A statistical study of the evolution of the orbits of long-period comets

Since orbital periods of long-period comets are much longer than those of perturbing planets (Jupiter and Saturn), energy perturbations of a comet can be regarded as a random variable which obeys a Gaussian or double exponential distribution. Starting with a given initial energy, energy states of a large number of comets are followed by a Monte Carlo method until they are lost to the solar system by dynamical expulsion or by physical disintegration. First, the lifetime distribution of comets is so computed. Secondly, the number of perihelion passages before escape or disintegration is calculated analytically and compared with the Monte Carlo result. Thirdly, and most important, the energy distribution among the cometary population is computed. (author)