Libration of Pluto’s argument of perihelion and the role of the major planets

Pluto’s argument of perihelion is known to librate around 90∘. This libration is related to the secular phenomenon known as the von Zeipel–Lidov–Kozai (vZLK) oscillation. In this work, we make a quantitative assessment of the influence of Neptune’s mean motion resonance and of the other giant planets’ secular perturbations on the libration of Pluto’s argument of perihelion. Here, a parameter k2=(1-e2)cos2I is the key where e is eccentricity and I is inclination. When k2 of a Pluto-like object is larger than a certain critical value, libration of its argument of perihelion would not occur. The secular effect of other disturbing planets (Jupiter, Saturn, Uranus) plays a significant role in determining the critical k2. The nonzero oscillation amplitude of the critical resonant argument also plays a role, although not a dominant one.