Method for Generating Closely Packed Orbital Shells and Orbital Capacity Implications

Abstract

Shell-wise orbital coordination in low Earth orbit can improve space safety, simplify space traffic coordination and management, and optimize orbital capacity. This work describes two methods to generate 2D lattice flower constellations (2D-LFCs) that are defined with respect to either an arbitrary zonal, or zonal, sectoral, and tesseral Earth geopotential. By generating orbital shells that are periodic with respect to the Earth geopotential, it is possible to safely stack shells with vertical separation distances smaller than the osculating variation in semimajor axis and radial distance of each shell, or a corresponding Keplerian 2D-LFC propagated under an aspherical geopotential. These methods exploit previous work on constellations based on time distributions and designs of closed 2D-LFCs under arbitrary Earth geopotentials using repeating ground track orbits. Factors that influence the widths and shapes of these shells are identified. Additionally, simplified formulas for estimating shell geometry and thickness are presented. Based on these results, it is shown that geopotential-aware periodic orbital shells significantly increase the number of admissible orbital shells while preserving shell separation. Finally, this work shows that sequencing shells to group similar or ascending inclinations can further improve capacity versus arbitrary inclination ordering, particularly for smaller shell separation distances.