Related papers: Resonant chains in triple-planetary systems
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…
We study a Hamiltonian system of type describing a charged particle resonant interaction with an electromagnetic wave. We consider an ensemble of particles that repeatedly pass through the resonance with the wave, and study evolution of the…
We investigate the resonant rotation of co-orbital bodies in eccentric and planar orbits. We develop a simple analytical model to study the impact of the eccentricity and orbital perturbations on the spin dynamics. This model is relevant in…
The TRAPPIST-1 planetary system consists of seven planets within 0.05 au of each other, five of which are in a multi-resonant chain. {These resonances suggest the system formed via planet migration; subsequent tidal evolution has damped…
We study the resonant dynamics in a simple one degree of freedom, time dependent Hamiltonian model describing spin-orbit interactions. The equations of motion admit periodic solutions associated with resonant motions, the most important…
Compact planetary systems with more than two planets can undergo orbital crossings from planet-planet perturbations. The time which the system remains stable without orbital crossings has an exponential dependence on the initial orbital…
The significant orbital eccentricities of most giant extrasolar planets may have their origin in the gravitational dynamics of initially unstable multiple planet systems. In this work, we explore the dynamics of two close planets on…
The resonant configurations and normal frequencies of a loaded hanging chain that is rotating uniformly about the vertical are examined for theoretical and experimental perspectives. The chain is assumed pinned at both ends, with an extra…
The continuation of resonant periodic orbits from the restricted to the general three body problem is studied in a systematic way. Starting from the Keplerian unperturbed system we obtain the resonant families of the circular restricted…
We compute the strengths of zero-th order (in eccentricity) three-body resonances for a co-planar and low eccentricity multiple planet system. In a numerical integration we illustrate that slowly moving Laplace angles are matched by…
It is widely believed that resonant orbits play an important role in formation and evolution of bars and large-scale spirals in galaxy discs. These resonant orbits have been studied in a number of specific potentials, often with an imposed…
Capture into mean motion resonance (MMR) is an important dynamical mechanism as it shapes the final architecture of a planetary system. We simulate systems of two or three planets undergoing migration with varied initial parameters such as…
Recent observations have revealed the distribution of orbital period ratios of adjacent planets in multiple super-Earth systems and how these distributions change with time. The aim of this study is to clarify under what conditions the…
Compact non-resonant systems of sub-Jovian planets are the most common outcome of the planet formation process. Despite exhibiting broad overall diversity, these planets also display dramatic signatures of intra-system uniformity in their…
We analyse the stability of the de Sitter equilibria in multi-resonant planetary systems. The de Sitter equilibrium is the dynamical state of the Laplace resonance in which all resonant arguments are librating. The sequence of equilibria…
This work investigates different models of rotational dynamics of two rigid bodies with the shape of an ellipsoid, moving under their gravitational influence. The focus of this study is on their behavior, their linear stability, and…
Non-autonomous perturbations of isochronous systems in the plane are considered. It is assumed that the intensity of perturbations decays with time, and the frequency is asymptotically constant with the limiting value satisfying a resonance…
Since the launch of the Kepler space telescope in 2009 and the subsequent K2 mission, hundreds of multi-planet systems have been discovered. The study of such systems, both as individual systems and as a population, leads to a better…
The orbits in the HD 160691 planetary system at first appeared highly unstable, but using the MEGNO and FLI techniques of global dynamics analysis in the orbital parameter space we have found a stabilizing mechanism that could be the key to…
Convergent migration involving multiple planets embedded in a viscous protoplanetary disc is expected to produce a chain of planets in mean motion resonances, but the multiplanet systems observed by the Kepler spacecraft are generally not…