A package of mass 8 kg sits at the equator of an airless asteroid of mass 4.0 1020 kg and radius 1.3 105 m.

A package of mass 8 kg sits at the equator of an airless asteroid of mass 4.0 1020 kg and radius 1.3 105 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 229 m/s. We have a large and powerful spring whose stiffness is 1.8 105 N/m. How much must we compress the spring?