Abstract
The dynamics of satellites formation is of great interest for the space mission. This work discusses a more efficient model of the relative motion dynamics of satellites formation. The model is based on employing the concepts restricted three-body problem (R3BP) and for more accuracy, it considers the effects of both oblateness and radiation pressure on deputy relative motion w.r.t the chief satellite. A model of deputy relative motion w.r.t the chief satellite is derived in the local-vertical local-horizontal system and simplified assuming the concept of the circular restricted three-body problem (CR3BP). The deputy equations of motion were rewritten in the form of recurrence relations and solved numerically using the Lie series approach. Assuming that the formation is revolving around the Moon in the Earth-Moon system, the effects of both oblateness and radiation pressure on the deputy satellite orbit were assessed through a particular example of satellites formation. A comparison between the perturbed and unperturbed R3BP shows a significant difference in the deputy relative position that has to be considered for the formation dynamics.
Highlights
Parallel to the start of the space programs, the study of spacecraft relative dynamics became one of the most important aspects in designing and analyzing space missions
The model is based on employing the concepts restricted three-body problem (R3BP) and for more accuracy, it considers the effects of both oblateness and radiation pressure on deputy relative motion w.r.t the chief satellite
The current study aims to get a more accurate formulation of the relative motion employing the perturbed restricted three-body problem
Summary
Parallel to the start of the space programs, the study of spacecraft relative dynamics became one of the most important aspects in designing and analyzing space missions. The most famous models of relative motion, Clohessy-Wiltshire and Tschauner-Hempel, have been used to analyze relative guidance, navigation and control systems These two models assumed that the spacecraft relative dis-. They assume pure Kepler motion (e.g. two-body problem without including any perturbations) [1] [2]. In 2019, Giovanni Franzini and Mario Innocenti studied the relative motion dynamics using the classical restricted three-body problem (unperturbed problem). Many authors are interested in modelling the formation dynamics employing the restricted three-body problem and studied the relative motion around the libration points [10] [11] [12] [13] [14]. The numerical application is performed assuming a circular three-dimensional problem
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