ThreeBody 3.0.1 Build 193

This application illustrates some solutions of the 3 bodies problem in celestial mechanic

ThreeBody program is an illustration of the three body problem. This problem is a clasical question in Celestial Mecanic: determine the trajectories in an univers limited to three planets and the law of the universal gravitation.

The interesting thing is that this problem has no explicit solution like the two body problem where we known since, Isaac Newton, that the trajectories a plane conical curves (ellipse, parabola and hyperbola).

In the threebodies case it's not possible to tell about the asymtotic behavior of the system for arbitrary initial conditions.

Computers cannot lead to an answer to this problem because they cannot work for an infinite time (or at least for periods representing the solar system live expectation, few billions of years) and because they are working with a finite numbers of digits and this yelds to a limited precision and error accumulations so that their predictions are not reliable.

With ThreeBody you can enjoy the variety of solutions in the case of 3 planets with identical mass.

· A first case discovered by Joseph Louis, comte de Lagrange (Giuseppe Lodovico Lagrangia in italian, born January, 25 1746 in Torino - dead April, 10 1813 in Paris) in 18th century where the trajectories a periodic in time.
· A second case discovered at the end of the 20th century by Alain Chenciner and Richard Montgomery ; Annals of Mathematics (2) 152 (2000), no. 3, 881-901 where the trajectories are also periodic.
· Finaly one may choose arbitray initials conditions by changing the positions and velocities from the 2 previous cases.

In the three cases, ThreeBody assume that the total momentum (product of the mass by the velocity) of the planets is zero. With this condition, the center of gravity of the planets stay in place.