A package of mass 7 kg sits at the equator of an airless asteroid of mass 8.0 1020 kg and radius 3.3 105 m.

A package of mass 7 kg sits at the equator of an airless asteroid of mass 8.0 1020 kg and radius 3.3 105 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 179 m/s. We have a large and powerful spring whose stiffness is 1.5 105 N/m. How much must we compress the spring?