Designing a Reference Trajectory for Frozen Repeat Near-Equatorial Low Earth Orbits

Abstract

Numerical techniques for designing frozen repeat orbits as reference trajectories have been extensively studied for polar orbit missions. For near-equatorial orbits, larger perturbing forces are experienced at lower inclinations. The greater perturbations make such near-equatorial orbits’ long-periodic behavior much more sensitive to changes in initial conditions. Thus, a more careful selection of optimization parameters and a longer convergence time is often required. This makes the numerical optimization stage for a near-equatorial orbit more delicate. Past proven techniques involved a preliminary estimate, a first optimization for the initial osculating elements, and a second optimization to ensure end-cycle continuity. This paper first reviews these techniques specific to near-equatorial frozen repeat orbit design and evaluates them in comparison with polar orbit designs. Then, this paper counterproposes a more efficient orbit design scheme that reduces the design process from two optimizations to only one optimization with a filtering stage. As a result, the orbit design process is much more efficient and less prone to convergence issues, especially when addressing orbit end-cycle discontinuity.