Celestial mechanics and dynamical astronomy最新文献

Coupling between the rotational and translational motion of a rigid body can have a profound effect on spacecraft motion in complex dynamical environments. While there is a substantial amount of study of rigid-body coupling in a non-uniform gravitational field, the spacecraft is often considered as a point-mass vehicle. By contrast, the full-N body problem (FNBP) evaluates the mutual gravitational potential of the rigid-body celestial objects and any other body, such as a spacecraft, under their influence and treats all bodies, including the spacecraft, as a rigid body. Furthermore, the perturbing effects of the FNBP become more pronounced as the celestial bodies become smaller and/or more significantly aspherical. Utilizing the comprehensive framework of dynamics and gravitational influences within the FNBP, this research investigates the dynamics of spacecraft modeled as rigid bodies in binary systems characterized by nearly circular mutual orbits. The paper presents an examination of the perturbation effects that arise in this circular restricted full three-body problem (CRF3BP), aiming to assess and validate the extent of these effects on the spacecraft’s overall motion. Numerical results provided for spacecraft motion in the CRF3BP in a binary asteroid system demonstrate non-negligible trajectory divergence when utilizing rigid-body versus point mass spacecraft models. These results also investigate the effects of shape and inertia tensors of the bodies and solar radiation pressure in those models.

Future missions to Enceladus would benefit from multi-moon tours that leverage (V_infty ) on resonant orbits to progressively transfer between moons. Such resonance hopping trajectories present a vast search space for global optimization due to the different combinations of available resonances and flyby velocities. The proposed multi-objective tour design algorithm optimizes entire moon tours from Titan to Enceladus via grid-based dynamic programming, in which the computation time is significantly reduced by discretization of the design variables and pre-computation of a database of (V_infty )-leveraging transfers. The result unveils a complete trade space of the moon tour design to Enceladus, and the obtained solution is validated in a full-ephemeris model.

Li and Liao announced (New Astron 70:22–26, 2019, arXiv:1805.07980v1) discovery of 313 periodic collisionless orbits’ initial conditions (i.c.s), 30 of which have equal masses, and 18 of these 30 orbits have physical periods (scale-invariant periods) (T^{*}<80). We revisited this work with the intention to improve both, its logical consistency and the numerical efficiency of the method. We have conducted a new search for periodic free-fall orbits, limited to the equal-mass case. Our search produced 24,582 i.c.s of equal-mass periodic orbits with scale-invariant period (T^{*}<80), corresponding to 12,409 distinct solutions, 236 of which are self-dual.

While the Circular Restricted Three-Body Problem (CR3BP) provides useful structures for various applications, transitioning the solutions from the CR3BP to a higher-fidelity ephemeris model while maintaining specific characteristics remains non-trivial. An analytical approach is leveraged to provide additional insight on the perturbations that are present in an ephemeris model. For the Earth–Moon CR3BP, pulsation of the Earth–Moon distance and solar gravity are identified as key components contributing to the additional accelerations, where patterns are illustrated through simplified mathematical relationships and graphics. Utilizing these findings, capabilities and limitations of two intermediate models, the Elliptic Restricted Three-Body Problem and the Bi-Circular Restricted Four-Body Problem, are assessed within the context of transitioning from the CR3BP to a realistic ephemeris model. A sample transition process for Earth–Moon L2 halo orbits is provided, leveraging the insight from the proposed analytical approach.

This paper presents an improved alpha shape-based linear interpolation method, and an improved binning method within the continuum method framework for accurate and efficient planar phase space long-term density propagation. The density evolution equation is formulated for the continuum density propagation under the influence of the solar radiation pressure and Earth’s oblateness using semi-analytical equations. The concept of the alpha shape is included to get accurate interpolated density within the non-convex hull enclosing all the samples for the highly deformed and elongated density distribution. The improved binning method increases the density accuracy by considering the variant nonlinearity of the density within each alpha shape triangulation, which calculates the joint and marginal density as the weighted sum of density weights per bin area and per bin width, respectively. The suitable sample number for the continuum method and the suitable grid number for performing the linear interpolation are selected by trading off the density accuracy and the computational effort. The superiority of the improved alpha shape-based continuum method is demonstrated for accurate and efficient density propagation in the context of the high-altitude and high area-to-mass ratio satellite long-term propagation.

