Related papers: Study of Resonances for the Restricted 3-Body Prob…
The Restricted 3-Body Problem models the motion of a body of negligible mass under the gravitational influence of two massive bodies called the primaries. If one assumes that the primaries perform circular motions and that all three bodies…
The K2-138 system hosts six planets and presents an interesting case study due to its distinctive dynamical structure. Its five inner planets are near a chain of 3/2 two-body mean-motion resonances, while the outermost body (planet {\it g})…
In this paper, we present the most comprehensive study to date on Neptune's mean-motion resonances (MMRs) in the distant Kuiper belt from 50 to 100 AU. Over 200 resonant Kuiper belt objects (KBOs) have been identified in this region,…
The rectilinear elliptic restricted Three Body Problem (TBP) is the limiting case of the elliptic restricted TBP when the motion of the primaries is described by a Keplerian ellipse with eccentricity $e'=1$, but the collision of the…
In this paper on mean motion resonances in the Kuiper belt we consider effects on resonant bodies captured in an earlier migration by determining levels of chaos as a function of eccentricity, e, at the most stable orbital configuration. We…
We propose a semianalytical method for the calculation of widths, libration centers and small amplitude libration periods of the mean motion resonances k_p:k in the framework of the circular restricted three body problem valid for arbitrary…
The behaviour of resonances in the spin-orbit coupling in Celestial Mechanics is investigated. We introduce a Hamiltonian nearly-integrable model describing an approximation of the spin-orbit interaction. A parametric representation of…
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…
The size distribution of the stability region around the Lagrangian point L4 is investigated in the elliptic restricted three-body problem as the function of the mass parameter and the orbital eccentricity of the primaries. It is shown that…
Mean motion resonances (MMRs) are a key phenomenon in orbital dynamics. The traditional disturbing function expansion in celestial mechanics shows that, at low eccentricities, $p$:$p-q$ MMRs exhibit a clear hierarchy of strengths, scaling…
The focus of this work is the current distribution of asteroids in co-orbital motion with Venus, Earth and Jupiter, under a quasi-coplanar configuration and for a medium-term timescale of the order of 900 years. A co-orbital trajectory is a…
We study the dynamics of the restricted planar three-body problem near mean motion resonances, i.e. a resonance involving the Keplerian periods of the two lighter bodies revolving around the most massive one. This problem is often used to…
To better understand the orbital dynamics of exoplanets around close binary stars, i.e., circumbinary planets (CBPs), we applied techniques from dynamical systems theory to a physically motivated set of solutions in the Circular Restricted…
We investigate the dynamics of satellites and space debris in external resonances, namely in the region outside the geostationary ring. Precisely, we focus on the 1:2, 1:3, 2:3 resonances, which are located at about 66 931.4 km, 87 705.0…
We study the dynamics of the space debris in regions corresponding to minor resonances; precisely, we consider the resonances 3:1, 3:2, 4:1, 4:3, 5:1, 5:2, 5:3, 5:4, where a j:l resonance (with j, l integers) means that the periods of…
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…
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…
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 conducted extensive numerical experiments of equal mass three-body systems until they became disrupted. The system lifetimes, as a bound triple, and the Lyapunov times show a correlation similarto what has been earlier obtained for small…
We explore the possibility that extrasolar planets might be found in the 1:1 mean-motion resonance. There are a variety of stable co-orbtial configurations, and we specifically examine three different versions of the 1:1 resonance. These…