Related papers: Relativistic Mean Motion Resonance
Orbital resonances are ubiquitous in the Solar system. They play a decisive role in the long term dynamics, and in some cases the physical evolution, of the planets and of their natural satellites, as well as the evolution of small bodies…
Extrasolar systems with planets on eccentric orbits close to or in mean-motion resonances are common. The classical low-order resonant Hamiltonian expansion is unfit to describe the long-term evolution of these systems. We extend the…
We present the details of a model in general relativity of a small charged black hole moving in an external gravitational and electromagnetic field. The importance of our model lies in the fact that we can derive the equations of motion of…
After black holes collide, the remnant settles to a stationary state by emitting gravitational waves. Once non-linearities subside, these ringdown waves are dominated by exponentially-damped sinusoids, or quasinormal modes. We develop a…
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…
Periodic orbits exhibiting zoom-whirl behavior have become attractive topics for studying particle dynamics and gravitational wave emission in extreme-mass-ratio inspirals (EMRIs). This study systematically investigates periodic orbits…
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…
Stability of Hilda Asteroids in the solar system around the 3:2 resonance point is analyzed in terms of the Sun-Jupiter-asteroid elliptic restricted three-body problem. We show that the Hamiltonian of the system is well-approximated by a…
We evaluate general-relativistic effects in motion of stationary accretion disks around a Schwarzschild black hole, assuming the first post-Newtonian (1PN) approximation. There arises an integrability condition, that leads to the emergence…
The inspiral of stellar-mass compact objects, like neutron stars or stellar-mass black holes, into supermassive black holes provides a wealth of information about the strong gravitational-field regime via the emission of gravitational…
We map the general relativistic two-body problem onto that of a test particle moving in an effective external metric. This effective-one-body approach defines, in a non-perturbative manner, the late dynamical evolution of a coalescing…
We study the influence of relativity on the chaotic properties and dynamical outcomes of an unstable triple system; the Pythagorean three-body problem. To this end, we extend the Brutus N-body code to include Post-Newtonian pairwise terms…
This paper continues previous work on the effects of turbulence on mean motion resonances in extrasolar planetary systems. Turbulence is expected to arise in the disks that form planets, and these fluctuations act to compromise resonant…
Extreme mass-ratio inspirals, in which solar-mass compact bodies spiral into supermassive black holes, are an important potential source for gravitational wave detectors. Because of the extreme mass-ratio, one can model these systems using…
Type-I disk migration can form a chain of planets engaged in first-order mean-motion resonances (MMRs) parked at the disk inner edge. However, while second- or even third-order resonances were deemed unlikely due to their weaker strength,…
We present a numerical study on the stability of the 1/2, 2/1 and 1/1 retrograde mean motion resonances in the 3-body problem composed of a solar mass star, a Jupiter mass planet and an additional body with zero mass (elliptic restricted…
The coherent torques between stars on orbits near massive black holes (MBHs) lead to resonant angular momentum relaxation. Due to the fact that orbits are Keplerian to good approximation, the torques efficiently change the magnitude of the…
We consider the 3-body problem in relativistic lineal gravity and obtain an exact expression for its Hamiltonian and equations of motion. While general-relativistic effects yield more tightly-bound orbits of higher frequency compared to…
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…
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…