Analytical Treatment of Planetary Resonances
arXiv:1305.6513 · doi:10.1051/0004-6361/201220907
Abstract
An ever-growing observational aggregate of extrasolar planets has revealed that systems of planets that reside in or near mean-motion resonances are relatively common. While the origin of such systems is attributed to protoplanetary disk-driven migration, a qualitative description of the dynamical evolution of resonant planets remains largely elusive. Aided by the pioneering works of the last century, we formulate an approximate, integrable theory for first-order resonant motion. We utilize the developed theory to construct an intuitive, geometrical representation of resonances within the context of the unrestricted three-body problem. Moreover, we derive a simple analytical criterion for the appearance of secondary resonances between resonant and secular motion. Subsequently, we demonstrate the onset of rapid chaotic motion as a result of overlap among neighboring first-order mean-motion resonances, as well as the appearance of slow chaos as a result of secular modulation of the planetary orbits. Finally, we take advantage of the integrable theory to analytically show that, in the adiabatic regime, divergent encounters with first-order mean-motion resonances always lead to persistent apsidal anti-alignment.
21 pages, 13 figures, accepted to A&A
References in corpus (13)
- Origin of the Structure of the Kuiper Belt during a Dynamical Instability in the Orbits of Uranus and Neptune
- Migration and the formation of systems of hot super-Earths and Neptunes
- Statistical Study of the Early Solar System's Instability with 4, 5 and 6 Giant Planets
- Dynamics of the giant planets of the solar system in the gaseous proto-planetary disk and relationship to the current orbital architecture
- Three-dimensional simulations of multiple protoplanets embedded in a protostellar disc
- Resonant Repulsion of Kepler Planet Pairs
- Long-term tidal evolution of short-period planets with companions
- On corotation torques, horseshoe drag and the possibility of sustained stalled or outward protoplanetary migration
- HD45364, a pair of planets in a 3:2 mean motion resonance
- Dissipation in planar resonant planetary systems
- Simulating planet migration in globally evolving disks
- Mean Motion Resonances in Exoplanet Systems: An Investigation Into Nodding Behavior
- Stochastic orbital migration of small bodies in Saturn's rings
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- Evidence for a Distant Giant Planet in the Solar System
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- Eccentricity Driven Climate Effects in the Kepler-1649 System
- The role of dissipative evolution for three-planet, near-resonant extrasolar systems
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- Alleviating the transit timing variation bias in transit surveys. I. RIVERS: Method and detection of a pair of resonant super-Earths around Kepler-1705
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- K2-19b and c are in a 3:2 Commensurability but out of Resonance: A Challenge to Planet Assembly by Convergent Migration
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- Stability of exomoons around the Kepler transiting circumbinary planets
- The Stability Boundary of the Distant Scattered Disk
- On the coplanar eccentric non restricted co-orbital dynamics
- Resonance in the K2-19 system is at odds with its high reported eccentricities
- celmech: A Python package for celestial mechanics
- Resonant Laplace-Lagrange theory for extrasolar systems in mean-motion resonance
- Long-term tidal evolution of the TRAPPIST-1 system
- Forming the Trappist-1 system in two steps during the recession of the disc inner edge
- Dissipative Capture of Planets Into First-Order Mean-Motion Resonances
- Terrestrial planet and asteroid belt formation by Jupiter-Saturn chaotic excitation
- Alleviating the Transit Timing Variations bias in transit surveys. II. RIVERS: Twin resonant Earth-sized planets around Kepler-1972 recovered from Kepler's false positive
- Enhanced Size Uniformity for Near-resonant Planets
- Apsidal Alignment and Anti-Alignment of Planets in Mean-Motion Resonance: Disk-Driven Migration and Eccentricity Driving
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- Inferred Properties of Planets in Mean-Motion Resonances are Biased by Measurement Noise
- Catastrophic events in protoplanetary disks and their observational manifestations
- Forming rocky exoplanets around K-dwarf stars
- Mapping the structure of the planetary 2:1 mean motion resonance. The TOI-216, K2-24, and HD27894 systems
- Planet formation: key mechanisms and global models
- Mathematical encoding within multi-resonant planetary systems as SETI beacons
- A Pair of Dynamically Interacting Sub-Neptunes Around TOI-6054
- Dynamics of co-orbital exoplanets
- Higher-Order Mean-Motion Resonances Can Form in Type-I Disk Migration
- Existence proof of librational invariant tori in an averaged model of HD60532 planetary system
- Dynamical Evolution of Planetary Systems
- Numerical approach to second-order canonical perturbation theory in the planetary 3-body problem: Application to exoplanets
- Exponential distance relation (aka Titius-Bode rule) in extra solar planetary systems
- Semi-analytical model for planetary resonances: application to planets around single and binary stars
- Dynamical Interactions in the Planetary System GJ4276
- Dynamical analysis of the 5:1 mean-motion resonance of the HD 202206 system