Sam Wishnek, BAE Systems; Scott Nonweiler, BAE Systems; Luke Tafur, BAE Systems
Keywords: Cislunar, parameterization, orbit determination, angles-only
Abstract:
Cislunar orbits can be particularly challenging to characterize and track. On top of the more complex dynamics in cislunar space, the large distances and long orbital periods involved can significantly slow down the process of collecting enough observations of a space object to accurately characterize its orbit. With orbital periods on the scale of weeks to a month, it can take days for the orbit to meaningfully evolve between observations. Follow up observations of the same target without sufficient time for the target’s state to evolve do not provide any new information about the target’s orbit. The scale of the distances involved further compounds this issue as even very tight measurement uncertainties translate to a large position uncertainty with angles-only observations. To approach this problem for objects suspected of being in periodic cislunar orbits, we propose a method for identifying feasible cislunar orbits based on a single angles-only observation and assess its efficacy in accurately characterizing orbits.
Periodic cislunar orbits fall into a small variety of families. These families may be stable against perturbations like the orbits around Lagrange points four and five, or they may be unstable like the halo orbits about Lagrange points one, two, and three. In either case, an active space object attempting to remain in one of these orbits should be able to approximately follow its target orbit via regular maintenance burns. In effect, this means that active satellites in a periodic cislunar orbit should appear to be following the orbit whether it is stable or not. In the proposed research, we will apply the assumption that an observed space object is following a periodic cislunar orbit to simplify the process of estimating its state.
Cislunar orbit families can be represented as individual surfaces in space. These surfaces are folded two-dimensional constructs. Accordingly, the state of a satellite in a known cislunar orbit family can be represented with only two parameters and a time. One parameter can represent the progress along its orbit, for example an angle about the Earth-Moon axis for halo orbits, while the other can be a component along the Earth-Moon axis representing where the individual orbit exists within the family of orbits. With only two parameters needed to define the state, a single angles-only observation is sufficient to identify a small finite number of potential orbit states. These are the points in the family-defined surface that the observation ray pierces. With a finite number of cislunar orbit families, this allows a single observation to identify a small finite set of potential orbits across all cislunar periodic orbit families.
A complicating factor in this approach is that these orbit family surfaces are not analytically defined. Rather, these surfaces must be defined by propagating out periodic orbits and stacking them together in space. This is a slow process and impedes our ability to identify pierce points in the surface given a ray defined by an observation angle and observer state. To solve this problem, we propose approximating the family-defining surface with spline surfaces. The computationally intensive work can then be performed only once per orbit family and then modeled with an analytical collection of spline surfaces. Once defined in this way, finding the pierce point of the observation ray on the surface becomes simple and fast. This spline model requires fewer resources to model than a full fidelity model and can be built at only the detail resolution required given the measurement uncertainty of the instrument. Orbit estimation with a single observation will therefore ensure significantly more timely orbit estimation.
The proposed work will include a description of the process in building a spline surface model of cislunar orbit families and an assessment of the accuracy of this model in cislunar orbit determination from single angles-only measurements. This analysis will cover the impact of various errors on the estimate accuracy including high fidelity orbit models, measurement uncertainty, and the target’s orbit family. In addition, this work will include how multiple observations of same target can be used to narrow down the potential solutions from the finite set from a single observation as well as how this approach can be used to associate observations of the same object.
Date of Conference: September 16-19, 2025
Track: Cislunar SDA