Celestial mechanics and dynamical astronomy最新文献

This contribution focuses on the use of finite-time Lyapunov exponent (FTLE) maps to investigate spacecraft motion within the context of the circular restricted three-body problem as a conceptual model. The study explores the advantages and limitations of FTLE maps by examining spacecraft trajectories in the vicinity of the Jovian moons, Ganymede and Europa. The paper introduces an atlas of FTLE maps for different energy levels surrounding Ganymede, highlighting critical regions that define types of motion and energy thresholds. Additionally, the authors also explore the symmetry relationships of the Lagrangian coherent structures that are defined within the FTLE maps. Establishing relationships between initial conditions within the FTLE maps is essential for understanding trajectory behaviors in the neighborhoods of moons. The results demonstrate that by utilizing FTLE maps, a better understanding of spacecraft behavior in the vicinity of celestial bodies emerges, potentially enabling more precise mission planning and execution. The findings and methodologies are extendable to other planet–moon systems, providing a valuable framework for future space missions.

We discuss a model describing the spin orbit resonance cascade. We assume that the body has a two-layer (core–shell) structure; it is composed of a thin external shell and an inner and heavier solid core that are interacting due to the presence of a viscous friction. We assume two sources of dissipation: a viscous one, depending on the relative angular velocity between core and shell and a tidal one, smaller than the first, due to the viscoelastic structure of the core. We show how these two sources of dissipation are needed for the capture in spin–orbit resonance. The shell and the core fall in resonance with different time scales if the viscous coupling between them is big enough. Finally, the tidal dissipation of the viscoelastic core, decreasing the eccentricity, brings the system out of the resonance in a third very long time scale. This mechanism of entry and exit from resonance ends in the 1 : 1 stable state.

Spacecraft trajectories near the south pole of Enceladus violate the Brillouin sphere associated with the convergence radius of spherical harmonics models. In this study, a shifted coordinate frame is demonstrated to ensure a convergent model is available in regions of operational interest. Hypothetical experiments are performed around a simulated celestial body where the truth exterior gravity fields are known exactly. The divergence of the harmonics below the Brillouin sphere of the unshifted models is confirmed, while the shifted harmonics model converges. The method is next applied to the Cassini-derived gravity field for Enceladus, including uncertainties. Using these low-degree and low-order reference models, expected for use in an operational setting, the results show that the shifted and body-centered harmonics models agree to near machine precision for all evaluations at or above the surface, and no divergence is noticed. The results imply that mission designers and navigation engineers can safely use a traditional spherical harmonics field for Enceladus, even in regions that dip below the Brillouin sphere. For low-flying missions to celestial bodies besides Enceladus, the experiments conducted in this study can be repeated. The need for an alternative to the traditional spherical harmonics, such as the presented shifted model, increases for bodies that are increasingly non-spherical and orbits that are deeper inside the Brillouin sphere.

Spin–orbit coupling is widespread in binary asteroid systems, and it has been widely studied for the case of ellipsoidal secondary. Due to angular momentum exchange, dynamical coupling is stronger when the orbital and rotational angular momenta are closer in magnitudes. Thus, the spin–orbit coupling effects are significantly different for ellipsoidal secondaries and primaries. In the present work, a high-order Hamiltonian model in terms of eccentricity is formulated to study the effects of spin–orbit coupling for the case of ellipsoidal primary body in a binary asteroid system. Our results show that the spin–orbit coupling problem for the ellipsoidal primary holds two kinds of spin equilibrium, while there is only one for the ellipsoidal secondary. In particular, 1:1 and 2:3 spin–orbit resonances are further studied by taking both the classical pendulum approximation and adiabatic approximation (Wisdom’s perturbative treatment). It shows that there is a critical value of total angular momentum, around which the pendulum approximation fails to work. Dynamical structures are totally different when the total angular momentum is on two sides of the critical value.

A numerical approach to solve the perturbed Lambert’s problem is presented. The proposed technique uses the theory of functional connections, which allows the derivation of a constrained functional that analytically satisfies the boundary values of Lambert’s problem. The propagation model is devised in terms of three new variables to mainly avoid the orbital frequency oscillation of Cartesian coordinates. Examples are provided to quantify robustness, efficiency, and accuracy on Earth- and Sun-centered orbits with various shapes and orientations. Differential corrections and a robust Lambert solver are used to validate the proposed approach in various scenarios and to compare it in terms of speed and robustness. Perturbations due to Earth’s oblateness, third body, and solar radiation pressure are introduced, showing the algorithm’s flexibility. Multi-revolution solutions are obtained. Finally, a polynomial analysis is conducted to show the dependence of convergence time on polynomial type and degree.

