Did the Neptune and Pluto trajectories ever cross or was it a mere reclassification? Do studies say that I can predict an intersection between 2 trajectories or movements based on data now? Do I have to consider at least 3 solid or larger space bodies moving in a way like the 3-body problem?

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    $\begingroup$ It's very unclear what's being asked here. $\endgroup$ – Russell Borogove Jan 7 '15 at 22:46
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    $\begingroup$ Did they ever cross? Yes. See any map or orbits of the solar system. $\endgroup$ – HDE 226868 Jan 7 '15 at 23:15
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    $\begingroup$ Whoops, I meant "of", not "or". I think it's unclear what the question is asking, because the first sentence appears to be unrelated to the rest of the question. $\endgroup$ – HDE 226868 Jan 8 '15 at 1:06
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    $\begingroup$ Intersection? Do not forget to include inclination to the ecliptic in any calculations. Neptune's is 1.77°, while Pluto inclines a whopping 17°. en.wikipedia.org/wiki/Orbital_inclination $\endgroup$ – Wayfaring Stranger Jan 8 '15 at 1:16

If you project the orbits onto a plane, for example the plane of the ecliptic, the projections will cross. But that's only because you're looking at a 3D problem in 2D. If you look at the orbits in 3D, you'll see that Pluto's orbit is highly inclined (17º) from the ecliptic, so it never actually passes through Neptune's orbit. Each time it seems to cross (in the 2D view), it's actually well above or well below Neptune's orbit. Pluto and Neptune never come closer than about 17AU.

At least for now. Minor perturbations over tens of millions of years may change that. Or might not. Pluto and Neptune currently have a 3:2 resonance, and such resonances tend to be stable.

You might want to look at http://en.wikipedia.org/wiki/Pluto, especially the section "Relationship with Neptune".

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  • $\begingroup$ Thank you for the answer. I was wondering how difficult it is to know whether a satellite rotating around a larger Newtonian body will cross paths with a third planet, moon, asteroid (or similar larger space object) so that it can be known in advance if one satellite in the future will be outside the other (when in fact now it could be inside the other's orbit.) I hope the question is understood. I'm wondering how exactly we are sure that Mercury always will be closest to earth if all we know is the state of the data. Will the planets in this solar system always be in the order they are today? $\endgroup$ – Niklas R. Jan 8 '15 at 7:06

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