Review of the Theories of Motion of the Natural Satellites

Abstract

Most of the natural satellites of the planets of the solar system may be put into one of three main groups, according as to which of three main influences dominate the perturbation of their motion from Keplerian motion about the primary planet. The first of these is the attraction of the Sun, which governs the perturbations of the Moon's motion about the Earth, and those of the outer satellites of Jupiter (satellites VI to XIII), and Saturn's satellite Phoebe. The second is the departure of the gravitational field of the planet from that of a spherically symmetric body (the “figure terms”), and this governs the perturbations of the two satellites of Mars, Jupiter's satellite Amalthea (V), Neptune's satellite Triton, is probably the most important influence on Uranus' satellites, and is important, though not dominant, for the inner satellites of Saturn. The third influence is the mutual attraction of the satellites themselves. An order of magnitude argument suggests that periodic perturbations from this cause could scarcely be expected to be measureable from Earth, were it not that the frequent appearance of small-integer near-commensurabilities of pairs of orbital periods, and the consequent argumentation of the associated perturbations by a variety of types of resonance effects, in the systems of Jupiter and Saturn, causes mutual perturbations to dominate the orbital theories of three of the four great satellites of Jupiter, and six of the nine satellites of Saturn, and enables the masses of most of the satellites involved to be determined with otherwise unexpected relative precision (in some favourable cases, of the order of one per-cent) from Earth based data. Let us now consider the satellite systems of each of the outer planets in a little more detail.