Planar Motion

A space vehicle orbiting the Earth has large potential and kinetic energy—for each kg in a low Earth orbit the total energy amounts to about 30 MJ. This energy content will be even higher for vehicles entering the Earth’s sphere of influence at hyperbolic velocities, typically associated with return flights from the Moon or interplanetary trajectories from Mars. When the vehicle needs to return to Earth, it has to reduce this large energy to the level of potential energy that the vehicle has after landing on the surface of Earth, and—what is even more constraining—with zero relative velocity.