Lie series solution of the bicircular problem

The present work performs a semi-analytical solution for the orbit of an infinitesimal particle in the framework of the bicircular Sun-Earth-Moon system. In particular, Lie series technique is applied to find the solution of the equations of motion of bicircular Sun-Earth-Moon system with radiating bigger primary. To apply Lie-series technique, the second order system of ordinary differential equations has been reduced to the corresponding first order system. Then, a set of recurrence relations is obtained in the Lie series solutions of the bicircular model (BCM) and graphical representations of the orbit for short, intermediate and long time are shown. Moreover, we study the effect of the radiation parameter on the orbit of the massless body and demonstrate that this parameter as well as the initial conditions affect its size. Specifically, it is observed that the trajectory enlarges further when the values of the radiation parameter increase while additionally its size enlarges or compacts according to the selected set of initial conditions.

Automated summary

This study provides a semi-analytical solution for the orbit of an infinitesimal particle in the bicircular Sun-Earth-Moon system, using Lie series technique. It explores the impact of the radiation parameter and initial conditions on the trajectory size, showing that the trajectory enlarges with higher radiation parameter values and adjusts according to different initial conditions.