With growing concerns over the impact threat of near-Earth small bodies and the utilization of space resources, the orbital evolution of binary asteroid systems has become an important subject in space science. When describing the full two-body dynamics of such systems, the gravitational potential of irregular bodies is determined by both their positions and attitudes, leading to coupling between translational and rotational motions, and the resulting model complexity significantly exceeds that of the classical two-body problem. Although existing numerical methods, such as explicit Runge–Kutta integrators, are widely used, they fail to preserve the symplectic structure and Lie group geometric properties of the system. In long-term simulations, key conserved quantities such as total energy and angular momentum are prone to numerical drift, severely undermining the long-term credibility of orbital predictions. While Lie group variational integrators can preserve geometric structure to a certain extent, their implicit equations are formulated on Lie group elements, which incurs substantial computational overhead. Therefore, how to construct a high-performance integration method that simultaneously achieves numerical accuracy, structure preservation, and computational efficiency has become a core challenge in the long-term evolutionary simulation of binary asteroid systems.

With the intensifying space confrontation in geostationary orbit (GEO), the U.S. GSSAP (Geosynchronous Space Situational Awareness Program) satellites have conducted hundreds of close-range observation operations on dozens of on-orbit satellites in the vicinity of GEO. The acquisition of multi-aspect information from non-cooperative targets has thus become a critical component of space security assessment. Close-range spacecraft operations, which employ relative motion configurations such as fly-around, hovering, and drifting flight, provide an effective technical means for approaching and observing targets to obtain multi-aspect payload information. However, existing studies predominantly focus on the control design of a single relative motion configuration, which fails to satisfy the complex mission requirements of multi-aspect observation. The combination of multiple models for observation presents multiple challenges, including smooth switching between modes, fuel optimization, strategy design algorithms, and analysis of payload parameter effects. Therefore, how to coordinately plan a sequential combination of multiple close-range operation models under minimum fuel constraints to efficiently acquire multi-aspect information of non-cooperative targets has become a key bottleneck in enhancing space situational awareness capabilities.

With the increasing demand for high-altitude high-speed vehicles in complex adversarial environments, autonomous navigation under conditions of GNSS signal unavailability or damaged ground infrastructure has become a critical technological bottleneck. Existing navigation means—including visual navigation, terrain matching, inertial navigation, celestial navigation, and geomagnetic navigation—each have inherent limitations, making it difficult to simultaneously satisfy requirements for all-weather operation, high accuracy, and long endurance. Inspired by the use of relative position vectors for absolute navigation in spacecraft formation flying, this paper extends this principle to high-altitude high-speed vehicles that are significantly influenced by non-conservative forces such as engine thrust and aerodynamic forces. However, it is necessary to utilize accelerometer measurements from inertial navigation to subtract the effects of non-conservative accelerations, so that the gravitational acceleration information—which reflects the absolute position—can be extracted from the relative position vectors. Nevertheless, the influence of multi-source uncertainties—including accelerometer noise and bias, relative position measurement errors, and star tracker attitude errors—on navigation accuracy remains unclear, and how to achieve high-precision autonomous navigation under this framework remains a key issue to be resolved.

As orbital space resources become increasingly scarce, the problem of orbital pursuit-evasion games among spacecraft has attracted widespread attention. In multi-to-one pursuit-evasion scenarios, multiple pursuit spacecraft are required to cooperatively capture a non-cooperative evasive target under impulsive maneuver and fuel constraints, giving rise to an optimal control problem characterized by strong nonlinearity and complex constraints. Existing differential game methods suffer from high computational complexity and poor real-time performance; numerical optimization approaches are sensitive to initial guesses and struggle to handle long-duration constraints; and although deep reinforcement learning has demonstrated advantages in some scenarios, it lacks proactive prediction capability when confronting unknown evasion strategies, thereby limiting pursuit performance. Consequently, how to predict the actions of the evading spacecraft in multi-to-one scenarios and accordingly optimize the cooperative strategies of multiple pursuers has become a key challenge for improving pursuit efficiency in complex orbital games.