The evolution of long-period comets

We study the evolution of long-period comets by numerical integration of th eir orbits, a more realistic dynamical approach than the Monte Carlo and an alytic 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 as well as 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 simil ar physical process that depletes the population of older comets. We invest igate several simple fading laws, Ne can match the observed orbit distribut ion if the fraction of comets remaining observable after m apparitions is p roportional to m(-0.6+/-0.1) (close to the fading law originally proposed b y Whipple 1962); or if approximately 95% of comets live for only a few (sim ilar to 6) returns and the remainder last indefinitely, Our results also yi eld statistics such as the expected perihelion distribution, distribution o f aphelion directions, frequency of encounters with the giant planets and t he rate of production of Halley-type comets. (C) 1999 Academic Press.