Periodic Orbits of the Restricted Three-Body Problem Based on the Mass Distribution of Saturn’s Regular Moons

Abstract

This paper uses the Kolmogorov–Smirnov test to perform a fitting analysis on the mass data of Saturn’s regular moons and found that the lognormal distribution is its best-fitting distribution with an extremely high p-value of 0.9889. Moreover, novel dynamic equations for the variable-mass restricted three-body problem are established based on the newly discovered distribution of mass data, rather than the empirical Jeans’ law, and the Lindstedt–Poincaré perturbation method was used to give the approximate analytical periodic orbits near the Lagrangian point L3. Furthermore, this paper also discusses the influence of the three-body gravitational interaction parameter, the variable-mass parameter of the third body, and the scale parameter in the statistical results on the periodic orbits and the position of the Lagrangian point L3 through numerical simulation.

Determination of the doubly symmetric periodic orbits in the restricted three-body problem and Hill’s lunar problem

“…Qi and Xu (2015) considered the long-term behavior of the spatial orbits near the Moon in the earth-moon-spacecraft CRTBP and calculated some spatial periodic orbits. Cheng and Gao (2022) studied the lognormal distribution of the mass of Saturn's regular moons by the nonparameter test method in statistics, and obtained the analytical expression of the approximate periodic orbit near the Lagrangian point L 3 by the Lindstedt-Poincaré technique. Also, the influence of some parameters on the periodic orbits is also discussed.…”