Variation of the equator due to a highly inclined and eccentric disturber (Q966270)

Summary: The New Horizons project is currently in progress, but until recently years ago, a mission to Neptune-Triton System predicted in the mid term 2008-2013 was one of the priorities of NASA's Solar System Exploration theme. Any way, it is important to increase our knowledge on the dynamics of the inner satellites of Neptune, since according to some authors, this was a key question in the mission to Neptune-Triton system. In a previous work, we presented the expansion of the disturbing function for the dynamics of this system. Here we derive the averaged classical equations of the precession of the equator for this problem. The highly inclined and retrograde orbit of Triton makes this problem very unusual. Therefore, the classical truncations in the inclinations are not acceptable, so that the precession equations must be obtained in closed form for the inclination. With a significant mass and due to its distance from Neptune, which is continuously decreasing, Triton should exert in the future, important precession on Neptune's equator. The effects of this precession on the inner satellites are shown, including some resonant cases predicted in the future. Although Triton's orbit is almost circular, no expansion in the eccentricity is needed.