Explosions or collisions of satellites around the Earth generate space debris, whose uncontrolled dynamics might raise serious threats for operational satellites. Mitigation actions can be realized on the basis of our knowledge of the characteristics of the fragments produced during the breakup event and their subsequent propagation. In this context, important information can be obtained by implementing a breakup simulator, which provides, for example, the number of fragments, their area-to-mass ratio or the relative velocity distribution as a function of the characteristic length of the fragments. Motivated by the need to analyze the dynamics of the fragments, we reconstruct a simulator based on the NASA/JSC breakup model EVOLVE 4.0 that we review for self-consistency. This model, created at the beginning of the XXI century, is based on laboratory and on-orbit tests. Given that materials and methods for building satellites are constantly progressing, we leave some key parameters variable and produce results for different choices of the parameters. We will also present an application to the Iridium–Cosmos collision and we discuss the distribution function after a breakup event. The breakup model is strongly related to the propagation of the fragments; in this work, we discuss how to choose the models and the numerical integrators, we propose examples of how fragments can disperse in time, and we study the behavior of multiple simultaneous fragmentations. Finally, we compute some indicators for detecting streams of fragments. Breakup and propagation are performed using our own simulator SIMPRO, built from EVOLVE 4.0; the executable program will be freely available on GitHub.

The exploration of small bodies in our solar system is of great interest for the planetary science community due to their high scientific value. However, their generally weak and irregular gravity fields increase the difficulty associated with close proximity operations. Moreover, solar radiation pressure (SRP) can significantly perturb the motion of objects in their vicinity, particularly for bodies with high area-to-mass ratios. In this work, we adopt the polyhedral gravity model and identify natural dynamical structures that can be used for mission operations. Further, we study forced periodic motion in the body fixed frame while accounting for the effect of SRP with eclipses. Overall, our work seeks to identify suitable orbits and locations in the vicinity of small bodies that can be exploited for the design of science orbits. To obtain periodic orbits in the model accounting for SRP perturbations, we use a Melnikov function to find orbits that satisfy resonances with the asteroid spin and show no net change in energy over the orbit. We then use a differential correction scheme to find numerical solutions in the time-periodic model. Our test cases are potentially hazardous asteroid 101955 Bennu and main belt asteroid 16 Psyche.

We study the perturbed-from-synchronous librational state of a double asteroid, modeled by the Full Two Rigid Body Problem (F2RBP), with primary emphasis on deriving analytical formulas which describe the system’s evolution after deflection by a kinetic impactor. To this end, both linear and nonlinear (canonical) theories are developed. We make the simplifying approximations (to be relaxed in a forthcoming paper) of planar binary orbit and axisymmetric shape of the primary body. To study the effect of a DART-like hit on the secondary body, the momentum transfer enhancement parameter (beta ) is introduced and retained as a symbolic variable throughout all formulas derived, either by linear or nonlinear theory. Our approach can be of use in the context of the analysis of the post-impact data from kinetic impactor missions, by providing a precise modeling of the impactor’s effect on the seconadry’s librational state as a function of (beta ).

This paper investigates the motion of a small particle moving near the triangular points of the Earth–Moon system. The dynamics are modeled in the Hill restricted 4-body problem (HR4BP), which includes the effect of the Earth and Moon as in the circular restricted 3-body problem (CR3BP), as well as the direct and indirect effect of the Sun as a periodic time-dependent perturbation of the CR3BP. Due to the periodic perturbation, the triangular points of the CR3BP are no longer equilibrium solutions; rather, the triangular points are replaced by periodic orbits with the same period as the perturbation. Additionally, there is a 2:1 resonant periodic orbit that persists from the CR3BP into the HR4BP. In this work, we investigate the dynamics around these invariant objects by performing a center manifold reduction and computing families of 2-dimensional invariant tori and their linear normal behavior. We identify bifurcations and relationships between families. Mechanisms for transport between the Earth, (L_4), and the Moon are discussed. Comparisons are made between the results presented here and in the bicircular problem (BCP).