Question

A satellite has a mass of 6255 kg and is in a circular orbit 4.30 × 105 m above the surface of a planet. The period of the orbit is 2.2 hours. The radius of the planet is 4.49 × 106 m. What would be the true weight of the satellite if it were at rest on the planet’s surface?

Answer 1

Gravitational constant = G = 6.674 x 10^-11 m³kg^-1s^-2

Mass of the planet = M

Mass of the satellite = m = 6255 kg

Radius of the planet = R_p = 4.49 x 10⁶ m

Distance of the satellite from the surface of the planet = H = 4.3 x 10⁵ m

Radius of orbit = R

R = R_p + H

R = 4.49x10⁶ + 4.3x10⁵

R = 4.92 x 10⁶ m

Time period of orbit = T = 2.2 hours = 7920 sec

Speed of the satellite = V

VT = 2R

V(7920) = 2(4.92x10⁶)

V = 3903.19 m/s

The gravitational force on the satellite due to the planet provides the necessary centripetal force required by the satellite for the circular motion.

M = 1.123 x 10²⁴ kg

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

Weight of the satellite on the planet's surface is equal to the gravitational force exerted by the planet on it.

W = 23254.15 N

Weight of the satellite on the planet's surface = 23254.15 N