Search Results (7)

In this work, particle dynamics in a binary asteroid system is analyzed within the Circular Restricted Three-Body Problem (CRTBP) framework, assuming the largest body is treated as a mass point. The secondary body is modeled as a mass dipole in synchronous rotation with its orbital motion, which leads to the spin–orbit resonance. The third body is a point of negligible mass whose motion is restricted to the orbital plane of the primary bodies. We considered asymmetrical and symmetrical dipole cases. The number and positions of the equilibrium points are determined for the dynamical analysis, and the zero-velocity curves are studied. This model preserves the number and geometric arrangement of the equilibrium points compared to the CRTBP. The equilibrium points adjacent to the dipole are the most sensitive in position to the variations in physical parameters. Considering the solar radiation pressure on the third body, different initial conditions for its motion in the vicinity of the dipole are analyzed. As a result, the particle survival time in orbital motion is estimated before colliding or suffering gravitational ejection from the system. Full article

This paper investigates the design of optimal low-thrust transfers between relative planar and spatial quasi-satellite orbits (QSOs) in the Earth–Moon system under the Circular Restricted Three-Body Problem (CR3BP). A key contribution is the adaptation of a trajectory optimization framework, previously applied to halo orbit transfers, to accommodate the unique challenges of QSO families, especially the transition between planar and spatial configurations. The method employs a refined beam search strategy to construct diverse initial guess chains, which are then optimized via a successive convexification algorithm tailored for the spatial dynamics of QSOs. Additionally, a linear–quadratic regulator (LQR)-based control scheme is implemented to ensure long-term station-keeping of the final 3D-QSO. Simulation results demonstrate the feasibility of connecting planar and spatial QSOs with minimum-fuel trajectories while maintaining bounded terminal deviations, offering new tools for future Earth–Moon logistics and navigation infrastructure. Key findings include the successful design of low-thrust transfer trajectories between planar QSOs and 1:5 3D-QSOs, with a minimum total $\mathsf{\Delta }V$ of 195.576 m/s over a time of flight (ToF) of 261 days, and a minimum ToF of 41 days with a total $\mathsf{\Delta }V$ of 270.507 m/s. Additionally, the application of LQR control demonstrated the ability to maintain 1:5 3D-QSO families around the Moon with less than 12 mm/s $\mathsf{\Delta }V$ over two months. This research provides valuable insights into the optimization of low-thrust transfer trajectories and the application of advanced control techniques for space missions, particularly those targeting lunar and planetary satellite exploration. Full article

This study numerically explores the dynamics of the photogravitational circular restricted three-body problem, where an infinitesimal particle moves under the gravitational influence of two primary bodies connected by a massless rod. These primary masses revolve in circular orbits around their common center of mass, which remains fixed at the origin of the coordinate system. The distance between the two masses remains constant, independent of their rotation period. The third body, being infinitesimally small compared to the primary masses, has a negligible effect on their motion. The primary mass is considered as a radiating body, while the secondary is modeled as an elongated one comprising two hypothetical point masses separated by a fixed distance. The analysis focuses on determining the number, location, and stability of equilibrium points, as well as examining the structure of zero-velocity curves under the influence of system parameters such as mass and force ratio, radiation pressure and geometric configuration of the secondary body. The system is found to allow up to six equilibria: four collinear and two non-collinear. Their number and positions are significantly affected by variations in the system’s parameters. Stability analysis reveals that the two non-collinear equilibrium points can exhibit stability under specific parameter configurations, while the four collinear points are typically unstable. An exception is the innermost collinear equilibrium point, which can be stable for certain parameter values. Our numerical investigation on periodic orbits around the collinear equilibrium points of the asteroid triple-system 2001SN₂₆₃ show that a variation, either to the values of radiation or the force ratio parameters, influence their special characteristics such as period and stability. Also, their continuation in the space of initial conditions shows that all families terminate naturally at collision orbits with either the primary or the secondary. Full article

