Abstract
This paper discusses two alternative models to the Restricted Three Body Problem (RTBP) for the study 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.
Highlights
During the last years, the scientific community has increased its interest in the natural motions occurring in the Earth-Moon system
Perhaps the most illustrative example for the purpose of this work is the existence of the Trojan asteroids that can be predicted using the effective stability of the triangular points of the Sun-Jupiter Restricted Three Body Problem (RTBP)
The Bicircular Problem (BCP) is a periodic perturbation of the RTBP that takes into account the direct gravitational effect of a third primary on the particle
Summary
The scientific community has increased its interest in the natural motions occurring in the Earth-Moon system. The BCP is a periodic perturbation of the RTBP that takes into account the direct gravitational effect of a third primary (in our case, Sun) on the particle This model captures the non-stable character of the triangular points. To build the QBCP it is necessary to compute a quasi-bicircular solution of the three body problem, in this case, for the Earth-Moon-Sun case. We believe that the value of this work is, precisely, giving a wide perspective and help the interested reader to choose a suitable simple model to face a first exploration related to a problem concerning the Earth-Moon system. The advantage of this model with respect to the RTBP is that it captures the unstable character of the triangular points in the real system.
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