Abstract
The relative motion of an outline of the rendezvous problem has been studied by assuming that the chief satellite is in circular symmetric orbits. The legitimacy of perturbation techniques and nonlinear relative motion are investigated. The deputy satellite equations of motion with respect to the fixed references at the center of the chief satellite are nonlinear in the general case. We found the periodic solutions of the linear relative motion satellite and for the nonlinear relative motion satellite using the Lindstedt–Poincaré technique. Comparisons among the analytical solutions of linear and nonlinear motions and the obtained solution by the numerical integration of the explicit Euler method for both motions are investigated. We demonstrate that both analytical and numerical solutions of linear motion are symmetric periodic. However, the solutions of nonlinear motion obtained by the Lindstedt–Poincaré technique are periodic and the numerical solutions obtained by integration by using explicit Euler method are non-periodic. Thus, the Lindstedt–Poincaré technique is recommended for designing the periodic solutions. Furthermore, a comparison between linear and nonlinear analytical solutions of relative motion is investigated graphically.
Highlights
This view can be applied for the model of relative motion satellite, because the relative distance is very small compared to the initial position of the target satellite
We studied the relative motion of an outline of the space rendezvous problem, assuming that the chief satellite was in circular symmetric orbits
It was found that the equations that describe the motion of the deputy satellite with respect to the references fixed at the center of the chief satellite is nonlinear in the general case
Summary
Relative motion is considered one of the fundamental problems in orbital mechanics, it has different applications that arise in the literature of astrodynamics for rendezvous and formation of flying satellites. Most applications to relative motion are in the formation satellites, which have a considerable significance, because the use of a large number of satellites with low impact satellites running, in a concrete style, could introduce a better outcome than a single high implementation satellite. These formations do not require a big cost, which means a great opportunity for space mission success with more resiliency. Satellite formations have good benefits for Earth observation of space missions, where the group distribution of low resolution devices, operating in conjunction with each other, may provide a higher overall information quality than a single high resolution device
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