The origin of chaos in the orbit of comet 1P/Halley

According to Muñoz-Gutiérrez et al. the orbit of comet 1P/Halley is chaotic with a surprisingly small Lyapunov time-scale of order its orbital period. In this work we analyse the origin of chaos in Halley's orbit and the growth of perturbations, in order to get a better understanding of this un...

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Bibliographic Details
Published in:Monthly notices of the Royal Astronomical Society 2016-10, Vol.461 (4), p.3576-3584
Main Authors: Boekholt, T. C. N., Pelupessy, F. I., Heggie, D. C., Portegies Zwart, S. F.
Format: Article
Language:English
Subjects:
Astrophysics
Chaos theory
Comets
Dynamical systems
Encounters
Mathematical models
Numerical analysis
Orbits
Origins
Perturbation methods
Planetology
Simulation
Solar system
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Summary:According to Muñoz-Gutiérrez et al. the orbit of comet 1P/Halley is chaotic with a surprisingly small Lyapunov time-scale of order its orbital period. In this work we analyse the origin of chaos in Halley's orbit and the growth of perturbations, in order to get a better understanding of this unusually short time-scale. We perform N-body simulations to model Halley's orbit in the Solar system and measure the separation between neighbouring trajectories. To be able to interpret the numerical results, we use a semi-analytical map to demonstrate different growth modes, i.e. linear, oscillatory or exponential, and transitions between these modes. We find the Lyapunov time-scale of Halley's orbit to be of order 300 yr, which is significantly longer than previous estimates in the literature. This discrepancy could be due to the different methods used to measure the Lyapunov time-scale. A surprising result is that next to Jupiter, also encounters with Venus contribute to the exponential growth in the next 3000 yr. Finally, we note an interesting application of the sub-linear, oscillatory growth mode to an ensemble of bodies moving through the Solar system. Whereas in the absence of encounters with a third body the ensemble spreads out linearly in time, the accumulation of weak encounters can increase the lifetime of such systems due to the oscillatory behaviour.
ISSN:0035-8711
1365-2966
DOI:10.1093/mnras/stw1504