A Bus Between the Planets Scientific American

Gravity-assist trajectories between Earth and Mars would reduce the cost of shuttling human crews and their equipment. A gravity-assist maneuver can be likened to a rubber ball bouncing off a wall. In this analogy, the spacecraft is like the rubber ball, and the planet is like the wall. As the ball bounces off the wall, the bounce-off velocity will be higher or lower if the wall is moving toward or away from the ball as they meet. The mathematical relation is described by a fundamental principle of Newtonian physics: conservation of momentum. The change in the ball’s momentum is balanced by an inverse change in the wall’s momentum.