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Optimizing Solar Escape: A 3-Body Problem

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N. J. Harmon, J. F. Lindner

Using a custom computer program Escape!, we study the trajectory of an
infinitesimal ballistic projectile escaping an arbitrary binary solar system,
an instance of the circular planar restricted 3-body problem.
Our results confirm and generalize previous work regarding escape from Earth and Sun.

The minimum direct escape speed results from a compromise between launching tangentially,
which optimizes the boost from Earth's motion, and launching radially,
which minimizes the distance to escape Sun's gravity. For different binary mass fractions,
different initial directions yield the minimum escape speed. For some mass fractions,
a direct escape is optimal; for others, a "slingshot" escape is optimal.