Period of satellite question (1 Viewer)

[abdog]

A satellite in orbit at a distance R from the centre of the earth has a period of 12 hours. What is the period of a satellite orbiting at a distance 3R?

ANS: 62 hours.

How do you get 62 hours?

 

[pdang]

The equation for the period is T = 2pi * sqrt(r^3/GM) which in this case equals 12
If you replaced r with 3r you would have T = 2pi * sqrt(27r^3/GM)
This can be rewritten as sqrt(27) * 2pi * sqrt(r^3/GM)
which, when you sub in the original value, is sqrt(27) * 12 = 62