Parametric design method for general periodic relative orbits

This paper explores the orbital characteristics and design challenges of general Periodic Relative Orbits (PROs). It analyzes the characteristics of general PROs and proposes an efficient analytical design method with clearly defined physical parameters. First, the initial conditions for the formation of general PROs expressed in terms of an intermediate variable are obtained through a detailed analysis of the relative orbital dynamics, and the orbital characteristics of general PROs are investigated based on this intermediate variable. Then, based on the study of the orbital characteristics, an efficient analytical design method for general PROs is proposed using the orbital plane orientation and relative distance as the design parameters. Finally, the algorithm is quantitatively evaluated and validated by introducing a design example for general PROs. The simulation results validate the theoretical analysis.