physics question help please

Question

A 25 kg satellite orbiting a planet of an unknown mass in a circular path that has a radius of 2.0 ×106 m above the planet’s surface with a period of 8.5 h, the gravitational acceleration on the planet’s surface is 8 m/s2, what are the mass and radius of the planet?

Answer 1

The centripetal force = mv²/r if the gravitational force = G(Mm)/r²

^{The force are the same so set the equations equation to each other}

mv²/r = G(Mm)/r²

^{Cancel small mass (m) of little satellite and rearrange for M, which is mass of planet. G = Gravitational constant, not the little g of gravity.}

M = (rv²) /G. You can solve for the speed with V = (2pi r)/T

pi stand for pie as in 3.14 number

If you substitute velocity and no solve separately, then M = (4pi² r³)/(GT²)

As for the radius of the planet g = G(M)/R² , rearrange to get R which is the radius of the planet since you have M now.