Chaotic zones around gravitating binaries

Abstract

The extent of the continuous zone of chaotic orbits of a small-mass tertiary around a system of two gravitationally bound primaries (a double star, a double black hole, a binary asteroid, etc.) is estimated analytically, in function of the tertiary's orbital eccentricity. The separatrix map theory is used to demonstrate that the central continuous chaos zone emerges (above a threshold in the primaries mass ratio) due to overlapping of the orbital resonances corresponding to the integer ratios p:1 between the tertiary and the central binary periods. In this zone, the unlimited chaotic orbital diffusion of the tertiary takes place, up to its ejection from the system. The primaries mass ratio, above which such a chaotic zone is universally present at all initial eccentricities of the tertiary, is estimated. The diversity of the observed orbital configurations of biplanetary and circumbinary exosystems is shown to be in accord with the existence of the primaries mass parameter threshold.

arXiv comment23 pages, including 4 figures

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• The Origin of Chaos in the Orbit of Comet 1P/Halley
• Habitability properties of circumbinary planets
• Dynamical environments of MU69 and similar objects
• Pulsar Timing Signatures of Circumbinary Asteroid Belts
• Chaotic enhancement of dark matter density in binary systems
• Tidal decay of circumbinary planetary systems
• The likelihood of not detecting cavity-carving companions in transition discs -- A statistical approach
• Simulations of the dynamics of the debris disks in the systems Kepler-16, Kepler-34, and Kepler-35
• "Horseshoe" Structures in the Debris Disks of Planet-Hosting Binary Stars
• Light equation in eclipsing binary CV Boo: third body candidate in elliptical orbit
• Dynamical environments of relativistic binaries: The phenomenon of resonance shifting