相关论文: An integrable model for first-order three-planet m…

A resonant chain may be formed in a multi-planetary system when ratios of the orbital periods can be expressed as ratios of small integers $T_1:T_2: \cdots :T_N=k_1: k_2: \cdots: k_N$. We investigate the dynamics and possible formation of…

Extrasolar systems with planets on eccentric orbits close to or in mean-motion resonances are common. The classical low-order resonant Hamiltonian expansion is unfit to describe the long-term evolution of these systems. We extend the…

The results of an extensive numerical study of the periodic orbits of planar, elliptic restricted three-body planetary systems consisting of a star, an inner massive planet and an outer mass-less body in the external 1:2 mean-motion…

We establish the criterion for chaos in three-planet systems, for systems similar to those discovered by the Kepler spacecraft. Our main results are as follows: (i) The simplest criterion, which is based on overlapping mean motion…

We analyze the possible relationship between the current orbital elements fits of known exoplanets in the 2/1 mean-motion resonance and the expected orbital configuration due to migration. It is found that, as long as the orbital decay was…

Migration of planetary systems caused by the action of dissipative forces may lead the planets to be trapped in a resonance. In this work we study the conditions and the dynamics of such resonant trapping. Particularly, we are interested in…

Following the general numerical analysis of Melita and Woolfson (1996), I showed in a recent paper that a restricted, planar, circular planetary system consisting of Sun, Jupiter and Saturn would be captured in a near (2:1) resonance when…

A new era of directly imaged extrasolar planets has produced a three-planet system (Marois et al. 2008), where the masses of the planets have been estimated by untested cooling models. We point out that the nominal circular, face-on orbits…

The gravitation interaction between particles is taken into account in central configuration model. After that, the resonance perturbation of the particle of the central configuration by distant satellite is considered in the restricted…

A Hamiltonian formulation of generic many-particle systems with space-dependent balanced loss and gain coefficients is presented. It is shown that the balancing of loss and gain necessarily occurs in a pair-wise fashion. Further, using a…

We study the time evolution of two protoplanets still embedded in a protoplanetary disk. The results of two different numerical approaches are presented and compared. In the first approach, the motion of the disk material is computed with…

The planetary restricted three-body problem (RTBP) is considered. The primary mass M is much more than another masses mj, i=1..N, which revolve around M. The massless probe particle m moves on elliptic orbit, is perturbed by mj. It is well…

Mean motion resonances play a fundamental role in the dynamics of the small bodies of the Solar System. The last decades of the 20th century gave us a detailed description of the dynamics as well as the process of capture of small bodies in…

Most recently, machine learning has been used to study the dynamics of integrable Hamiltonian systems and the chaotic 3-body problem. In this work, we consider an intermediate case of regular motion in a non-integrable system: the behaviour…

Resonant populations of trans-Neptunian objects serve as crucial dynamical archives for unraveling the early migratory history of the Solar System. A quantitative assessment of the capture efficiency into various mean motion resonances…

We investigate the dynamics of small trojan exoplanets in domains of secondary resonances within the tadpole domain of motion. We consider the limit of a massless trojan companion of a giant planet. Without other planets, this is a case of…

The characteristics of the resonant disturbing function for an asteroid perturbed by a planet in circular orbit are discussed. The location of the libration centers and their dependence with the orbital elements of the resonant orbit are…

Assuming that giant planets are formed in thin protoplanetary discs, a '3D' system can form, provided that the mutual inclination is excited by some dynamical mechanism. Resonant interactions and close planetary encounters are thought to be…

We apply the analytical disturbing function for arbitrary inclination derived in our previous work to characterize resonant width and libration of mean motion resonances at arbitrary inclination obtained from direct numerical simulations of…

Pairs of migrating extrasolar planets often lock into mean motion resonance as they drift inward. This paper studies the convergent migration of giant planets (driven by a circumstellar disk) and determines the probability that they are…