The ``Escape Set" elucidates chaos in the restricted three-body problem

We analyze solar escape as a special case of the restricted three-body problem. By numerically integrating the trajectories of millions of particles shot from Earth with different initial conditions, we determine their displacements after a fixed time. On a polar plot of (pseudo) energy radially and initial direction angularly, we color code these distances. The resulting ``Escape Set'' elucidates chaos in the three-body problem in the same way that the Mandelbrot set illustrates complexity in nonlinear maps: at low energies, the projectile is trapped; at high energies, it easily escapes; at intermediate energies, it executes intricate chaotic orbits with unbounded excursions and repeated returns. We acknowledge support from NSF-REU grant DMR 0243811.