(a) Asteroids have average densities of about 2500 kg/m' and radii from 470 km down to less than a kilometer. Assuming that the asteroid has a spherically symmetric mass distribution, estimate the radius of the largest asteroid from which you could escape simply by jumping off. (Hint: You can estimate your jump speed by relating it to the maximum height that you can jump on earth.)
(b) Europe, one of Jupiter's four large moons, has a radius of 1570 km. The acceleration due to gravity at its surface is 1.33 m/s'. Calculate its average density.