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The subsection Mercury–Jupiter 1:1 perihelion-precession resonance in the Wikipedia article Stability of the Solar System links to the article Solar system could go haywire before the Sun dies in the NewScientist, which references two articles that were still in press back in 2008 when it was published.

More time (both people-time and CPU-time) has passed. In 2016, is there still thought to be a 2% chance that when Jupiter increases Mercury's eccentricity beyond 0.6, it could get ejected?

I bring this up because the question of weather an orbit is "stable" or "unstable" always dances around the fact that many things are really in the middle ground - stable for months, or eons, but not necessarily actually stable in the sense that two masses orbiting in an otherwise totally empty Euclidian non-relativistic universe would be gravitationally stable. Put a handful (or more) bodies in orbit and chaotic behavior can arise.

So I'm looking for a good example of "stability is an illusion" loosely speaking, and Mercury is the best one I can think of at the minute - only I'm stuck in Wikipedia in 2008.

Has there been any further analysis?

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  • $\begingroup$ Is the actual question just about Mercury (as the title states), or are you looking for examples of particularly unstable orbits elsewhere? $\endgroup$ – Andy May 11 '16 at 9:42
  • $\begingroup$ @Andy within the solar system, artificial or natural. I almost did put this in Astronomy. I waffled a bit, but after considering the excellent answers I get here and the sometimes flaky responses I get there, I thought I would test the water here first. When I think about careful planetary orbit calculations I think of JPL and similar organizations, and that leads me back here. I like to think of the Oort cloud as the soft delimiter between Space SE and Astronomy SE. But that's just space, I guess a billion years might suggest going the other way. $\endgroup$ – uhoh May 11 '16 at 9:57
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    $\begingroup$ This question has been reopened in accordance with the new policy established here. $\endgroup$ – called2voyage♦ Apr 10 '20 at 14:13
  • $\begingroup$ See Laskar and Gastineau theory of mercury orbit: here and here $\endgroup$ – Nilay Ghosh Nov 14 '20 at 9:07
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    $\begingroup$ Yes, I could but I won't. It's an interesting question and deserves a proper answer but I do not have the sufficient knowledge on this topic and hence not confident in answering. I can only provide a head start by commenting and I hope other users who are interested and knowledgeable would take it as a reference in answering (you can make some edits so that it bumps to the front page). [Also, I have left comments/links in two of your other (unanswered) questions in astro.SE related to meteors (I think), I dunno if you've seen it?] $\endgroup$ – Nilay Ghosh Nov 15 '20 at 5:01

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