A Method for Generating Closely Packed Orbital Shells and the Implication on Orbital Capacity

Abstract: Shell-wise orbital slotting in Low Earth Orbit (LEO) can improve space safety, simplify space traffic coordination and management, and optimize orbital capacity. This paper describes two methods to generate 2D Lattice Flower Constellations (2D-LFCs) that are defined with respect to either an arbitrary degree or an arbitrary degree and order Earth geopotential. By generating shells that are quasi-periodic and frozen with respect to the Earth geopotential, it is possible to safely stack shells with vertical separation distances smaller than the osculating variation in semi-major axis of each shell or a corresponding Keplerian 2D-LFC propagated under an aspherical geopotential. This helps mitigate the single inclination per shell requirement in prior work by admitting more shells for a given orbital volume while retaining self-safe phasing in each shell. These methods exploit previous work on the Time Distribution Constellation formulation and designs of closed 2D-LFCs under arbitrary Earth geopotentials using repeating ground track orbits. Factors that influence the widths and shapes of these frozen shells are identified. Simplified formulas for estimating shell geometry and thickness are presented. It is shown that sequencing shells to group similar or ascending inclinations improves capacity versus arbitrary inclination ordering.