Parametric Approach for Satellite Relative Orbit Designs and Constellations

This paper proposes a dynamics solution that creates an identical constellation pattern of multiple satellites with the parameterization of relative motion dynamics. The parameterization illustrates that the complexity of relative motion dynamics is interpreted by a Ptolemaic model of an epicycle and deferent system. All possible relative orbits can be represented by a hypo-epi curve or a deformed curve on the x-y plane and a simple z-axis harmonic oscillator motion. The designed relative orbits are used to create identical constellation patterns of multiple satellites, called parametric constellations in this study, by closed-form formulas and satellite phasing rules obtained from the geometrical relationship and periodic conditions. In conclusion, the resulting solution contributes to solving technical dynamics and tracking problems by simply designing complex relative motions in free space.