Analysis of the Quasi-Critical Inclination under Third-Body Perturbation

Authors

1 Astronomy and Space Science Department, Faculty of Science Cairo University, Cairo, Egypt

2 Astronomy and Meteorology Department, Faculty of Science Al-Azhar University, Cairo, Egypt

3 National Research Institute of Astronomy and Geophysics (NRIAG), Cairo, Egypt

Abstract

The critical inclination orbits are important and desirable for determining space missions. This inclination is a special value of the inclination of the orbital plane that makes the argument of the perigee staying constant, on average, when some perturbations are considered. We investigated the quasi-critical inclination problem in the current study. The considered perturbations include the oblateness and rotation of the planetary satellite (main body), as well as the gravitational influence of a third body. The third body is considered to move in a circular orbit. The equations of motion are formulated using the well-established Delaunay variables. Then the short and long-period terms are then eliminated using the Lie perturbation approach. Two canonical transformations are affected to obtain the normalized form of the Hamiltonian function of the dynamical system. Finally, we carried out several numerical explorations for the two planetary satellites Callisto and our Moon. The presence of the third celestial body significantly impacts the critical inclination value.
Al-Azhar Bulletin of Science
Volume 2024, Issue 1
January and February 2024

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