With the release of Netflix’s 3 Body Problem, based on the acclaimed novel series by Liu Cixin, we have seen many people ask what exactly the three-body problem is. So join us on a trip into physics and math that started at the very beginning of modern science and continues to vex scientists and thinkers to this day.
Newton’s laws of motion and his law of universal gravitation underpinned classical physics and were able to explain the behavior of a wide array of phenomena. In particular, the motion of planets around a star can be easily described with them – these are two-body problems, a star and its planet or the Earth and the Moon.
These two-body problems can be solved exactly, providing a great power of prediction. Knowing the initial conditions, we can work out how the system will evolve forever. Now, let’s add a third body. You might think that it would add some difficulties but that it will still be solvable, however, reality must have a wicked sense of humor. The two-body problem is perfectly solvable, but the three-body problem is not.
There is no generalized solution that allows you to predict the behavior of three objects (or particles or planets) under the laws of motion and force. It is possible to find solutions to specific cases and some not-so-specific cases, but there is no way to solve the three-body problem for all possible cases.
Originally, the question of the three-body (and then the n-body) problem was about the stability of the Earth-Moon-Sun system and the Solar System as a whole. The search for solutions has brought forth new mathematical tools such as perturbation theory to improve on the numerical solution found for the motion of planetary bodies.
It also led to the prediction of trojan asteroids on the orbit of Jupiter by Italian-born mathematician Joseph-Louis Lagrange, who was studying a particular case of the three-body problem.
A still from episode three of the 3 Body Problem.
Image Credit: Netflix
While the three-body problem using Newtonian gravity is seen as the traditional one to solve, the problem is found in quantum mechanics too. A helium atom with a positive nucleus orbited by two negative electrons is also an example of a three-body problem.
And if you like gravity but you prefer to make your life hell, why not try to find a solution to the three-body problem using general relativity? This comes in handy near black holes.
New solutions to specific three-body problems are found every few years. And you never know, you might need it to make sense of a mysterious, hyper-realistic videogame…
Source Link: What Is The Three-Body Problem?
