Question

A satellite has a mass of 6372 kg and is in a circular orbit 4.05 × 10⁵ m above the surface of a planet. The period of the orbit is 2.1 hours. The radius of the planet is 4.41 × 10⁶ m. What would be the true weight of the satellite if it were at rest on the planet’s surface?

Answer 1

The height of orbit is H
The radius of the planet is R
Distance between the planet and the satellite is H+R

The centripetal force F_c is given by the force of gravity F_g

where G is gravity constant,
M is the mass of the planet,
m is the mass of the satellite,
is the angular velocity of the orbit

, where T is the period of the orbit

Now we have

The mass of the planet

The gravitational force, F_g is also equal to mg. To find the acceleration

At the surface of the planet the gravitation will be

So, F_g = mg = 6372 x 3.3 = 21027 = 21 kN

The weight of the satellite is 21 kN