 x 10¹² kg.m²/s