After centuries of hard work, mathematicians have finally arrived at the definitive answer of whether or not the gravitational perturbations of the planets will ever cause them to disrupt their "fine and regular harmony". The answer is: Absolutely maybe.
The problem, alas, is that there is a difference between the real solar system and the mathematical one. The mathematical one deals with n planets and a center of attraction that is so much more massive than the others that its gravitation is the major influence in the motion of the planets. This is almost the case in the solar system.
Because universal gravitation is, well, universal, every body in the universe attracts every other body. A true model of the solar system would not only include the nine planets, the sun, the thousands of asteroids, billions of comets, and every spec of dust in the solar system, every space probe that has ever been launched, and every passing atom of hydrogen, but it would also have to take into account things like the gravitational attraction of Alpha Centauri, M31, and the most distant quasar. In this sense, we are qualitatively no better off than we are by assuming that the planets are attracted by the sun alone. (Quantitatively, of course, we can ignore the gravitational effects of just about everything except for the larger planets and still get good matches with observation)
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