Editing Pluto (section)

==== Other factors ====
Numerical studies have shown that over millions of years, the general nature of the alignment between the orbits of Pluto and Neptune does not change.<ref name="huainn01" /><ref name="williams71" /> There are several other resonances and interactions that enhance Pluto's stability. These arise principally from two additional mechanisms (besides the 2:3 mean-motion resonance).

First, Pluto's [[argument of perihelion]], the angle between the point where it crosses the ecliptic (or the [[invariant plane]]) and the point where it is closest to the Sun, [[libration|librates]] around 90°.<ref name="williams71" /> This means that when Pluto is closest to the Sun, it is at its farthest north of the plane of the Solar System, preventing encounters with Neptune. This is a consequence of the [[Kozai mechanism]],<ref name="huainn01" /> which relates the eccentricity of an orbit to its inclination to a larger perturbing body—in this case, Neptune. Relative to Neptune, the amplitude of libration is 38°, and so the angular separation of Pluto's perihelion to the orbit of Neptune is always greater than 52° {{nowrap|(90°–38°)}}. The closest such angular separation occurs every 10,000 years.<ref name="sp-345" />

Second, the longitudes of ascending nodes of the two bodies—the points where they cross the [[invariant plane]]—are in near-resonance with the above libration. When the two longitudes are the same—that is, when one could draw a straight line through both nodes and the Sun—Pluto's perihelion lies exactly at 90°, and hence it comes closest to the Sun when it is furthest north of Neptune's orbit. This is known as the ''1:1 superresonance''. All the [[Jovian planets]] (Jupiter, Saturn, Uranus, and Neptune) play a role in the creation of the superresonance.<ref name="huainn01" />