Satellite orbits and fractional mechanics
Keywords:
oblate spheroid, quadratic drag, equatorial orbits, analytical solutions, Caputo derivativeAbstract
The motion of a satellite or a spacecraft in the vicinity of the Earth is subject to numerous perturbations from a variety of sources some of which are transitory or “random”. It is not feasible to incorporate all these perturbations analytically within the framework of Newton’s second law. In this paper we put forward the proposition that fractional derivatives can provide a lumped sum parameter approach to incorporate all these interactions based on the “historical trajectory data” of the satellite. This may lead to longer (in time) and more accurate prediction of its trajectory. To demonstrate (theoretically) the feasibility of this conjecture we consider two test cases. The first is for the motion of a satellite under the influence of quadratic drag. The second is for the motion of a satellite in the gravitational field of oblate Earth. In both cases we show that fractional derivatives models can lead to results which are very close to the numerical solutions which incorporate the impact of these perturbations on the motion of the satellite.
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