You stand on a spherical asteroid of uniform density whose mass is 2 × 1016 kg and whose radius is 10 km (104 m). These are typical values for small asteroids, although some asteroids have been found...

You stand on a spherical asteroid of uniform density whose mass is 2 × 1016 kg and whose radius is 10 km (104 m). These

are typical values for small asteroids, although some asteroids have been found to have much lower average density and are

thought to be loose agglomerations of shattered rocks.

(a) How fast do you have to throw the rock so that it never comes back to the asteroid and ends up traveling at a speed

of 3 m/s when it is very far away?

(b) Sketch graphs of the kinetic energy of the rock, the gravitational potential energy of the rock plus asteroid, and their

sum, as a function of separation (distance from center of asteroid to rock). Label the graphs clearly.