Discuss the below:
Q: On Wednesday 9th of November 2011 asteroid 2005 YU55 passed by the Earth at a distance of 323,469 km, which is closer than the Moon. There was no possibility of it hitting the Earth - this time. Just for interests sake, assume there was an asteroid heading for Earth, and it was necessary to blow it up, so that instead of a large chunk of rock potentially ploughing into a densely populated city we ended up with a spectacular meteor shower as the fragments burned up in the outer atmosphere. Also assume an astronaut lands on the asteroid to plant the explosives and then just using the strength in their legs "jumps" off again to return to their spaceship. What is the maximum radius the asteroid can have for the astronaut to be able to jump completely away from it assuming the average density of the asteroid is the same as the Earth? The astronaut, in full spacesuit can jump about half a metre on Earth.