The flux-based statistical theory of the non-hierarchical three-body system predicts that the chaotic outcome distribution reduces to the chaotic emissivity function times a known function, the asymptotic flux. Here, we measure the chaotic emissivity function (or equivalently, the absorptivity) through simulations. More precisely, we follow millions of scattering events only up to the point when it can be decided whether the scattering is regular or chaotic. In this way, we measure a trivariate absorptivity function. Using it, we determine the flux-based prediction for the chaotic outcome distribution over both binary binding energy and angular momentum, and we find good agreement with the measured distribution. This constitutes a detailed confirmation of the flux-based theory and demonstrates a considerable reduction in computation to determine the chaotic outcome distribution.

The Dawn spacecraft approached the asteroid Vesta and descended from a high-altitude mission orbit to a low-altitude mission orbit using low-thrust propulsion. During this descent, the spacecraft crossed the 2:3 and 1:1 ground-track resonances with Vesta, which posed a risk of capture that might strongly perturb the spacecraft’s orbit. This study analyzes the effects of these resonances on the spacecraft’s orbital elements and estimates the probability of capture into it through Monte Carlo simulations. Specifically, a comprehensive investigation is performed to assess the effects of 1:1 and 2:3 ground-track resonances on the semimajor axis, eccentricity, and inclination. The dynamical model includes the gravitational field of Vesta using a spherical harmonics approximation up to the fourth degree and order and the low-thrust acceleration that is assumed to be opposite to the spacecraft’s velocity vector direction. It is observed that the eccentricity evolution is mostly influenced by the 2:3 ground-track resonance which results in a large variation when the spacecraft crosses that ground-track resonance, while the semimajor axis and inclination are mostly influenced by the 1:1 ground-track resonance. Then, the probability of capture into 1:1 ground-track resonance is found to have a negative correlation with the spacecraft’s thrust magnitude and the probability of capture into 2:3 ground-track resonance is found to arise as the spacecraft’s mass increases. It is found that for circular orbits below a certain inclination value the spacecraft’s trajectory is subject to the “automatic entry into libration” phenomenon, due to the singularity in the Hamiltonian function. This research contributes to the design of successful transfer strategies when crossing resonance for future missions.

This paper presents a new approach to approximate the solution of Kepler’s equation. It is found that by means of a series approximation, an angle identity, the application of Sturm’s theorem, and an iterative correction method, the need to evaluate transcendental functions or query lookup tables is eliminated. The final procedure builds upon Mikkola’s approach. Initially, a fifteenth-order polynomial is derived through a series approximation of Kepler’s equation. Sturm’s theorem is used to prove that only one real root exists for this polynomial for the given range of mean anomaly and eccentricity. An initial approximation for this root is found using a third-order polynomial. Then, a single generalized Newton–Raphson correction is applied to obtain fourteenth-place accuracies in the elliptical case, which is near machine precision. This paper will focus on demonstrating the procedure for the elliptical case, though an application to hyperbolic orbits through a similar methodology may be similarly developed.

Confidence regions for spacecraft state can be constructed in phase space which encapsulate some region where there is a likelihood for the state to reside. These regions can be treated as phase space distributions or structures. Structures, such as surfaces or volumes, are constrained to preserve specific properties as they evolve in phase space under Hamiltonian dynamics. Thus, spacecraft uncertainty is then constrained by Hamiltonian flow which can provide insight into state determination. This work examines the modified constraints in the presence of non-conservative forces which relate to both probabilistic and geometric properties of the evolving uncertainty structure. The modified constraints are then derived for a Two-Body and drag environment and are shown to be valid after comparison with alternative methods. Applying the modified constraints, the constrained evolution of the confidence region is then tied to a simple physical explanation for the changing knowledge in our spacecraft state, in the atmospheric drag environment and Poynting–Robertson drag environment.

We present a planar four-body model, the Circular Planar (2+2)-Body Problem, for the motion of two asteroids (having small but positive masses) moving under the gravitational attraction of each other and under the gravitational attraction of two primaries (with masses much larger than the two smaller mass bodies) moving in uniform circular motion about their center of mass. We show the Circular Planar (2+2)-Body Problem has (at least) 6 relative equilibria and (at least) 10 one-parameter families of periodic orbits, two of which are of Hill-type. The existence of six relative equilibria and eight one-parameter families of periodic orbits is obtained by a reduction of the Circular Planar (2+2)-Body Problem in which the primaries have equal mass, the asteroids have equal mass, and the positions of the asteroids are symmetric with respect to the origin. The remaining two one-parameter families of periodic orbits, which are of comet-type, are obtained directly in the Circular Planar (2+2)-Body Problem.