The Three-Body Problem, Classical Version: given three objects/particles interacting according to a 1/r2 law, which means gravity or electricity, can we write and solve the equation of motion in closed form?
Category Archives: Multibody Problems
The One-Body Problem
The traditional One-Body Problem is solving the equation of motion for a single body in space, often where the space has an energy potential, described by an equation, that affects the body. What’s artificial about this is that space and the potential surface are taken as one unified thing. Or the potential surface is changing slowly vis-a-vis the body motion. These are relatively tractable situations.
In reality the potential surface is determined by the interaction of the test body and all outside objects, with the material of space as the intermediary transmitting those interactions. So separate the potential surface from space itself, then are the solutions absolute in space or only relative to other outside objects (which together with the test particle, create the potential surface)?
The One-Body Problem, Classical Version: given an object/particle in space, can we know and/or does it have an absolute position and momentum (not merely relative to the rest of the objects out there)?
The Two-Body Problem
The Two-Body Problem, Classical Version: given two objects/particles interacting according to a 1/r2 law, which means gravity or electricity, can we write and solve the equation of motion in closed form?
The Three-Body Problem
With two interacting bodies, interacting via the r-squared forces of gravity or electricity, and obeying classical mechanics, the equation of motion can be written down in closed form.
With three interacting bodies, the equation of motion can’t be written down in closed form.
So the three-body problem can’t be solved exactly (and this is just for classical mechanics and r-squared forces). Algebraic approximations or numerical simulations can do a good job, but they’re not exact.
So what’s it mean?
Very Universe 