Related papers: Relativistic Mean Motion Resonance
In some planetary systems, the orbital periods of two of its members present a commensurability, usually known by mean-motion resonance. These resonances greatly enhance the mutual gravitational influence of the planets. As a consequence,…
We show that transient resonances occur in the two body problem in general relativity, in the highly relativistic, extreme mass-ratio regime for spinning black holes. These resonances occur when the ratio of polar and radial orbital…
Mean motion resonances are a common feature of both our own Solar System and of extrasolar planetary systems. Bodies can be trapped in resonance when their orbital semi-major axes change, for instance when they migrate through a…
Mean motion resonances are a common feature of both our own Solar System and of extrasolar planetary systems. Bodies can be trapped in resonance when their orbital semi-major axes change, for instance when they migrate through a…
In a previous investigation, a model of three-body motion was developed which included the effects of gravitational radiation reaction. The aim was to describe the motion of a relativistic binary pulsar that is perturbed by a third mass and…
Mean motion resonances play a fundamental role in the dynamics of the small bodies of the Solar System. The last decades of the 20th century gave us a detailed description of the dynamics as well as the process of capture of small bodies in…
A massive black hole binary might resonantly trap a star (e.g. a white dwarf) and the gas released by its tidal disruption might emit electromagnetic wave signals around the coalescence of the binary. With post-Newtonian equations of motion…
In a previous paper (Gayon & Bois 2008a), we have shown the general efficiency of retrograde resonances for stabilizing compact planetary systems. Such retrograde resonances can be found when two-planets of a three-body planetary system are…
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…
One component of a massive black hole binary (MBHB) might capture a small third body, and then a hierarchical, inclined triple system would be formed. With the post-Newtonian approximation including radiation reaction, we analyzed the…
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…
We consider the three-body mean motion resonance defined by the Jovian moons Io, Europa, and Ganymede, which is commonly known as the Laplace resonance. In particular, we construct approximate models for the evolution of the librating…
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…
The early stages of dynamical evolution of planetary systems are often shaped by dissipative processes that drive orbital migration. In multi-planet systems, convergent amassing of orbits inevitably leads to encounters with rational period…
Mean motion resonances (MMRs) are a generic outcome of convergent migration for bodies embedded in accretion disks around a central mass. Long studied in planetary systems, the same phenomenon should occur for stellar-mass black holes (BHs)…
Motivated by the large number of extrasolar planetary systems that are near mean motion resonances, this paper explores a related type of dynamical behavior known as "nodding". Here, the resonance angle of a planetary system executes…
The dynamical system studied in previous papers of this series, namely a bound time-like geodesic motion in the exact static and axially symmetric space-time of an (originally) Schwarzschild black hole surrounded by a thin disc or ring, is…
Mean motion resonances [MMRs] play an important role in the formation and evolution of planetary systems and have significantly influenced the orbital properties and distribution of planets and minor planets in the solar system as well as…
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…
The identification of mean motion resonances in exoplanetary systems or in the Solar System might be cumbersome when several planets and large number of smaller bodies are to be considered. Based on the geometrical meaning of the resonance…