A package of mass 7 kg sits on an airless asteroid of mass 7.0 × 1020 kg and radius 8.6 × 105 m. We want to launch the package in such a way that it will never come back, and when it is very far from the asteroid it will be traveling with speed 250 m/s. We have a large and powerful spring whose stiffness is 2.8 × 105 N/m. How much must we compress the spring?

It may seem strange that the selected velocity does not depend on either the mass or the charge of the particle. (for example, would the velocity of a neutral particle be selected by passage through this device? ) the explanation of this is that the mass and the charge control the resolution of the device--particles with the wrong velocity will be accelerated away from the straight line and will not pass through the exit slit. if the acceleration depends strongly on the velocity, then particles with just slightly wrong velocities will feel a substantial transverse acceleration and will not exit the selector. because the acc