This fundamental deficiency has hindered the development of an effective space situational awareness framework for this strategically vital region. A research team from the National University of Defense Technology has developed a parameterization method for orbits near collinear libration points that enables systematic cataloging and robust identification of cislunar objects.
The study, published in the Chinese Journal of Aeronautics, constructs a new set of dynamical parameters by applying canonical transformations and center manifold theory within the Circular Restricted Three Body Problem. This procedure effectively translates the complex dynamics near libration points into a set of intuitive parameters suitable for cataloging, visualization, and analysis.
The new framework defines six characteristic parameters that maintain a one to one correspondence with the full state of an object near a collinear libration point. Two hyperbolic parameters, denoted q1 and p1, describe motion along the invariant manifolds associated with the libration orbit, while four additional parameters capture the quasi periodic behavior in the central manifold.
The hyperbolic parameters function as a monitor for transfer activity, signaling when a spacecraft moves into or out of a libration point orbit and identifying its associated invariant manifold. According to the team, this is crucial for understanding spacecraft maneuvers because many fuel efficient cislunar transfers exploit these invariant manifolds, and the parameters provide direct insight into transfer events and subsequent orbital changes.
The center manifold parameters, labeled I2, theta2, I3, and theta3, characterize the quasi periodic motion of a spacecraft around the libration point in both horizontal and vertical directions. To facilitate visualization and analysis, the researchers employ Poincare sections that project the four dimensional phase space onto a two dimensional plane, where each orbit corresponds to a unique point defined by its amplitudes.
On these Poincare maps, classic orbital families such as Lyapunov, Halo, and Lissajous orbits each occupy distinct, identifiable regions. This turns the Poincare section into a practical cataloging chart, allowing operators to group and label libration point trajectories without relying solely on long numerical ephemerides or mission specific naming schemes.
The framework directly enables orbit identification from tracking data. Given a segment of an observed spacecraft trajectory, the method determines the best matching CRTBP reference orbit by minimizing the discrepancy between their respective action variables, effectively fitting the measured path to a modeled libration orbit.
A sensitivity analysis demonstrates the robustness of the method, showing reliable identification performance for position errors up to about 100 kilometers and velocity errors below roughly 1 meter per second. The results also suggest that improving velocity measurement accuracy is more important for future cislunar tracking systems than further reductions in position error.
At present, the framework is primarily applicable to the collinear libration points L1 and L2 within the simplified Circular Restricted Three Body Problem that includes only Earth and Moon as massive bodies. The team notes that the same assumptions become inadequate near the triangular libration points L4 and L5, where solar gravity exerts a strong influence on local dynamics.
The researchers plan to extend the parameterization to a more realistic, non autonomous ephemeris model that incorporates gravitational perturbations from the Sun. Their ultimate goal is to establish a single, unified parameterization and cataloging system applicable to all libration points within the Earth Moon system, providing a standardized common language for cislunar space situational awareness.
Such a comprehensive framework would support the safe and efficient utilization of cislunar space as activity increases in the coming decades. By enabling operators to tag, track, and manage libration point objects with a compact, uncertainty aware parameter set, the method aims to underpin future architectures for collision avoidance, traffic coordination, and mission planning in the Earth Moon environment.
Research Report:Orbital parameter characterization and objects cataloging for Earth-Moon collinear libration points
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