Abstract
There is a large set of papers and monographs which consider the restricted three-body problem and apply the results to the orbits of satellites or spacecrafts in the Earth–Moon system. These studies ignore the impact of the Sun on these orbits. This approximation is justified for satellites in close Earth orbit. However, for satellites whose orbit is around the Sun, the Earth and the Moon or one of the Lagrange points the impact of the Sun’s presence cannot be ignored and one has to consider a four-body problem. In this paper, we derive the general equations of motion for satellites in a system that consists of a central body (Sun), first and second primaries and a satellite. These equations can be used for mission planning in general. Obvious practical example of such a system consists of the Earth and the Moon as the first and second primaries. These equations are then used in this paper to illustrate the impact of the central body on the motion of satellites around the two primaries.
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Data Availability
All MATLAB programs that were used to derive the numerical results of this paper are available upon request from the author. The only data used in this paper are in the public domain (see reference Szebehely (1967)).
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The author is indebted to the anonymous referee of one of his previous papers who suggested the topic addressed in this paper.
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Humi, M. Satellites’ orbits in the Sun–Earth–Moon system. Celest Mech Dyn Astron 135, 30 (2023). https://doi.org/10.1007/s10569-023-10146-3
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DOI: https://doi.org/10.1007/s10569-023-10146-3