Analysis of motion in RTBP with variable mass based on Loglogistic distribution

Abstract

Recent literature has stated that the physical characteristics of natural satellites in Jupiter’s Ananke and Carme groups, such as mass, exhibit the same statistical law, with the best-fitting distribution being a Loglogistic distribution. This paper establishes dynamical equations for the variable-mass restricted three-body problem based on this new statistical law. In addition to discussing the influence of the Jacobian constant related to the system energy on the accessible region of the third body, it also uses the Lindstedt–Poincaré perturbation method to give an analytical periodic orbit of second- and third-order around the triangular Lagrangian point. Numerical simulations show that as the value of the variable mass parameter of the third body becomes smaller, the corresponding periodic orbit is affected less and less.