Celestial mechanics and dynamical astronomy最新文献

In this paper, the Lidov–Kozai mechanism was studied in the region of the Hilda group and Jupiter Trojans. Asteroids of these populations move in 3:2 and 1:1 orbital resonances with Jupiter. The study was carried out using numerical integration of real asteroids’ equations of motion. A simplified dynamical model was adopted. Perturbations from only Jupiter moving in a fixed elliptical orbit were taken into account. Classical secular perturbations were excluded from osculating elements at every print step, and derived orbital inclinations and eccentricities were plotted versus a perihelion argument (omega ). As a result, it was found that usual positions of a maximum of the eccentricity and, accordingly, a minimum of the inclination ((omega = 90^{circ }), (270^{circ })) are shifted in these resonant regions. For Hildas, the maximum of the eccentricity is achieved with perihelion argument values (omega =0^{circ }), (180^{circ }). For L4 Trojans, it is achieved with (omega = 30^{circ }), (210^{circ }), and for L5 Trojans—with (omega = 150^{circ }), (330^{circ }).

We study the linear stability of regular n-gon rotating equilibria in the n-body problem with logarithm interaction. We find that linear stability is insured if a central mass M if M is bounded below and above by constants depending on the number and mass of the (equal) outer n bodies. Moreover, we provide explicit formulae for these bounds. In the absence of a central mass, we find that the regular n-gon is linearly stable for (n =2,3,ldots 6) only.

It is desirable to design low-altitude and near-polar science orbits for missions to Galilean moons. However, the long-term perturbation from a distant perturber may lead such a kind of orbits to quick impacts, indicating that initial conditions of working orbits need to be well-designed. To this end, long-lifetime working orbits around oblate satellites are investigated in this work. Initially, numerical maps of lifetime around oblate satellites are produced under the long-term dynamical model and they show that initial conditions of long-lifetime orbits are distributed in the form of strips in the space spanned by initial longitude of ascending node and argument of pericenter. This phenomenon is known to be caused by the effect of nodal phasing due to the existence of the mother planet’s obliquity. To understand the mechanism of nodal phasing, we adopt Lie-series transformation to formulate an integrable Hamiltonian model, where the dynamical structures in phase space can be uncovered by phase portraits. Furthermore, we provide three constraints for solving the initial conditions of long-lifetime orbits: the first one states that the Hamiltonian of long-lifetime orbits should be equal to that of the stable manifold, the second and third ones are associated to given initial eccentricity and inclination. By solving these constraint equations and performing direct transformation, analytical strips are produced. It is shown that the analytical and numerical strips are in good agreement. At last, the analytical approach is applied to missions to Galilean moons.

In a recent paper of Philcox, Goodman and Slepian, the solution of the elliptic Kepler’s equation is given as a quotient of two contour integrals along a Jordan curve that contains in its interior the unique real solution of the elliptic Kepler’s equation and does not include other complex zeroes. In this paper, we show that a similar explicit integral solution can be given for the hyperbolic Kepler’s equation. With this purpose, we carry out a study of the complex zeros of the hyperbolic Kepler’s equation in order to define suitable Jordan contours in the integrals. Even more, we show that appropriate elliptic Jordan contours can be defined for such integrals, which reduces the computing time. Moreover, using the ideas behind the fast Fourier transform (FFT) algorithm, these integrals can be approximated by the composite trapezoidal rule which gives an algorithm with spectral convergence as a function of the number of nodes. The results of some numerical experiments are presented to show that this implementation is a reliable and very accurate algorithm for solving the hyperbolic Kepler’s equation.

Smart dust devices are tiny systems-on-a-chip platforms capable of sensing, storing and transmitting data wirelessly as part of a large network with distributed capabilities. Previous works investigated the long-term orbital evolution of smart dust in space by studying the combined effect of gravitational perturbations, solar radiation pressure (SRP) and atmospheric drag. In the current work, the problem of finding long-term orbital equilibria conditions for smart dust is recast and extended to include Poynting–Robertson and Solar Wind (PRSW) drag. By including the PRSW effects and defining new equilibrium conditions on the orbital orientation, some additional partial equilibrium solutions are found. Moreover, it is shown that even though PRSW is not dominant compared to SRP or (J_2), it still influences the evolution of the relative Sun-orbit orientation. For orbits with higher initial perigee altitudes, where drag and (J_2) effects subside, it is shown that PRSW influences long-term orbital behavior, and should be considered in the orbit design scheme of smart dust devices.

Abstract

The study of resonances in celestial mechanics is crucial for understanding the dynamics of planetary or stellar systems. This study focuses on presenting a method for investigating the topology and resonant structures of a dynamical system. To illustrate the strength of the method, we have applied our method to retrograde resonances in the planar circular restricted three-body problem within binary star systems. Because of the high mass ratio systems, the techniques based on perturbation of the two-body orbit are not the ideal to analyze the system. Consequently, resonant angles could be meaningless, necessitating alternative methods for resonance identification. To address this challenge, an image classification-based machine learning model is implemented to identify resonances based on the shape of orbits in the rotating frame. Initially, the model is trained on empirical cases with low mass ratios using the resonant angle as a starting point for resonance identification. The model’s performance is validated against existing literature results. The model results demonstrate successful classification and identification of retrograde resonances in both empirical and non-empirical cases. The model accurately captures the resonance patterns and provides initial insights into the short-term stability of the corresponding resonances.