Help please?

Question

A satellite cirlces planet Roton every 2.8 h in an orbit having a radius of 1.2x10^7 m. If the radius of Roton is 5.0x10^6 m, what is the magnitude of the free fall acceleration on the surface of Roton?

Answer 1

Calculate the satellites velocity as v = 2πr/T where r is the radius of it's orbit (in meters) and T is its orbital period (in seconds). Then calculate the centripital accelleration of gravity (at 1.2*10^7 meters) as a = v²/r. Now calculate the ratio of the orbit of the satellite to the radius of the planet, square that, and you'll have the acceleration at the surface (since gravity varies as the square of distance)


Doug