Question

A satellite of mass 350 kg is in a circular orbit around the Earth at an altitude equal to the Earth's mean radius.

(a) Find the satellite's orbital speed.
m/s
(b) What is the period of its revolution?
min
(c) Calculate the gravitational force acting on it.
N

Answer 1

Part (a)

Consider gravitational force law and second law of motion.

Grav Force, = G.M.m/r²

centripetal force = m.v²/r

Gravitational force = centripetal force

We get

  v² = G.M/r

Here r = r_e + r_e  ( mean radius of Earth)

v² = 6.67x10^-11x5.98x10²⁴/2x6.37x10⁶

  v = 5.60x10³ m/s

(b)

Calculate time period of revolution.

Time period, T = 2.π.r/v

= 2×3.14 x 2x6.37x10⁶/5.63x10³

= 1.42x10⁴s

= 2236.67min

(c)

Calculate gravitational force acting on it.

F' = GM.m/r²

= 350 x(5.60x10³)²/2x6.37x10⁶

= 861.5N