Question

A spherical asteroid has a radius of 500 km and the gravitational acceleration on the surface of the asteroid is 3 m/s?. (a) What is the minimum kinetic energy required for a 20 kg of object to escape from the asteroid? (b) At what speed will the object hit the surface of the asteroid if it is dropped from a height of 10 km?

Answer 1

a)

$E=\frac{mv^2}2=\frac{mgr}2=15~MJ.$

b)

$v=\sqrt{2gh}=245~\frac ms.$