The Evolution of Long-Period Comets

We study the evolution of long-period comets by numerical integration of their orbits, a more realistic approach than the Monte Carlo and analytic methods previously used to study this problem. We follow the comets from their origin in the Oort cloud until their final escape or destruction, in a model solar system consisting of the Sun, the four giant planets and the Galactic tide. We also examine the effects of nongravitational forces and the gravitational forces from a hypothetical solar companion or circumsolar disk. We confirm the conclusion of Oort and other investigators that the observed distribution of long-period comet orbits does not match the expected steady-state distribution unless there is fading or some similar process that depletes the population of older comets. We investigate several simple fading laws. We can match the observed orbit distribution if the fraction of comets remaining observable after m apparitions is ∝ m (close to the fading law originally proposed by Whipple 1962); or if approximately 95% of comets live for only a few (∼ 6) returns and the remainder last indefinitely. Our results also yield statistics such as the expected perihelion distribution, distribution of aphelion directions, frequency of encounters with the giant planets and the rate of production of Halley-type comets.