The Loss of Long-Period Comets from the Solar System

Abstract
The changes in orbital binding-energy of comets through planetary action are comparable with these energies, and can be estimated from the few cases for which detailed paths have been computed. They have also been found theoretically by means of a restricted three-body problem, and are such that a steady loss of long-period comets from the solar system must result. Not only are the known comets probably less than 1 in a 1,000 of the whole family, but it is not feasible to follow adequately the successive orbits of individual comets. The problem has therefore been treated statistically, with successive energy-changes regarded as steps in a random-walk process, but that the interval between successive returns varies inversely as the three-halves power of the energy renders the mathematical problem complicated. The later stages of development of a group of comets can be found by means of asymptotic theory, while the use of Brownian theory is also considered. Detailed development of a set of comets of the same initial binding-energies has been studied by Monte-Carlo analysis for a number of cases with the energy-changes selected randomly from an appropriate distribution. Repeated runs show close agreement in the proportions of comets remaining after given intervals of time. After M million years, the percentage remaining tends to about 20 M−2/3. If new comets are being added at an independent rate, the total number will increase statistically as the cube-root of the age of the solar system, and it appears that the most likely number of long-period comets at present is between 2 and 3 million.

This publication has 0 references indexed in Scilit: