4. The Evolution of Comet Orbits as Perturbed by Uranus and Neptune
International Astronomical Union Colloquium
When the perturbing planets are Uranus and Neptune, the perturbations on comets are so much weaker than with Jupiter and Saturn that a study of the comets' orbital evolution, using exact numerical integration, would require 200 times more revolutions. This is hardly practical with present computers. Here we describe results with a simulation approach, the "Monte Carlo (random walk) method." The proper distribution shape for the perturbations in energy are found from a few thousand numerical
... usand numerical integrations, then this distribution of perturbations is applied to millions of simulated orbit-revolutions. This method reproduces earlier Jupiter results in 1/500 the former computation time. We find that Neptune can capture near-parabolic comets with perihelia in the range of 30 to 34 AU, increasing their 1/a-values and decreasing their perihelia until they reach a region where Uranus can interact. Uranus in turn passes some of these on to Saturn, who passes some to Jupiter. Ultimately a few reach the orbits of the visible short-period comets. The process requires about 200,000 comet orbit-revolutions, 4 × 108years, and the efficiency is one in 6000. The rest of the comets are ejected on hyperbolic orbits.