An astronaut lands on a new planet of radius R= 3000 km, and wants to measure its density. In order to do that, he drops a stone of unknown mass from the top of the space shuttle, which has a height of 92.5m and measures the time it takes it to reach the ground. He measures t = 5s.
a) Estimate the escape velocity from that planet?
b) Evaluate the density of the planet?
c) If the astronaut would throw the stone from the top of the shuttle horizontally with an initial velocity 10m/s, find how long would it take the stone to reach the ground? And find how far from the shuttle would it land?