Yesterday’s Astrolunch talk was given by Prof. Mike Disney on the Stability of the Solar System. It was the first of two talks, and in of itself was very informative. Prof. Disney discussed the history of the question of whether or not the Solar System is a stable system. The final answer surprised me.
In his Principia Mathematica, Newton notes that the planets of the Solar System ought not to remain in their orbits indefinitely. He ascribes their apparent stability and endurance to an act of God, and uses that fact as evidence for the existence of God.
Laplace (another great mathematician of Western history), some hundred years later countered Newton’s argument. He showed that the evidence was actually quite the contrary and in fact the Solar System was stable after all. When asked what this meant about the existence of God, he replied, “I don’t need that hypothesis”.
In 1900, Poincare said that in fact Laplace was the one who was wrong! He argued that in any sufficiently complex, non-linear system, boundary conditions will experience such large-scale effects that the system cannot be stable. This is what is now known as Chaos Theory and it put the nail in the coffin for the idea that the Solar System could ever be considered stable.
Finally in the 1990s, computers became powerful enough that they could simulate the main bodies of the Solar System and answer the question more-or-less once and for all. And what did they find? Well Newton was right about one thing.
In fact, the Solar System is not stable. It sits on a fine line between stability and chaos and oscillates either side of that line on a timescale of roughly one Hubble Time. How does that affect you and me? Well it means that any time now, the Solar System could start to fall out of stability and chuck out a planet… or not.
Discussion after the talk lead me to believe that Mercury would be a best candidate for expulsion from the Solar System. Pluto might be more likely, but the simulations only include the planets, so I think we ought to make moves to get the Earth classified as a dwarf planet immediately.
You can download the 1803 publication Newton’s Principia Mathematica for free, from Google Books as a
Orbiting Frog 
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