Other factors Numerical studies have shown that over periods of millions of years, the general nature of the alignment between Pluto and Neptune's orbits does not change.   There are several other resonances and interactions that govern the details of their relative motion, and enhance Pluto's stability. These arise principally from two additional mechanisms (besides the 3:2 mean motion resonance). First, Pluto's argument of perihelion , the angle between the point where it crosses the ecliptic and the point where it is closest to the Sun, librates around 90°.  This means that when Pluto is nearest the Sun, it is at its farthest above the plane of the Solar System, preventing encounters with Neptune. This is a direct consequence of the Kozai mechanism ,  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° (= 90°–38°). The closest such
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This note was uploaded on 12/15/2011 for the course AST AST1002 taught by Professor Emilyhoward during the Fall '10 term at Broward College.