AUTHOR=Jorba-Cuscó Marc , Farrés Ariadna , Jorba Àngel 

TITLE=Two Periodic Models for the Earth-Moon System

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=4

YEAR=2018

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2018.00032

DOI=10.3389/fams.2018.00032

ISSN=2297-4687

ABSTRACT=<p>This paper discusses two alternative models to the Restricted Three Body Problem (RTBP) for the motion of a massless particle in the Earth-Moon system. These models are the Bicircular Problem (BCP) and the Quasi-Bicircular Problem (QBCP). While the RTBP is autonomous, the BCP and the QBCP are periodically time dependent due to the inclusion of the Sun's gravitational potential. Each of the two alternative models is suitable for certain regions of the phase space. More concretely, we show that the BCP is more adequate to study the dynamics near the triangular points while the QBCP is more adequate for the dynamics near the collinear points.</p>