"Pluto & Neptune: Their orbits overlap, so one might worry that they'd collide but pluto's orbit is twisted, while Neptune's isn't and so, they never collide. The twisted Pluto must need to meet a straight- orderly Neptune then. Thanks to their mysterious order in the Solar System it's an extraordinary relationship"- This quote is from a Korean Drama where the guy is trying to console the girl about how she might be a complete mess and he might be this perfect guy but it doesn't mean they aren't meant for each other and how sometimes that is what it takes to make a relationship special. (I can't be sure which one. It could be Love Marriage 연애결혼 ... I can totally remember the scene but I can't remember even the actors!!!)
Pluto's Relationship with Neptune: The Science behind it...
At the simplest level, one can examine the two orbits and see that they do not intersect. When Pluto is closest to the Sun, and hence closest to Neptune's orbit as viewed from above, it is also the farthest above Neptune's path. Pluto's orbit passes about 8 AU above that of Neptune, preventing a collision. Pluto's ascending and descending nodes, the points at which its orbit crosses the ecliptic, are currently separated from Neptune's by over 21°.
However, this alone is not enough to protect Pluto; perturbations from the planets (especially Neptune) could alter aspects of Pluto's orbit (such as its orbital precession) over millions of years so that a collision could be possible. Some other mechanism or mechanisms must therefore be at work. The most significant of these is that Pluto lies in the 3:2 mean motion resonance with Neptune: for every three of Neptune's orbits around the Sun, Pluto makes two. The two objects then return to their initial positions and the cycle repeats, each cycle lasting about 500 years. This pattern is configured so that, in each 500-year cycle, the first time Pluto is near perihelion Neptune is over 50° behind Pluto. By Pluto's second perihelion, Neptune will have completed a further one and a half of its own orbits, and so will be a similar distance ahead of Pluto. Pluto and Neptune's minimum separation is over 17 AU. Pluto comes closer to Uranus (11 AU) than it does to Neptune.
The 3:2 resonance between the two bodies is highly stable, and is preserved over millions of years. This prevents their orbits from changing relative to one another; the cycle always repeats in the same way, and so the two bodies can never pass near to each other. Thus, even if Pluto's orbit were not highly inclined the two bodies could never collide.
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