ThreeBody

Approval level: 70%
Updated : 2012-02-15
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ThreeBody is an application that shows some solutions to the problem of three bodies, well-known in celestial mechanics. This three body problem tries to determine the trajectories in a universe limited to three planets and subject to the universal law of gravity.



The interesting thing about the problem is the there is no explicit solution, which happens for example with two bodies (which Isaac Newton solved with plane cone trajectories - elipses, parabolics or hyperbolics). In the case of three bodies, it isn´t possible to determine the behaviour of the system with initially arbitrary conditions.



Computers don´t work to find the answer, because they can´t work during an infinite time, and only with finite numbers. This limits the results, and with progressively bigger margins of error. They aren´t very reliable calculations.



Thanks to ThreeBody you can get an interesting variation of solutions with planets of identical mass:



* The first case was discovered by Lagrange in the 18th Century with periodic trajectories over time.

* The second case was discovered by Alain Chenciner and Richard Montgomery at the end of the 20th Century, also with periodic time trajectories.

* And finally another case is one you can choose yourself, changing the speed and position of these two previous cases.



In these three cases, ThreeBody assumes a total moment (the moment is the product of mass and speed) of the planets is equal to zero. With this condition the centre of gravitiy of the planets is always invariable.