Related papers: Periodic orbits of the retrograde coorbital proble…
The origins of irregular satellites of the giant planets are an important piece of the giant "puzzle" that is the theory of Solar System formation. It is well established that they are not "in situ" formation objects, around the planet, as…
The planet Mercury is locked in a spin-orbit resonance where it rotates three times about its spin axis for every two orbits about the Sun. The current explanation for this unique state assumes that the initial rotation of this planet was…
We investigate the resonance spectrum of the H\'enon-Heiles potential up to twice the barrier energy. The quantum spectrum is obtained by the method of complex coordinate rotation. We use periodic orbit theory to approximate the oscillating…
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…
An ever-growing observational aggregate of extrasolar planets has revealed that systems of planets that reside in or near mean-motion resonances are relatively common. While the origin of such systems is attributed to protoplanetary…
Hilda asteroids, which orbit in a 3:2 resonance with Jupiter, serve as key indicators of dynamical processes in the early solar system. Their spin rates, an important probe of these mechanisms, can constrain their density and collisional…
The population of natural objects in a 1:1 mean motion resonance with Earth are known as Earth's co-orbitals. Main belt objects can dynamically evolve into Earth co-orbitals but taxonomic studies of some of them have suggested that they are…
We present the dynamical structure of the phase space of the planar planetary 2/1 mean-motion resonance (MMR). Inside the resonant domain, there exist two families of periodic orbits, one associated to the librational motion of the critical…
We investigate the condition for capture into first-order mean motion resonances using numerical simulations with a wide range of various parameters. In particular, we focus on deriving the critical migration timescale for capture into the…
We study the migration of three-planet systems in an irradiated 1+1D $\alpha$-disc with photoevaporation. We performed $2700$ simulations with various planets' masses and initial orbits. We found that most of the systems which ended up as…
We have investigated the dependence of the prograde/retrograde temporary capture of asteroids by a planet on their original heliocentric semimajor axes through analytical arguments and numerical orbital integrations in order to discuss the…
All near-Earth asteroids (NEAs) that reach sufficiently small perihelion distances will undergo a so-called super-catastrophic disruption. The mechanisms causing such disruptions are currently unknown or, at least, undetermined. To help…
We present a planar four-body model, called the Binary Asteroid Problem, for the motion of two asteroids (having small but positive masses) moving under the gravitational attraction of each other, and under the gravitational attraction of…
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…
The discovery of 1I/2017 U1 ('Oumuamua) has provided the first glimpse of a planetesimal born in another planetary system. This interloper exhibits a variable colour within a range that is broadly consistent with local small bodies such as…
Coorbital bodies are observed around the Sun sharing their orbits with the planets, but also in some pairs of satellites around Saturn. The existence of coorbital planets around other stars has also been proposed. For close-in planets and…
By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…
Based on the value of the orbital eccentricity of a particle and also its proximity to the exact resonant orbit in a three-body system, the Pendulum Approximation (Dermott & Murray 1983) or the Second Fundamental Model of Resonance (Andoyer…
We carry out numerical simulations to explore the dynamical evolution of the HD 82943 and HD 37124 planetary systems,which both have two Jupiter-like planets. By simulating various planetary configurations in the neighborhood of the fitting…
The multiple-planet systems discovered by the Kepler mission show an excess of planet pairs with period ratios just wide of exact commensurability for first-order resonances like 2:1 and 3:2. In principle, these planet pairs could have both…