1. The problem statement, all variables and given/known data A package of mass m sits at the equator of an airless asteroid of mass M, radius R, and spin angular speed. 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 v. We have a powerful spring whose stiffness is ks. How much must we compress the spring? (Use m for m, k_s for ks, v for v, w for , R for R, M for M, and R for R as necessary.) 2. Relevant equations -refer to 3. 3. The attempt at a solution I looked through the section in my book, but couldn't find correct equations. I assumed that you could solve for potential energy required to launch the package out of orbit then set it equal to 1/2 * k_s * s^2 and solve for s. The real problem here, I do not know how to calculate the required force/energy to launch the package so it will be at a specific speed where gravity will no longer be affecting it. My first idea (doesn't seem correct when looking at it though) combine the following equations.. v=wd w=sqrt(k_s / m) U=1/2*mv^2 d=2[tex]\pi[/tex]r to make.. U = 1/2*m*w^2*(2[tex]\pi[tex]r)^2 The problem I had with it was that I did not see any correlation to the forces of gravity and centripetal, nor its initial/final velocities.