# On the dynamics of Comet 1P/Halley: Lyapunov and power spectra

## TL;DR

This study analyzes the chaotic dynamics of comet 1P/Halley over 200,000 years using Lyapunov and power spectra, revealing transient chaos and estimating a Lyapunov time of approximately 562 years.

## Contribution

It provides the first detailed numerical analysis of Halley's orbit dynamics, highlighting transient chaos and the non-convergence of the Lyapunov exponent.

## Key findings

- Power spectra show planetary frequency peaks and resonances.
- Lyapunov time estimated at about 562 years.
- Results suggest eventual ejection due to transient chaos.

## Abstract

Using a purely Newtonian model for the Solar System, we investigate the dynamics of comet 1P/Halley considering in particular the Lyapunov and power spectra of its orbit, using the nominal initial conditions of JPL's Horizons system. We carry out precise numerical integrations of the $(N+1)$-restricted problem and the first variational equations, considering a time span of $2\times10^5$~yr. The power spectra are dominated by a broadband component, with peaks located at the current planetary frequencies, including contributions from Jupiter, Venus, the Earth and Saturn, as well as the $1:6$ resonance among Halley and Jupiter and higher harmonics. From the average value of the maximum Lyapunov exponent we estimate the Lyapunov time of the comet's nominal orbit, obtaining $\tau_L \simeq 562$~yr; the remaining independent Lyapunov exponents (not related by time-reversal symmetry) tend asymptotically to zero as $t^{-1/2}$. Yet, our results do not display convergence of the maximum Lyapunov exponent. We argue that the lack of convergence of the maximum Lyapunov exponent is a signature of transient chaos which will lead to an eventual ejection of the comet from the Solar System.