Related papers: Bridges and gaps at low-eccentricity first-order r…
Close-in planetary systems detected by the Kepler mission present an excess of periods ratio that are just slightly larger than some low order resonant values. This feature occurs naturally when resonant couples undergo dissipation that…
Planets close to their stars are thought to form farther out and migrate inward due to angular momentum exchange with gaseous protoplanetary disks. This process can produce systems of planets in co-orbital (Trojan or 1:1) resonance, in…
Orbits of known extrasolar planets that are located outside the tidal circularization regions of their parent stars are often substantially eccentric. By contrast, planetary orbits in our Solar System are approximately circular, reflecting…
Trappist-1 hosts 7 planets where period ratios of neighbouring pairs are close to the 8:5, 5:3, 3:2, 3:2, 4:3, and 3:2 ratios in increasing distance from the star. The Laplace angles associated with neighbouring triplets are observed to be…
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…
Planets migrating in their natal discs can be captured into mean-motion resonance (MMR), in which the planets' periods are related by integer ratios. Recent observations indicate that planets in MMR can be either apsidally aligned or…
Observed pileups of planets with period ratios $\approx 1\%$ wide of strong mean motion resonances (MMRs) pose an important puzzle. Early models showed that they can be created through sustained eccentricity damping driving a slow…
We study bridging transitions between spherically and cylindrically shaped particles (colloids) of radius $R$ separated by a distance $H$ that are dissolved in a bulk fluid (solvent). Using macroscopics, microscopic density functional…
Applying the method of analytical continuation of periodic orbits, we study quasi-satellite motion in the framework of the three-body problem. In the simplest, yet not trivial model, namely the planar circular restricted problem, it is…
Comet-type periodic orbits of the circular restricted three-body problem (CR3BP) are periodic solutions that are generated from very large retrograde and direct circular Keplerian motions around the common center of mass of the primaries.…
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…
The multiple-planet systems discovered by the Kepler mission exhibit the following feature: planet pairs near first-order mean-motion resonances prefer orbits just outside the nominal resonance, while avoiding those just inside the…
In our previous study of Neptune's 4:7 mean motion resonance (MMR), we discovered that its resonant angle can only librate within a specific eccentricity ($e$) versus inclination ($i$) region, determined by a theoretical limiting curve…
We examine the dynamics of small bodies in orbits similar to that of comet 29P/Schwassmann-Wachmann 1, i.e. near-circular orbits between Jupiter and Saturn. As of late 2019, there are 14 other known bodies in this region that lie in similar…
We present a theoretical framework for investigating a two-planet system undergoing convergent type I migration in a protoplanetary disk. Our study identifies the conditions for resonant capture and subsequent dynamical stability. By…
We study the dynamical evolution of the TRAPPIST-1 system under the influence of orbital circularization through tidal interaction with the central star. We find that systems with parameters close to the observed one evolve into a state…
In this investigation we treat a special configuration of two celestial bodies in 1:1 mean motion resonance namely the so-called exchange orbits. There exist -- at least -- theoretically -- two different types: the exchange-a orbits and the…
Orbital mean motion resonances in planetary systems originate from dissipative processes in disk-planet interactions that lead to orbital migration. In multi-planet systems that host giant planets, the perturbation of the protoplanetary…
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…
Transit and radial velocity observations indicate a dearth of sub-Jupiter--mass planets on short-period orbits, outlined roughly by two oppositely sloped lines in the period--mass plane. We interpret this feature in terms of…