2 λN−ϖP librates around 180° with an amplitude of about 80° and a libration period of about 2 × 104 yr.
The argument of perihelion of Pluto ωP=θ2=ϖP−ΩP librates around 90° with a period of about 3.8 × 106 yr. The dominant periodic variations of the eccentricity and inclination of Pluto are synchronized with the libration of its argument of perihelion. This is anticipated in the secular perturbation theory constructed by Kozai (1962).
The longitude of the node of Pluto referred to the longitude of the node of Neptune，θ3=ΩP−ΩN， circulates and the period of this circulation is equal to the period of θ2 libration. When θ3 becomes zero， i.e. the longitudes of ascending nodes of Neptune and Pluto overlap， the inclination of Pluto becomes maximum， the eccentricity becomes minimum and the argument of perihelion becomes 90°. When θ3 becomes 180°， the inclination of Pluto becomes minimum， the eccentricity becomes maximum and the argument of perihelion becomes 90° again. Williams &a
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