#
Solar Escape as a Three-Body Problem

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John Lindner

Colors code escape distances for different initial velocities (Am. Journ. Phys. 76, 347 (2008)).

One of our spins on the 3-body problem: What is the easiest direction to
shoot a projectile out of the solar system, modeled as a planar circular
restricted 3-body problem (1 infinitesimal mass + 2 finite masses)? We have
created, most recently on a cluster of Mac OS X computers running under Xgrid,
initial-conditions plots that dramatically illustrate the dynamical complexity
of this problem; escape isn't so easy. For small (pseudo)energies, the
projectile escapes rapidly; for large (pseudo)energies it is trapped; in
between, its orbits are chaotic and arbitrarily complicated.

Through further computation and theoretical analysis, we hope to elucidate the
structures of the escape set, especially its spiral, elliptical, and hyperbolic
points. Many generalizations are possible, including incorporating Earth's spin,
exploiting the third dimension. Most cool might be attempting to (arbitrarily?!)
reduce the minimum escape speed by introducing and interacting with a second
projectile.