Physics rotating planet?

Question

Planet X rotates in the same manner as the earth, around an axis through its north and south poles, and is perfectly spherical. An astronaut who weighs w on the earth weighs w_1 at the north pole of Planet X and only w_2 at its equator. The distance from the north pole to the equator is L, measured along the surface of Planet X.

a) How long is the day on Planet X? Use g for free fall acceleration
b) If a m satellite is placed in a circular orbit h above the surface of Planet X, what will be its orbital period? Take free fall acceleration to be g

Answer 1

Get r from 4L=2 pr r
then
mv^2/r=w1-w2 where v=2 pi f r where f=frequency