Erin Fowler, University of Maryland, College Park; Derek Paley, University of Maryland College Park
Keywords: cislunar, xGEO, formation flight, interferometry, space situational awareness (SSA), space domain awareness (SDA)
Abstract:
The long-term goal of the research described here is to identify advantageous multi-spacecraft formations near Earth-Moon Lagrange points for interferometric imaging of other spacecraft in the cislunar regime, in order to offer new means of space domain awareness and spacecraft characterization in this regime. Advantageous formations will be assessed based on a metric for (u,v) plane coverage and image reconstruction as well as an instability metric to approximate the control cost for the proposed formation. Cislunar dynamics will be simulated using Matlab and Java-based code, and quantitative results will be shown in plots and tables to demonstrate the formations considered and their projected performance in an interferometric imaging mission.
The cislunar regime is of increasing interest to the space industry due to its value for applications such as astronomy, interplanetary mission staging, lunar exploration and communications, and Earth orbit insertion. However characteristic distances in the Earth-Moon system are very large. For instance, objects near the Moon are approximately ten times farther from the Earth than the farthest objects being tracked in traditional space domain awareness efforts (i.e., objects in geosynchronous Earth orbits). Due to these large distances, new space-based sensing strategies must be considered for cislunar space domain awareness and particularly for spacecraft characterization, which may require better resolution than any single optical telescope can offer, including exquisite and expensive sensors like the Hubble Space Telescope. Interferometric sensing strategies using multiple smaller and less expensive sensors promise resolution equivalent to what could be produced by a single telescope the size of the largest baseline, or distance between sensors, in the spatial direction of that baseline.
A formation flight design for interferometric imaging of resident space objects in the cislunar regime would enable novel and highly capable sensing at large distances for cislunar space domain awareness and other missions, but as of 2023 relative motion control has never been attempted near Earth-Moon Lagrange points, where Keplerian two-body astrodynamics are no longer applicable [1]. Trajectories in three-body dynamics must be identified numerically because no comprehensive analytical solution exists for the three-body equations of motion, whereas analytical solutions to the two-body equations of motion do exist and are used in the development of rendezvous algorithms. Although dynamics become nearly linear when satellites are in close proximity in Earth orbits, even at these close distances the dynamics near Lagrange points remain highly nonlinear, requiring a departure from two-body relative motion models and two-body algorithms for proximity operations. Algorithms like the well-known Hill-Clohessy-Wiltshire equations for two-body relative dynamics can be used to control relative motion in most Earth orbits, but solutions for relative motion in three-body dynamics are very specific to the chosen reference orbit (where options can include Lyapunov orbits in the plane of the Moons orbit about the Earth, Lissajous quasi-periodic orbits, halo orbits, distant retrograde orbits, and others).
Previous research related to this topic includes [2], which describes a continuous feedback control algorithm that maintains a formation of satellites in motion that is bounded relative to a halo orbit in the Sun-Earth/Moon system and shows image reconstruction and (u,v) plane coverage for interferometric satellite configurations for astronomy applications.
[1] S. Lizy-Destrez, L. Beauregard, E. Blazquez, A. Campolo, S. Manglativi, and V. Quet, Rendezvous strategies in the vicinity of earth-moon lagrangian points, Front. Astron. Space Sci., vol. 5, no. 45, 2019.
[2] K. C. Howell, L. D. Millard, Control of satellite imaging formation in multi-body regimes, Acta Astronautica, no. 64, 2009, pp. 554-570.
Date of Conference: September 19-22, 2023
Track: Cislunar SDA