Open Access

Quasi-analytical solutions for APSIDAL motion in the three-body problem: Sun—minor planet—Jupiter

Earth, Planets and Space201451:BF03351593

DOI: 10.1186/BF03351593

Received: 6 October 1998

Accepted: 31 August 1999

Published: 20 June 2014


This paper deals with the effect of a third body on the apsidal motion of two bodies. The specific case involves a third body-planet Jupiter and the apsidal line motion of a minor planet that orbits the Sun and has its apsidal line go through the major axis of an ellipse. The third body (Jupiter) which satisfies the Langrangian solution will affect the apsidal line motion and therefore affects the ascending and descending motions of the minor planet. In this case no analytical solutions can be obtained, and therefore specific assumptions are made along with numerical solutions. For convenience, we adopt the Lagrangian solution in the three-body problem and obtain quasi-analytical results, which are used to evaluate the effect of the planet on the dΩ/dt (Ω ascending node) of each minor planet. This method is beneficial for improving our knowledge of the orbital elements of the asteroids, and perhaps even much smaller effects such as the effects of the planets on the interplanetary dust complex. Information on the latter may be provided by using this method to investigate Jupiter’s effect on the inclination of the symmetry surface of the zodiacal dust cloud.