Evolution of Orbits and Encounters of Distant Planetary Satellites. Study Tools and Examples

摘要

This study of the orbital evolution and encounters of distant satellites of planets is aimed at determining their origin. It is also important for understanding the distribution of matter in the early stages of evolution of the Solar System. The mutual encounter of satellites is very weak because of their small sizes and masses. However, at very large time intervals, mutual encounter can be quite close to significantly changing the orbits of satellites. In order to study these factors, we have developed a special method and computer programs. For 107 distant satellites of Jupiter, Saturn, Uranus, and Neptune, motion parameters have been determined using observational data. On the basis of these parameters, a numerical integration of the equations of motion of the satellites has been carried out in time intervals of several thousand years. Using the original method of frequency analysis, we found rather simple analytical functions that correspond to the results of the numerical integration and make it possible to calculate orbital parameters at any time during a long interval. These tools make it possible to conduct extensive studies of changes in the form and relative position in space of the orbits of distant satellites of Jupiter, Saturn, Uranus, and Neptune. Several examples illustrate the possibilities offered by these tools. The computer software in the form of a service ephemeris of satellite orbits over a long interval of time is available via the Internet on the website of the State Astronomical Institute of the Moscow State University.