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T. Yokoyama, E.P. Marinho (UNESP)
Due to the tides the orbits of Phobos and Triton are spiralling in towards their host planets. On the contrary, our Moon is being driven away from the Earth. Most probably, in the past many other particles experienced similar variations. During this evolution, the semimajor axis assumes several values which can cause significant resonances, involving the node, pericenter and the longitude of the Sun. Recently Touma and Wisdom showed the decisive effect played by evection and iviction resonances in the Earth-Moon system. In this work we derive the averaged equations of a satellite disturbed by the Sun and the oblateness of the planet. Neglecting higher order (third) in the ratio of the distances, all possible resonances are studied. In general we are used to small values of the ecliptic. However in the past, the obliquity of the inner planets could have attained very high values (Laskar et all). Then taking into account large values of the obliquity we find some significant variations in the inclinations, besides others in the eccentricities. If some empirical law of the variation of the semimajor axis is assumed, then with the averaged equations we can easily see the jumps in these elements when the satellite crosses some resonance. Finally we show the possible variations in the Phobos' eccentricity since it will cross the evection resonance in the future. We also show some possible and significant resonances faced by Triton in the past.
For partial financial support we thank FAPESP.