Orbital Motion Around the Collinear Libration Points of the Restricted Three-Body Problem
A. H. Ibrahim
Department of Astronomy and Meterology, Faculty of Science, Al-Azhar University, Egypt.
M. N. Ismail *
Department of Astronomy and Meterology, Faculty of Science, Al-Azhar University, Egypt.
A. S. Zaghrout
Department of Mathematics, Faculty of Science (Girls), Al-Azhar University, Egypt.
S. H. Younis
Department of Mathematics, Faculty of Science (Girls), Al-Azhar University, Egypt.
M. O. El Shikh
Department of Mathematics, Faculty of Science (Girls), Al Qassim University, Saudi Arabia.
*Author to whom correspondence should be addressed.
Abstract
In this work, the special solutions of the Restricted Three-Body Problem (RTBP) are presented which specify the locations of the equilibrium points. The periodic orbits around these libration points are obtained analytically and numerically. The Lissajous orbits around the collinear libration points are focused in this work. Earth-Moon-Spacecraft system is carried out to illustrate this study.
Keywords: Lissajous orbits, periodic orbits, libration points, restricted three-body problem