Question

A satellite has a mass of 6392 kg and is in a circular orbit 4.88 × 10⁵ m above the surface of a planet. The period of the orbit is 1.7 hours. The radius of the planet is 4.89 × 10⁶ m. What would be the true weight of the satellite if it were at rest on the planet’s surface?

Answer 1

First of all, we need to find the mass of the planet. For that we will use Kepler's law

M = 4²(r³) / (T²G)

M = 4² (4.89e6 + 4.88e5)³ / ( 1.7² * 3600² * 6.67e-11)

M = 2.458e24 Kg

Now, we can find value of g for the planet

g = GM / r²

g = 6.67e-11 * 2.458e24 / 4.89e6²

g = 6.856 m/s²

therefore,

true weight on the surface

W = mg

W = 6392 * 6.856

W = 43826.65 N