The Origin of Chaos in the Orbit of Comet 1P/Halley

TL;DR

This study investigates the chaotic nature of Halley's comet orbit, revealing a longer Lyapunov time scale than previously thought and highlighting the roles of planetary encounters in orbital chaos.

Contribution

It provides a detailed analysis of the origin of chaos in Halley's orbit using N-body simulations and semi-analytical models, offering new insights into the growth modes of perturbations.

Findings

Lyapunov time scale of about 300 years for Halley's orbit

Encounters with Venus and Jupiter contribute to exponential divergence

Oscillatory growth mode can prolong system stability in the Solar System

Abstract

According to Munoz-Gutierrez et al. (2015) 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 years, 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 years. 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.