To observe lower-frequency gravitational waves (GWs), it is effective to utilize a large spacecraft formation baseline, spanning hundreds of thousands to millions of kilometers. To overcome the limitations of a gravitational-wave observatory (GWO) on specific orbits, a scientific observation mode and a non-scientific observation mode for GWOs are proposed. For the non-scientific observation mode, this paper designs equilateral triangle and equilateral tetrahedral array formations for a space-based GWO near a collinear libration point. A stable configuration is the prerequisite for a GWO; however, the motion near the collinear libration points is highly unstable. Therefore, the output regulation theory is applied. By leveraging the tracking aspect of the theory, the equilateral triangle and equilateral tetrahedral array formations are achieved. For an equilateral triangle array formation, two geometric configuration design methods are proposed, addressing the fuel consumption required for initialization and maintenance. To observe GWs in different directions and avoid configuration/reconfiguration, the multi-layer equilateral tetrahedral array formation is given. Additionally, the control errors are calculated. Finally, the effectiveness of the control method is demonstrated using the Sun–Earth circular-restricted three-body problem (CRTBP) and the ephemeris model located at Lagrange point $L_1$. Full article

Resonance transition periodic orbits exist in the chaotic regions where the 1:1 resonance overlaps with nearby interior or exterior resonances in the circular restricted three-body problem (CRTBP). The resonance transition periodic orbits have important applications for tour missions between the interior and the exterior regions of the system. In this work, following the increase of the mass parameter $\mu$ in the CRTBP model, we investigate the breakup of the first-order resonant periodic families and their recombination with the resonance transition periodic families. In this process, we can describe in detail how the 1:1 resonance gradually overlaps with nearby first-order resonances with increasing strength of the secondary’s perturbation. Utilizing the continuation method, features of the resonance transition periodic families are discussed and characterized. Finally, an efficient approach to finding these orbits is proposed and some example resonance transition periodic orbits in the Sun–Jupiter system are presented. Full article

Some asteroids flying close to Earth may pose a threat of impact. Among them, the structural and dynamical characteristics of rubble-pile asteroids can be changed because of the tidal force of the Earth in this process. This can provide key information for predicting the dynamical evolution of potentially hazardous asteroids. In this study, the long-term evolution of the coupling orbit–attitude–structure of these small bodies is presented numerically based on the integration of two models. One is the 3D discrete element method, which models the structure and irregular shape of the rubble-pile asteroid. The other is the dynamical model of the circular restricted three-body problem (CRTBP). This provides a more precise dynamical environment of the asteroid orbital deflection, morphological modification, and attitude angles analysis compared to the frequently adopted two-body problem. Parametric studies on the asteroid evolution were performed focusing on its flyby distance and the bulk porosity. Numerical results indicate that the Earth flyby can form different patterns of modification of asteroids, where the rubble-pile structure can be destructed by considering the bulk porosity. The asteroid orbital deflection and attitude variational trends are also summarized based on the simulations of multi-orbital revolutions. Full article

The research on highly inclined mean motion resonances (MMRs), even retrograde resonances, has drawn more attention in recent years. However, the dynamics of polar resonance with inclination $i\approx {90}^{\circ }$ have received much less attention. This paper systematically studies the dynamics of polar resonance and their effects on the Kozai–Lidov mechanism in the circular restricted three-body problem (CRTBP). The maps of dynamics are obtained through the numerical method and semi-analytical method, by mutual authenticating. We investigate the secular dynamics inside polar resonance. The phase-space portraits on the $e-\omega$ plane are plotted under exact polar resonance and considering libration amplitude of critical angle $\sigma$. Simultaneously, we investigate the evolution of 5000 particles in polar resonance by numerical integrations. We confirm that the $e-\omega$ portraits can entirely explain the results of numerical experiments, which demonstrate that the phase-space portraits on the $e-\omega$ plane obtained through the semi-analytical method can represent the real Kozai–Lidov dynamics inside polar resonance. The resonant secular dynamical maps can provide meaningful guidance for predicting the long-term evolution of polar resonant particles. As a supplement, in the polar $2/1$ case, we analyze the pure secular dynamics outside resonance, and confirm that the effect of polar resonance on secular dynamics is pronounced and cannot be ignored. Our work is a meaningful supplement to the general inclined cases and can help us understand the evolution of asteroids in polar resonance with the planet. Full article