English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

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 d /dt ( 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. line. Specifically, we apply our analysis of this problem to situations in the solar system in an effort to further refine our knowledge of the gravitational effects of the planet Jupiter on other minor planets such as the asteroids. Later, it may be possible to delineate minute effects of Jupiter on the orbital elements of the symmetry surface of the zodiacal dust cloud. The three-body problem here is assumed to be the Sun, an orbiting dust particle with its distance from the Sun much greater than the Sun's diameter, and the third body being Jupiter. Kopal (1959) showed that the effect of the third body will be very complicated and that analytical solutions cannot be obtained. In dealing with the effect of a third body (that satisfies the Lagrangian solution) on the three-body problem, we make some specific assumptions and use numerical calculations. But before going into the mathematical details we give here a short summary of the importance of this work in evaluating the motion of the apsidal line (which is the major axis of the ellipse of the minor planet to the Sun ) and searching for minute gravitational perturbations of Jupiter on the ascending node of the "Symmetry Surface" of the zodiacal cloud.

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