Resonance locking between Jupiter and Uranus

Abstract

Kinoshita and Nakai¹ have recently performed the longest numerical integration of the outer bodies of the Solar System ever attempted. The positions and velocities of Jupiter, Saturn, Uranus, Neptune and Pluto for the 5 Myr that they computed extended the integration time by a factor 5 with respect to previous ephemerides computed by Cohen et al.². Although this is only one-thousandth of the present age of the Solar System, our analysis of the data using new methods^3–5, shows surprising dynamical features. Stability is monitored by separating the system into three-body subsystems. It is found that the outer Solar System is made up of two main subsystems, Sun–Jupiter–Saturn and Sun–Uranus–Neptune, exchanging angular momentum over a period of 1.1 Myr. The dynamical mechanism responsible for locking the two subsystems together is a libration of the angle between Jupiter's and Uranus' perihelion around 180° with the same period of 1.1 Myr. No dynamical locking over such a long period of time has been found in the Solar System, although similar mechanisms have been predicted.