Question

A satellite has a mass of 6463 kg and is in a circular orbit 4.82 × 105 m above the surface of a planet. The period of the orbit is 2.0 hours. The radius of the planet is 4.29 × 106 m. What would be the true weight of the satellite if it were at rest on the planet’s surface?

Answer 1

The weight of the planet is 29083.5 N .

Step-by-step explanation:

mass of satellite, m = 6463 kg

height of orbit, h = 4.82 x 10^5 m

period, T = 2 h

radius of planet, R = 4.29 x 10^6 m

Let the acceleration due to gravity at the planet is g.

`T = 2\pi\sqrt((R+h)^3)/(gR^2)\\\\2* 3600 = 2*3.14\sqrt((4.29+0.482)^3*10^(18))/(g* 4.29* 4.29* 10^(12) )\\\\24.2 g =108.67\\\\g = 4.5 m/s^2`

The weight of the satellite at the surface of the planet is

W = m g = 6463 x 4.5 = 29083.5 N