# ASTR 450

Dynamical Evolution of the Solar System

The following example shows that solar perturbations acting on
planetary satellites on large orbits rapidly destabilize the
orbits. If the moon's orbit were about twice as large as it actually
is, it would follow a chaotic orbit which would bring it within a few
thousand miles of the Earth! Ultimately it would escape onto an
independent orbit around the Sun. The blue orbital trajectory cannot
cross the red curves, which are constraints imposed by the Jacobi
Constant, a combination of energy and angular momentum. The Sun is
located along the positive x-axis. The green crosses are the Lagrange
Points where the Earth's gravity balances the tidal forces from the
Sun.

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Last modified: Wed Sep 4 10:29:27 2002