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The dynamical interactions that occur in newly formed planetary systems may reflect the conditions occurring in the protoplanetary disk out of which they formed. With this in mind, we explore the attainment and maintenance of orbital…
Perturbative analyses of planetary resonances commonly predict singularities and/or divergences of resonance widths at very low and very high eccentricities. We have recently re-examined the nature of these divergences using…
I consider the dynamics of mean motion resonances between pairs of co-planar planets and derive a new integrable Hamiltonian model for planets' resonant motion. The new model generalizes previously-derived integrable Hamiltonians for…
Lunar mean-motion resonances (MMRs) significantly shape cislunar dynamics beyond GEO, forming stable-unstable orbit pairs with corresponding intermingled chaotic and regular regions. The resonance zone is rigorously defined using the…
Recent observations of Kepler multi-planet systems have revealed a number of systems with planets very close to second-order mean motion resonances (MMRs, with period ratio $1:3$, $3:5$, etc.) We present an analytic study of resonance…
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 this work, we investigate configuration formation of two inner terrestrial planets near mean motion resonance (MMRs) induced by the perturbation of a distant gas-giant for the Kepler-68 system, by conducting thousands of numerical…
A key feature of close-in, multiple super-Earth (SE) systems is the tendency for adjacent planet pairs to lie just wide of low-order mean-motion resonances (MMR). This period ratio distribution has motivated numerous theoretical studies,…
Recent works on three-planet mean motion resonances (MMRs) have highlighted their importance for understanding the details of the dynamics of planet formation and evolution. While the dynamics of two-planet MMRs are well understood and…
Mean-motion resonances (MMRs) form through convergent disc migration of planet pairs, which may be disrupted by dynamical instabilities after protoplanetary disc (PPD) dispersal. This scenario is supported by recent analysis of TESS data…
Mean-motion resonances between a Keplerian disc and an orbiting companion are analysed within a Hamiltonian formulation using complex canonical Poincare variables, which are ideally suited to the description of eccentricity and inclination…
Our concern here is the nature of secondary resonances--commensurabilities between apsidal and libration periods lying within first-order mean motion resonances [mmr] in the solar system. At the 4/3 and 3/2 mmr in the asteroid belt, we find…
The observed deficit and excess of adjacent planet pairs with period ratios narrow and wide of 3:2 and 2:1, the nominal values for the corresponding mean motion resonances (MMRs), have intrigued many. Previously, using a suite of…
Mean motion commensurabilities in multi-planet systems are an expected outcome of protoplanetary disk-driven migration, and their relative dearth in the observational data presents an important challenge to current models of planet…
The characteristics of the resonant disturbing function for an asteroid perturbed by a planet in circular orbit are discussed. The location of the libration centers and their dependence with the orbital elements of the resonant orbit are…
TESS and Kepler have revealed that practically all close-in sub-Neptunes form in mean-motion resonant chains, most of which unravel on timescales of 100 Myr. Using N-body integrations, we study how planetary collisions from destabilized…
We consider the dynamical evolution of two planets orbiting in the vicinity of a first order mean motion reso- nance while simultaneously undergoing eccentricity damping and convergent migration. Following Goldreich & Schlichting (2014), we…
A number of multiplanet systems are observed to contain planets very close to mean motion resonances, although there is no significant pileup of precise resonance pairs. We present theoretical and numerical studies on the outcome of capture…
In order to study the origin of the architectures of low mass planetary systems, we perform numerical surveys of the evolution of pairs of coplanar planets in the mass range $(1-4)\ \rmn{M}_{\oplus}.$ These evolve for up to $2\times10^7…
The presence of mean-motion resonances (MMRs) in exoplanetary systems is a new exciting field of celestial mechanics which motivates us to consider this work to study the dynamical behaviour of exoplanetary systems by time evolution of the…