Satellite Orbits and Relative Motion in Levi-Civita Coordinates

Mayer Humi

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arXiv · 1507.07245

Satellite Orbits and Relative Motion in Levi-Civita Coordinates

Mayer Humi

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Abstract

In this paper we consider satellite trajectories in central force field with quadratic drag using two formalisms. The first using polar coordinates in which the angular momentum plays a dominant role. The second is in Levi-Civita coordinates in which the energy plays a central role. We then unify these two formalisms by introducing polar coordinates in Levi-Civita space and derive a new equation for satellite orbits in which energy and and angular momentum are on equal footing {and thus characterize the orbit by its two invariants}. In the second part of the paper we derive in Levi-Civita coordinates a linearized equation for the relative motion of two satellites whose trajectories are in the same plane. We carry out also a numerical verification of these equations.

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Mayer Humi. 2015-07-26. Satellite Orbits and Relative Motion in Levi-Civita Coordinates. https://arxiv.org/abs/1507.07245

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