A mechanical system with three objects, say the Earth, Moon and Sun, constitutes a three-body problem. Mathematicians in the 1950s managed an elegant proof that it is impossible to solve. However, approximate solutions can be very useful, particularly when the masses of the three objects differ greatly.

http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/lagpt.html

http://www.askamathematician.com/2011/10/q-what-is-the-three-body-problem/


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