8. Centripetal Forces & Gravitation

You're on a satellite orbiting an unknown planet. The only property of this planet that you know is that days are 18 hours long. Your onboard sensors show that you're orbiting at 16,000 km above the surface, with a velocity of 3 km/s. You look down and notice that you're always above the same point on that planet as you orbit around it.
Calculate the mass of the planet.

What is the approximate orbital period of a geosynchronous satellite around $Earth$?

A satellite of mass $2000$kg is placed in a geosynchronous orbit around Earth. What is the weight of the satellite at that altitude? (Assume Earth's mass $M=5.97\times 10{24}^{\mathrm{}}$kg, gravitational constant $G=6.67\times 10{-}^{11}$m${-}^2$kg${-}^2$, and Earth's radius $R=6.37\times 106^{\mathrm{}}$m.)

Which of the following is true about geostationary satellites?