Solve the below:
Gravitation, centripetal acceleration, and weight
Q: Planet X rotates in the same manner as the earth, around an azis 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 quator is 18,850 km, measured along the surface of Planet X.
1. How long is the day on Planet X?
2. If a 45,000 kg satellite is placed in a cicular orbit 2000 km above the surface of Planet X, what will be its orbital period?