Question

The Canadian microsatellite MOST (Microvariability and Oscillations of Stars) has a mass of just 52 kg. It travels in an almost circular orbit at an average altitude of 820 km above Earth’s surface.

a) Calculate the gravitational force between Earth and the MOST satellite at this altitude.

b) What speed does the MOST satellite need to maintain its altitude? Express the speed in metres per second and kilometres per hour.

c) Determine the orbital Period of MOST.

Answer 1

(a) F=G•m•M/(R+h)²,
where the gravitational constant G =6.67•10^-11,
Earth’s mass is M = 5.97•10^24 kg,
Earth’s radius is R = 6.378•10^6 m.
h =8.2•10^5 m,
m = 52 kg.
(b) m•a = m•v²/(R+h) = G•m•M/(R+h)².
v =sqrt [G•M/(R+h)]
T =2•π• (R+h)/v =
=2•π•(R+h)/sqrt[G•M/(R+h].