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We investigate the heteroclinic connections between stable and unstable manifolds of unstable periodic orbits associated with the most important mean motion resonances (MMRs) in the Sun-Jupiter planar restricted three-body problem. We…
We analyze the distribution of known multi-planet systems ($N \geq 3$) in the plane of mean-motion ratios, and compare it with the resonance web generated by two-planet mean-motion resonances (2P-MMR) and pure 3-planet commensurabilities…
In cosmological simulations without baryons, the relation between the specific angular momentum $j_{\rm h}$ and mass $M_{\rm h}$ of galactic dark matter halos has the well-established form $j_{\rm h} \propto M_{\rm h}^{2/3}$. This is…
It has been proposed that mean motion resonances (MMRs) between Planet Nine and distant objects of the scattered disk might inform the semimajor axis and instantaneous position of Planet Nine. Within the context of this hypothesis, the…
In the framework of the concordance cosmological model the first-order scalar and vector perturbations of the homogeneous background are derived in the weak gravitational field limit without any supplementary approximations. The sources of…
Given the multi-frequency nature of relativistic orbits, transient orbital resonances are expected to be ubiquitous during an extreme-mass-ratio inspiral (EMRI). At a resonance, the orbital dynamics is modified in a nontrivial way,…
An intriguing trend among \kepler's multi-planet systems is an overabundance of planet pairs with period ratios just wide of a mean motion resonance (MMR) and a dearth of systems just narrow of them. Traditional planet formation models are…
It is proposed that meson resonances are linear combinations of q-qbar and meson-meson (MM); baryon resonances are combinations of qqq and meson-baryon (MB). Mixing between these combinations arises via decays of confined states to…
We study the evolution of two planets around a star, in mean-motion resonance and undergoing tidal effect. We derive an integrable analytical model of mean-motion resonances of any order which reproduce the main features of the resonant…
We present two-dimensional hydrodynamical simulations of pairs of planets migrating simultaneously in the Type I regime in a protoplanetary disc. Convergent migration naturally leads to the trapping of these planets in mean-motion…
Coronal mass ejections (CMEs) are the primary drivers of severe space weather disturbances in the heliosphere. Models of CME dynamics have been proposed that do not fully include the effects of magnetic reconnection on the forces driving…
The interactions among objects in a mean motion resonance are important for the orbital evolution of satellites and rings, especially Saturn's ring arcs and associated moons. In this work, we examine interactions among massive bodies in the…
In this paper, we study the behavior of a pair of co-orbital planets, both orbiting a central star on the same plane and undergoing tidal interactions. Our goal is to investigate final orbital configurations of the planets, initially…
We propose a semianalytical method to compute the strengths on each of the three massive bodies participating in a three body mean motion resonance (3BR). Applying this method we explore the dependence of the strength on the masses, the…
A condition upon which sporadic bursts (intermittent behaviour) of the relative energy become possible is derived for the motion in the chaotic layer around the separatrix of non-linear resonance. This is a condition for the existence of a…
The classical disturbing function of the three-body problem widely used in planetary dynamics studies is an expansion of the gravitational interaction of the three-body problem with respect to zero eccentricity and zero inclination. This…
Continuing our study of the effects of secular resonances on the formation of terrestrial planets in moderately close binary stars, we present here the results of an extensive numerical simulations of the formation of these objects.…
Many multiple-planet systems have been found by the Kepler transit survey and various radial velocity (RV) surveys. Kepler planets show an asymmetric feature, namely, there are small but significant deficits/excesses of planet pairs with…
The magnetorotational instability (MRI) is key physics in accretion disks and is widely considered to play some role in massive-star core collapse. Models of rotating massive stars naturally develop very strong shear at composition…
Diversity in the properties of exoplanetary systems arises, in part, from dynamical evolution that occurs after planet formation. We use numerical integrations to explore the relative role of secular and resonant dynamics in the long-term…