How far from the surface will a particle go if it leaves the asteroid's surface with a radial speed of 1000 m/s?
The radius of the asteroid is 565000 m, and the gravitational acceleration near the surface is 2.7 m/s^2
The Attempt at a Solution
I would have thought I could just see how much energy a particle of mass m has moving at 1000 m/s, and then see what radius r would be necessary to produce the gravitation potential energy of the asteroid-particle system equal to the initial kinetic energy. When I do this, solving for r gives me a very small number.