TERRAPUB Earth, Planets and Space

Earth, Planets Space, Vol. 51 (No. 11), pp. 1181-1194, 1999

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

Wan Xian Wang1 and N. Y. Misconi2

1Space Astronomy Laboratory, University of Florida, 1810 N.W. 6th Street, Gainesville, Florida 32609, U.S.A.
2College of Engineering, University of Central Florida, 1519 Clearlake Rd., Cocoa, Florida 32922, U.S.A.

(Received October 6, 1998; Revised July 16, 1999; Accepted August 31, 1999)

Abstract: 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 dW/dt (Wascending 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.

Corresponding author E-mail: nmisconi@mail.ucf.edu

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