ASTR 450
Dynamical Evolution of the Solar System

The following example shows that solar perturbations acting on distant planetary satellites rapidly destabilize their orbits. If our Moon's orbit were about twice as large as it actually is, it would follow the chaotic orbit shown here 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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