Question

A probe has been sent to investigate a peculiar asteroid that is 100km long and only 50m in radius. The probe's measurements reveal its mass is 5.3x1015kg. Right now, the probe is hovering about 50m from the surface of the asteroid about half way along its length. It needs to get back to the orbiter, 500m above the surface. To do that, it needs to conduct a sudden burn of its rockets to give it an initial speed away from the asteroid that will be sufficient to get it to the orbiter. You need to calculate how fast that initial speed should be.