Libration of Pluto-Neptune

Numerical integration of the orbits of the five outer planets over 120,000 years reveals that the distance between Pluto and Neptune at the closest approaches oscillates within a narrow range. The distance is never much less than the aphelion distance of Pluto from the orbit of Neptune. The near commensurability in the periods of Pluto and Neptune and the eccentricity of Pluto's orbit are responsible for the libratory motion.