Related papers: Three Body Resonance Overlap in Closely Spaced Mul…
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…
We herein utilize the general three-body problem (GTBP) as a model, in order to simulate resonant systems consisting of a star and two planets, where at least one of them is highly eccentric. We study them in terms of their long-term…
Mean motion resonances [MMRs] play an important role in the formation and evolution of planetary systems and have significantly influenced the orbital properties and distribution of planets and minor planets in the solar system as well as…
In spite of planetary resonances being a common dynamical mechanism acting on planetary systems, no general model exists for describing their properties, particularly for commensurabilities of any order and arbitrary values of the…
We present a numerical method to estimate the strengths of arbitrary three body mean motion resonances between two planets in circular coplanar orbits and a massless particle in an arbitrary orbit. This method allows us to obtain an atlas…
The complex scaling method permits calculations of few-body resonances with the correct asymptotic behaviour using a simple box boundary condition at a sufficiently large distance. This is also valid for systems involving more than one…
In this paper, we present preliminary results on the stability of massless particles in two and three-planet systems. The results of our study may be used to address questions concerning the stability of terrestrial planets in these systems…
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…
In the coming years, high contrast imaging surveys are expected to reveal the characteristics of the population of wide-orbit, massive, exoplanets. To date, a handful of wide planetary mass companions are known, but only one such…
Multi-planet systems face significant challenges to detection. For example, further orbiting planets have reduced signal-to-noise ratio in radial velocity detection methods, and small mutual inclinations between planets can prevent them…
Our aim is to identify and classify mean-motion resonances (MMRs) for the coplanar circular restricted three-body problem (CR3BP) for mass ratios between 0.10 and 0.50. Our methods include the maximum Lyapunov exponent, which is used as an…
Mean motion resonances are a common feature of both our own Solar System and of extrasolar planetary systems. Bodies can be trapped in resonance when their orbital semi-major axes change, for instance when they migrate through a…
A number of multiplanet systems are observed to contain planets very close to mean motion resonances, although there is no significant pileup of precise resonance pairs. We present theoretical and numerical studies on the outcome of capture…
It is demonstrated that the complex scaling method can be used in practical calculations to localize three-body resonances. Our model example emphasizes the fact that in three-body systems several essentially different asymptotic behaviors…
The restricted three-body problem describes the motion of a massless particle under the influence of two primaries of masses $1-\mu$ and $\mu$ that circle each other with period equal to $2\pi$. For small $\mu$, a resonant periodic motion…
Many multi-planet systems have been discovered in recent years. Some of them are in mean-motion resonances (MMR). Planet formation theory was successful in explaining the formation of 2:1, 3:1 and other low resonances as a result of…
The long-term stability of the evolution of two-planet systems is considered by using the general three body problem (GTBP). Our study is focused on the stability of systems with adjacent orbits when at least one of them is highly…
Modern applications of celestial mechanics include the study of closely packed systems of exoplanets, circumbinary planetary systems, binary-binary interactions in star clusters, and the dynamics of stars near the galactic centre. While…
The planetary dynamics of $4/3$, $3/2$, $5/2$, $3/1$ and $4/1$ mean motion resonances is studied by using the model of the general three body problem in a rotating frame and by determining families of periodic orbits for each resonance.…
Many exo-solar systems discovered in the last decade consist of planets orbiting in resonant configurations and consequently, their evolution should show long-term stability. However, due to the mutual planetary interactions a multi-planet…