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.

Communications satellites are placed in circular orbits where they stay directly over a fixed point on the equator as the Earth rotates. These are called geosynchronous orbits. The altitude of a geosynchronous orbit is 3.58 x 10⁷ m (approximately 22,00 miles). Astronomical data are inside the back cover of the book. Find the value of g at this altitude.

Communications satellites are placed in circular orbits where they stay directly over a fixed point on the equator as the Earth rotates. These are called geosynchronous orbits. The altitude of a geosynchronous orbit is 3.58 x 10⁷ m (approximately 22,00 miles). Astronomical data are inside the back cover of the book. What is the weight of a 2000 kg satellite in a geosynchronous orbit?

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?