A satellite moves in a irregular orbit around the Earth at a

A satellite moves in a irregular orbit around the Earth at a speed of 5.4 km/s. Determine the satellite\'s altitude above the surface of the Earth. Assume the Earth is a homogeneous sphere of radius 6370 km and mass 5.98 times 10^24 kg. The value of the universal gravitational constant is 6.67259 times 10^-11 N middot m^2/kg^2. Answer in units of km.

Solution

We are given...
v = 5400 m/s

The mass of Earth is...
M = 5.98e24 kg

Gravitational constant is...
G = 6.67259e-11 Nm2/(kg2)

For a circular orbit, here are two basic equations...
v = ( G M / r )
T = 2r / v
where r is the orbit radius of the satellite and T is the period


We get...
r = G M / v² = 3.99e7 m

Since Earth\'s radius is 6.37e6 m, we subtract to get...
altitude = 3.353e7 m = 33530 km