Optimal Exit: Solar Escape as a Restricted 3-body Problem

Christine Leidel, Nicholas Johann Harmon, John F. Lindner

We analyze solar escape as a special case of the restricted three-body problem. We systematically vary the parameters of our model solar system to show how optimal launch angle and minimum escape speed depend on the mass and size of Earth. In some cases, it is best to launch near the direction of Earth's motion, but slightly outward; in other cases, it is best to launch near the perpendicular to Earth's motion, but inward, toward Sun (so as to obtain a solar gravity assist). Between direct escapes for high launch speeds and trapped trajectories for low launch speeds is an irregular band of chaotic orbits that reveals something of the true complexity of solar escape and of the three-body problem. This research was partially supported by NSF-DMR 9987850.