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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