An astronaut is about to explore an asteroid of average density ρ = 5000 kg/m3. He is worr...

An astronaut is about to explore an asteroid of average density ρ = 5000 kg/m3. He is worried that he may accidentally jump from its surface and float off into space. How big (i.e., what diameter) must it be before he can neglect this possibility? The astronaut knows that his mass m, including space suit, is 91 kg (200 lb). He also knows that on the earth he can raise

his center of gravity 0.6 m by jumping with his space suit on. (This is only about two feet, but try it yourself sometime, even without a space suit.) It seems reasonable to assume that the maximum energy output of his legs will be the same on the asteroid as on the earth. For simplicity assumeM >>m, such thatM does not move significantly during the action, and then check this assumption.