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

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 x 10(5) yr. The power spectra are dominated by a broad-band 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) similar or equal to 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.