2015/07/26 by Mayer Humi, Humi, Mayer
Engineering · Physics and Astronomy · #70F15 70F05 70F40 #Astro and Planetary Science #FOS: Physical sciences #Mathematical Physics (math-ph) #Space Physics (physics.space-ph) #Space Satellite Systems and Control #Spacecraft Dynamics and Control
paper · pdf · doi:10.48550/arxiv.1507.07245
openalex publication_date 2015/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.