Question

You regularly fly your spaceship to a space station in orbit around Planet X. The planet has a mass of 4.0x 10^24 kg, and the space station orbits 9.9 x 10^4 m above the surface. From these trips, you know you need to go at least 1089 m/s to break free of the planet. What is the radius of Planet X? Round you answer to the nearest whole number.

Answer 1

$$v^2=\frac{2MG}{R+h}\\1089^2=\frac{2(4\cdot10^{24})(6.67\cdot10^{-11})}{R+9.9\cdot10^{4}}\\R=4.5\cdot10^{8}\ m$$