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Secular perturbations between a retrograde body and a prograde body

Vistas in Astronomy
Publication Date
DOI: 10.1016/0083-6656(88)90166-3


Abstract With use of secular perturbation theory, we can discuss a long-periodic behaviour of a system of a central body and prograde bodies that have small eccentricities and inclinations (Brouwer and Clemence, 1961). Classical secular perturbation theory, however, cannot treat a system of one retrograde body and one prograde body by simply interpreting the inclination of the retrograde body as nearly 180 degrees for the following reasons: 1. 1)the classical development of the disturbing function is not applicable to the retrograde case, 2. 2)the main term in the secular part between the retrograde body and the prograde body is different from that between two prograde bodies, 3. 3)the linearized equations of motion for the retrograde body have a different form from that for the prograde body. At first we study a system of a central body and one retrograde body and one prograde body, and extend the secular perturbation theory for a system of a central body and two bodies to a system of a central body and an arbitrary number of bodies that consist of both retrograde and prograde bodies. Our theory is compared with numerically integrated orbits. The theory presented here is applicable to the system of Jupiter and Saturn's satellites, and the system of outer planets which includes a hypothetical retrograde planet X.

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