Definition of Low Earth Orbit slotting architectures using 2D lattice flower constellations

Abstract

This work proposes the use of 2D Lattice Flower Constellations (2D-LFCs) to facilitate the design of a Low Earth Orbit (LEO) slotting system to avoid collisions between compliant satellites and to optimize the available orbital volume. Specifically, this manuscript proposes the use of concentric orbital shells of admissible ''slots" with stacked intersecting orbits that preserve a minimum separation distance between satellites at all times. The problem is formulated in mathematical terms and three approaches are explored: random constellations, single 2D-LFCs, and unions of 2D-LFCs. Each approach is evaluated in terms of several metrics including capacity, Earth coverage, orbits per shell, and symmetries. Additionally, a rough estimate for the capacity of LEO is generated, subject to certain minimum separation and station-keeping assumptions, and several trade-offs are identified to guide policy-makers interested in the adoption of a LEO slotting scheme for space traffic management.

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

“…In this work, we aim to explicitly study the nesting of concentric frozen orbital shells and to generate these shells using methods that, subject to numerical error and quasi-stability of frozen orbits, enforce periodicity and connect the generated shells to previous theoretical results on 2D Lattice Flower Constellations (2D-LFC) [8] that allow estimation of orbital capacity, reconfiguration, and optimization for minimum separation distances [9][10][11][12]. Rather than optimize individual satellite trajectories, we approach the problem by defining operational volumes, or slots, that evolve in a quasi-periodic manner and in which particular satellites can operate according to whatever control laws and internal positions they see fit.…”

Non-self-intersecting trajectories and their applications to satellite constellation design and orbital capacity

“…These optimal constellations can be obtained using the methodology proposed in Ref. [8] and are represented in Fig. 7 as black dots.…”

“…In this sense, this work aims to complement and extend the results presented in Ref. [8] for the Space Traffic Management problem by proposing a design framework to analytically estimate the maximum capacity of these systems while taking into account the minimum distance between satellites. To that end, this work focuses on the generation of satellite constellations based on circular orbits where spacecrafts are distributed following a single relative trajectory that present no self-intersections in a given rotating frame of reference.…”

“…In here instead, we follow the idea from Ref. [8] to create a system level solution based on defining slotting architectures that ensure that no conjunction will happen between satellites compliant with the defined structure. To that end, we make use of analytical constellation theory to define the positions of these slots and to analyze the results of the resultant distributions.…”

“…In particular, 2D Lattice Flower Constellations was the formulation proposed to generate optimal slotting architectures in Ref. [8].…”