相关论文: Some additional results of the Hilda group orbital…
The Hilda group is a set of asteroids whose mean motion is in a 3:2 orbital resonance with Jupiter. In this paper we use the planar Circular Restricted Three-Body Problem (CRTBP) as a dynamical model and we show that there exists a family…
In this paper we present our results of numerical integrations of orbits of fictive massless particle in vicinity of resonance. Our goal is to study the dependences of period (frequency) of resonance perturbations and the width of the…
Hilda-group asteroids librate in Jupiter's interior 3:2 mean motion resonance. We estimate that the Hilda group is observationally complete up to absolute magnitude $H\leq16.3$. This provides a statistically useful sample of thousands of…
Stability of Hilda Asteroids in the solar system around the 3:2 resonance point is analyzed in terms of the Sun-Jupiter-asteroid elliptic restricted three-body problem. We show that the Hamiltonian of the system is well-approximated by a…
This work introduces a new set of orbital elements to fully represent the zonal harmonics problem around an oblate celestial body. This new set of orbital elements allows to obtain a complete linear system for the unperturbed problem and,…
Limits and characteristic periods of variations in orbital elements of planets were studied by numerical integration of equations of motion. Interrelations between the characteristic periods of variations in orbital elements of some planets…
Proper elements are quasi-integrals of motion, meaning that they can be considered constant over a certain timespan, and they permit to describe the long-term evolution with a few parameters. Near-Earth objects (NEOs) generally have a large…
In this paper, a new parametrization of the relative motion between two satellites orbiting a central body is presented. The parametrization is based on the nodal elements: a set of angles describing the orbit geometry with respect to the…
This paper explores the problem of analytically approximating the orbital state for a subset of orbits in a rotating potential with oblateness and ellipticity perturbations. This is done by isolating approximate differential equations for…
We calculate numerically the periodic orbits of pseudointegrable systems of low genus numbers $g$ that arise from rectangular systems with one or two salient corners. From the periodic orbits, we calculate the spectral rigidity…
The traditional approach to analyzing mean motion resonances is through canonical perturbation theory. While this is a powerful method, its generality leads to complicated combinations of variables that are challenging to interpret and…
Hilda asteroids orbit at the outer edge, or just outside of the Main Belt, occupying the 2:3 mean motion resonance with Jupiter. It is known that the group shows a mixed taxonomy that suggests the mixed origin of Hilda members, having…
The 2:1 mean motion resonance orbit was integrated at the restricted planar 3-body problem in absolute frame. Orbit of Jupiter was assumed circular. Initial Jupiter longitude was assumed zero. The Runge-Kutta method was used. The start of…
The Hilda population of asteroids is located in a large orbital zone of long-term stability associated with the Jupiter J3/2 mean motion resonance. They are a sister population of the Jupiter Trojans, since both of them are likely made up…
We derive the secular evolution of the orbital elements of a stellar-mass object orbiting a spinning massive black hole. We use the post-Newtonian approximation in harmonic coordinates, with test-body equations of motion for the…
We study the dihedral multi-reference alignment problem of estimating the orbit of a signal from multiple noisy observations of the signal, acted on by random elements of the dihedral group. We show that if the group elements are drawn from…
In this article, equilibrium points and families of periodic orbits in the vicinity of the collinear equilibrium points of a binary asteroid system are investigated with respect to the angular velocity of the secondary body, the mass ratio…
Current models of Solar System evolution posit that the asteroid populations in resonance with Jupiter are comprised of objects scattered inward from the outer Solar System during a period of dynamical instability. In this paper, we present…
One often-used approximation in the study of binary compact objects (i.e., black holes and neutron stars) in general relativity is the instantaneously circular orbit assumption. This approximation has been used extensively, from the…
A moment approach for orbit determinations of an astrometric binary with low signal-to-noise ratio from astrometric observations alone is proposed, especially aiming at a close binary system with a short orbital period such as Cyg-X1 and…