Celestial mechanics and dynamical astronomy最新文献

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).

Two moons of Saturn, Janus and Epimetheus, are in co-orbital motion, exchanging orbits approximately every four Earth years as the inner moon approaches the outer moon and they gravitationally interact. The orbital radii of these moons differ by only 50 km (less than the moons’ mean physical radii), and it is this slight difference in their orbits that enables their periodic exchanges. Numerical n-body simulations can accurately model these exchanges using only Newtonian physics acting upon three objects: Saturn, Janus, and Epimetheus. Here we present analytical approaches and solutions, and corresponding computer simulations, designed to explore the effects of the initial orbital radius difference on otherwise similar co-orbital systems. Comparison with our simulation results illustrates that our analytic expressions provide very accurate predictions for the moon separations at closest approach and simulated post-exchange orbital radii. Our analytic estimates of the exchange period also match the simulated value for Janus and Epimetheus to within a few percent, although systems with smaller differences in their orbital radii are less well-modeled by our simple approach, suggesting that either full simulations or more sophisticated analytic approaches would be required to estimate exchange periods in those cases.

In this paper, we address the problem of computing a preliminary orbit of a celestial body from one topocentric position vector (mathcal{P}_1) and a very short arc (VSA) of optical observations (mathcal{A}_2). Using the conservation laws of the two-body dynamics, we write the problem as a system of 8 polynomial equations in 6 unknowns. We prove that this system is generically consistent, namely, for a generic choice of the data (mathcal{P}_1, mathcal{A}_2), it always admits solutions in the complex field, even when (mathcal{P}_1, mathcal{A}_2) do not correspond to the same celestial body. The consistency of the system is shown by deriving a univariate polynomial (mathfrak {v}) of degree 8 in the unknown topocentric distance at the mean epoch of the observations of the VSA. Through Gröbner bases theory, we also show that the degree of (mathfrak {v}) is minimum among the degrees of all the univariate polynomials solving this problem. Even though we can find solutions to our problem for a generic choice of (mathcal{P}_1, mathcal{A}_2), most of these solutions are meaningless. In fact, acceptable solutions must be real and have to fulfill other constraints, including compatibility with Keplerian dynamics. We also propose a way to select or discard solutions taking into account the uncertainty in the data, if present. The proposed orbit determination method is relevant for different purposes, e.g., the computation of a preliminary orbit of an Earth satellite with radar and optical observations, the detection of maneuvres of an Earth satellite, and the recovery of asteroids which are lost due to a planetary close encounter. We conclude by showing some numerical tests in the case of asteroids undergoing a close encounter with the Earth.

The dynamical environment around the asteroid (162173) Ryugu is analyzed in detail using a constant-density polyhedron model based on the measurements from the Hayabusa2 mission. Six exterior equilibrium points (EPs) are identified along the ridge line of Ryugu, and their topological classifications fall into two distinctive categories. The initial periodic orbit (PO) families are computed and analyzed, including distant retrograde/prograde orbit (DRO/DPO) families and fifteen PO families emanating from the exterior EPs. The fifteen PO families are further divided into three categories: seven converge to an EP, seven reach Ryugu’s surface, and one exhibits cyclic behavior during its progression. The existence of initial PO families converging to an EP is analyzed using the bifurcation of a degenerate EP. Connection between these families and similar ones in the circular restricted three-body problem (CRTBP) is also examined. Bifurcated PO families are identified and computed from the initial PO families, including ten families from the DROs, fifteen from the DPOs, and twenty-five associated with the EPs. The bifurcated families are separately analyzed and categorized in terms of their corresponding initial families. Connections established by the same bifurcation points between different bifurcated families are identified. A comparison is made for the dynamical environments of Ryugu and Bennu to evaluate the similarities and differences in the evolution of EPs and the progression of PO families in top-shaped asteroids.

For given k bodies of collinear central configuration of Newtonian k-body problem, we ask whether one can add other l bodies at the same time on the line without changing the configuration and motion of the initial bodies so that the total k (+) l bodies provide a central configuration. We call it k+l-Moulton configuration. We find the following. When l < k (+) 1, there exist only zero-mass solutions, masses of added bodies are all zero that means infinitesimal mass. When l (=) k (+) 1, we show the existence of k+l-Moulton configuration where masses are non-negative given as a one parameter family, ({mathbf {m_{B}}}={mathbf {m_{B_{0}}}}) t, t (ge ) 0. Then there exist not only zero-mass but also positive-mass solutions whose masses are all positive. Moreover when l > k (+) 1, there is not zero-mass solution because one cannot put more than one body in an interval which is separated by initial k bodies. Then maximum number of added bodies is k (+) 1 at once in zero-mass solutions.

In this paper, we present a way of combining the computation of invariant tori and their stable and unstable manifolds with the multiple shooting technique. We start by showing some of the results of Jorba (Nonlinearity 14(5):943–976, 2001) that should be modified in order to introduce the multiple shooting technique in these computations. After that, by a direct application in the planar elliptic restricted three-body problem (PERTBP), how to modify the equations and methods to compute the above-mentioned objects is introduced. In particular, the structure of the (systems of) equations and matrices involved in these computations is shown. An application of these computations can be found in Duarte and Jorba (Invariant manifolds of tori near ({L}_1) and ({L}_2) in the planar elliptic restricted three-body problem II. The Dynamics of Comet Oterma, Preprint 2023), where the dynamics of comet 39P/Oterma is modelled as a PERTBP.

The formation of the Inner Oort Cloud (IOC)—a vast halo of icy bodies residing far beyond Neptune’s orbit—is an expected outcome of the solar system’s primordial evolution within a stellar cluster. Recent models have shown that the process of early planetesimal capture within the trans-Neptunian region may have been sufficiently high for the cumulative mass of the Cloud to approach several Earth masses. In light of this, here we examine the dynamical evolution of the IOC, driven by its own self-gravity. We show that the collective gravitational potential of the IOC is adequately approximated by the Miyamoto–Nagai model and use a semi-analytic framework to demonstrate that the resulting secular oscillations are akin to the von Zeipel–Lidov–Kozai resonance. We verify our results with direct N-body calculations and examine the effects of IOC self-gravity on the long-term behavior of the solar system’s minor bodies using a detailed simulation. Cumulatively, we find that while the modulation of perihelion distances and inclinations can occur within an observationally relevant range, the associated timescales vastly surpass the age of the sun, indicating that the influence of IOC self-gravity on the architecture of the solar system is negligible.

Within the emerging age of lunar exploration, optimizing transfer trajectories is a fundamental measure toward achieving more economical and efficient lunar missions. This study addresses the possibility of reducing the fuel cost of two-impulse Earth–Moon transfers in a four-body model with the Earth, the Moon, and the Sun as primaries. Lawden’s primer vector theory is applied within this framework to derive a set of necessary conditions for a fuel-optimal trajectory. These conditions are used to identify which trajectories from an existing database could benefit from the insertion of an additional intermediate impulse. More than 10,000 three-impulse transfers are computed with a direct numerical optimization method. These solutions contribute to enriching the database of impulsive trajectories, useful to perform trade-off analyses. While the majority of trajectories exhibit only marginal improvements, a significant breakthrough emerges for transfers featuring an initial gravity assist at the Moon. Implementing a corrective maneuver after the lunar encounter yields substantial reductions in fuel costs.