Question

A satellite has a mass of 6189 kg and is in a circular orbit 4.84 × 10⁵ m above the surface of a planet. The period of the orbit is 2.4 hours. The radius of the planet is 4.80 × 10⁶ m. What would be the true weight of the satellite if it were at rest on the planet’s surface?

W = ?

Answer 1

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

Mass of the planet = M

Mass of the satellite = m = 6189 kg

Radius of the planet = R_p = 4.8 x 10⁶ m

Altitude of the satellite = H = 4.84 x 10⁵ m

Radius of orbit of the satellite = R

R = R_p + H

R = 4.8x10⁶ + 4.84x10⁵

R = 5.284 x 10⁶ m

Period of orbit = T = 2.4 hours = 2.4 x (3600) sec = 8640 sec

Orbital speed of the satellite = V

VT = 2R

V(8640) = 2(5.284x10⁶)

V = 3842.63 m/s

The gravitational force of the planet on the satellite provides the centripetal force for the circular motion of the planet.

M = 1.17 x 10²⁴ kg

Weight of the satellite on the planet's surface = W

W = 2.096 x 10⁴ N

Weight of the satellite if it were at rest on the planet's surface = 2.096 x 10⁴ N