ThreeBody is an application that illustrates some solutions to the problem of the three bodies, a classic issue in the celestial mechanical field. This problem of the three bodies tries to determine the trajectories in a universe limited to three planets and subject to the law of universal gravitation.
The interesting thing about the problem is that it does not have an explicit solution, as it does for example with the problem of the two bodies, which Isaac Newton solved by stating that the trajectories were flat conical curves (ellipse, parabola and hyperbola). In the case of the three bodies, it is not possible to determine the asymptotic behavior of the system for arbitrary initial conditions.
Computers do not serve to find an answer to this problem, because they cannot work for an infinite time, and because they work with finite numbers. This leads us to a very limited precision, and an error that is accumulating progressively. In short, the predictions made from calculations on the PC are not reliable.
Thanks to ThreeBody you can get an interesting variety of solutions in the case of 3 planets with identical masses:
· A first case discovered by Lagrange in the 18th century with periodic trajectories in time.
· A second case discovered at the end of the 20th century by Alain Chenciner and Richard Montgomery, in which the trajectories are also periodic.
· And finally another case in which we can choose the initial conditions ourselves, changing the position and speed of the two previous cases.
In all three cases, ThreeBody assumes that the total momentum (the moment is the product of mass and velocity) of the planets is zero. With this condition, the center of gravity of the planets is always invariable.
You can free download ThreeBody 32, 64 bit and safe install the latest trial or new full version for Windows 10 from the official site.