Consider a spaceship, initially at rest on the surface of a planet that has no atmosphere. It takes off with constant force from thrust. The fuel mass decreases linearly with time, and the rocket accelerates directly away from the planet (no curving off orbit the planet). Use GMm/r^2 for gravitational force. Produce an equation describing the rocket's distance from the planet for all time from 0 when the rocket starts to burn fuel until it runs out of fuel. I came up with this problem a while ago for fun, but it turned out to be much harder than I had imagined. The method that got me the farthest is energy density.