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The planet Mercury is especially susceptible to Jupiter's influence! Why? Mercury's perihelion, the point where it gets closest to the Sun, precesses at a rate of about 1.5 degrees every 1000 years. Jupiter's perihelion precesses just a little slower. (5/n)
In some simulations, Jupiter's gravitational tugs accumulate and pull Mercury off course 3-4 billion years from now. Astronomers estimate there's a 1-2% probability that it could collide with Venus, the Sun, or Earth - or even be ejected from the Solar System! (6/n)
In 1989, Jacques Laskar showed that the Earth's orbit is chaotic. An error as small as 15 meters in measuring the position of the Earth today would make it completely impossible to predict where the Earth would be in its orbit 100 million years from now! (7/n)
In 2008, Laskar and Gastineau simulated 2500 futures for the Solar System, changing the initial position of Mercury by about 1 meter. In 20 cases, Mercury went into a dangerous orbit! Often it collided with Venus or the Sun - but in one case it made Mars hit the Earth. (8/n)
But here's the good news: the work of Laskar and Gastineau - and also another team - shows that nothing dramatic should happen to the planets' orbits for the next billion years. So we can worry about other things. (9/n)
In the *really* long term, most of the stars in the Milky Way will be ejected. Through random encounters, individual stars will pick up enough speed to reach escape velocity. The whole Galaxy will slowly "boil away". It will dissipate in about 10^19 years. (10/n, n = 10)
First: what do we mean by an unstable solar system? One definition is that a major planet attains escape velocity. Determining stability may be a kind of Turing problem. Ie, we can show that some configurations are unstable, but we can never show that a configuration is stable.
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