Planet X rotates it the same manner as the earth, around an axis through its north and south poles, and is perfectly spherical. An astronaut who weighs 943.0 N on the earth weighs 915.0 N at the north pole of Planet X and only 850.0 N at its equator. The distance from the North Pole to the equator is 18,850 k/n, measured along the surface of Planet X.
(a) How long is the day on Planet X?
(b) If a 45,000-kg satellite is placed it a circular orbit 2000 k/n above the surface of Planet X, what will be its orbital period?