Surabhi Bhadauria, Purdue University; Carolin Frueh, Purdue University
Keywords: SDA, cislunar, optical observations
Abstract:
The missions into the cislunar realm, the space from the Earth including the lunar region, are about to increase in the foreseeable future. This development imposes a need for space domain awareness also in this spatial domain. Objects of interest include active spacecraft and space debris alike. The cislunar region is vast and its dynamics are complex, which allows for a plethora of possible orbits. In order to survey the entire region and establish situational awareness space-based and ground-based observers needs to be used. However, the challenge is the enormous phase space of space-based and ground-based observers, observation geometries, and configurations that is possible to be realized in this regime. The phase space is limited only insignificantly when restricting to optical sensors or other specific sensor types. A brute force optimization is hence impossible. Heuristic intuition-inspired initial constellation concepts that are usually a first step in near-Earth constellation design are likely to fail in the absence of conic regions.
In the past, single orbits, such as DROs, Lyapunov, resonant orbits, and others have been tested in a more or less haphazardous approach. A hypothetical space-based sensor has been placed in one or more of those orbits, followed by propagating the orbits numerically and evaluating the observation conditions for each specific epoch at a time and determining regions in which objects of a given size and geometry may be detectable and other regions where they are in principle undetectable. However, those classical orbits mentioned before are in large parts known because they have been proposed and explored for missions and not for the task at hand, to establish situational awareness.
In addition, even when using those orbits, precise numeric propagation is time-consuming, especially when exploring many orbits and configurations. Classically, the circular restricted three-body problem (CR3BP) has been used with its simplifying assumptions to speed up computation times. The three bodies are then the Earth, the Moon, and the spacecraft. While these, for low AMR objects, are the main perturbing forces in the cislunar regime, the CR3BP is not suitable to explore optical observation geometries, as phase angle information is missing.
In this paper, we propose the use of the bicircular restricted four-body problem (BCR4BP), with the bodies being the Earth, the Moon, the Sun and the spacecraft. We propose to introducing a negligible sun mass. This way the exact CR3BP orbits can be reproduced, but the geometry to the sun is preserved. The use of the BCR4BP allows rapid exploration of the parts of the vast phase space for observation geometries. Furthermore, we are reversing the problem, in an all-to-all configuration. Instead of exploring one orbit at a time looking at a grid of possible locations in the cislunar space of hypothetical target objects, we are using the full force of the BCR4BP to create a map for every grid point on how many other grid points can be seen at a given time. The epoch dependence, which is needed for the illumination and observation conditions, is naturally part of the BCR4BP and is absent in the CR3BP. The results of the BCR4BP are compared for selected cases with a high fidelity propagation using spice ephemeris data for all celestial body locations.
Date of Conference: September 27-20, 2022
Track: Cislunar SSA