Alexander Koenig, Massachusetts Institute of Technology; Phillip Cunio, ExoAnalytic Solutions; Juliana Chew, Massachusetts Institute of Technology
Keywords: Cislunar SSA, orbital mechanics, orbital regimes, libration points, three-body problem
Abstract:
To achieve cislunar SSA, we require adequate coverage of and revisit rates for all of cislunar space in order to acquire and maintain custody of objects of interest. We have the intuitive sense that not all areas of cislunar space should be weighted equally in terms of this coverage, however — the depth of the coverage should vary depending on parameters such as proximity to space-based infrastructure, or potential risk posed by the objects in question. To transform this qualitative sense of weighting into a quantitative one, we can turn to a risk map, which is the subject of this abstract. The risk map captures the time it would take an object at any position in cislunar space to reach a set of a few well-defined destinations where we would expect relevant infrastructure to reside. This time-to-contact duration is the theoretical minimum time it would take for an object in a given region to reach any individual target in the set of space-based infrastructure we will want to protect.
Say, for example, we have an unknown spacecraft with a presumed 650 m/s delta-V capability somewhere in the vicinity of the L4 libration point. Knowing its initial orbit, we can use a Lambert solver to determine how long it would require to reach any region that holds relevant infrastructure. If we do not know its initial orbit, we can perform this process several times over a set of many possible starting orbits and simply select the worst-case orbit to analyze. To maintain generality, the work has assumed that the geosynchronous earth orbit (GEO) belt, low Lunar orbit, and all Lagrange points could (or will eventually) contain infrastructure that we would like to protect. If, hypothetically, the spacecraft could reach L4 in 4 hours, or the L1 or L2 points in 12 hours, L5 in 24 hours, or the GEO belt in 72 hours, the time-to-contact duration for this spacecraft is 4 hours, since that is the minimum-time case we need to build our custody system to achieve in order to maintain full protection. Conversely, if there is an unknown spacecraft with presumed 650 m/s delta-V at one of the celestial poles, its fastest time-to-contact duration may be 72 hours to reach the GEO belt, and we would only need to build our custody system to a 72-hour specification for those regions.
The risk profile between these two hypothetical unknown spacecraft is clearly very different. One could potentially interact with infrastructure in a matter of hours, whereas the other would take half a week to reach even the closest region of interest — and that is in the worst-case, fastest-moving, most direct scenario. Knowing the time-to-contact durations for these spacecraft allows us to assign a weighting to determine the depth of coverage required in each region of cislunar space. That is not to say that we only need revisit rates exactly corresponding to the time-to-contact durations, of course, or not even necessarily some consistent fraction of that duration; we still need plenty of buffer to pick up movement in order to maintain custody and not have to perform wide searches when we miss an observation. But we can certainly use this weighting better to tune our systems to establish coverage of regions of cislunar space in a manner consistent with the risk profile that the objects in those regions may pose.
This paper will present a method for calculating such a risk map and will show results from a software tool developed to calculate a risk map if given initial inputs. One such set of results is shown as an example in the figure below.
Figure: Risk map as calculated for a hypothetical spacecraft with 300 m/s of dV at the lunar altitude.
This paper will also describe potential extensions of the risk map calculation methods to other infrastructure sites, and will provide a discussion of any particularly interesting features of generated risk maps.
Date of Conference: September 14-17, 2021
Track: Cislunar SSA