The motion of Pluto over the age of the solar system

Abstract

Pluto's motion is chaotic in the sense that the maximum Lyapunov exponent is positive and the Lyapunov time (the inverse of the Lyapunov exponent) is about 20 million years (Myr). We have carried out the numerical integration of Pluto over the age of the solar system (5.7 billion years towards the past and 5.5 billion years towards the future), which is about 280 times of the Lyapunov time. Our integration does not show any indication of gross instability in the motion of Pluto. The time evolution of Keplerian elements of a nearby trajectory of Pluto at first grow linearly with the time and then start to increase exponentially. These exponential divergences stop at about 420 Myr and saturate. The exponential divergences are suppressed by the following three resonances that Pluto has: (1)Pluto is in the 3:2 mean motion resonance with Neptune and the libration period of the critical argument is about 20000 years.(2)The argument of perihelion librates around 90 degrees and its period is 3.8 Myr.(3)The motion of the Pluto's orbital plane referred to the Neptune's orbital plane is synchronized with the libration of the argument of perihelion (a secondary resonance). The libration period associated with the second resonance is 34.5 Myr.We briefly discuss the motions of Kuiper belt objects in a 3:2 mean motion resonance with Neptune and several possible scenarios how Pluto evolves to the present stable state.