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Is the three-body problem still unsolvable even when the three bodies are located in the same plane?
rachmaninoff said:You can't have three bodies 'not in the same plane'. They define their own plane.
I wasn't thinking either actually, but yeah, what I meant is: can the 3-body problem be solved if the movement of the three bodies is coplanar? (like, when the plane defined by the three bodies isn't rotating)rachmaninoff said:duh! I was not thinking - apologies.
-rachmaninoff
The Three-Body Problem is a classic problem in physics that involves predicting the motions of three bodies that are gravitationally interacting with each other. While there are some special cases where an analytical solution has been found, in general, the Three-Body Problem cannot be solved analytically. This is due to the complex nature of the problem and the fact that it involves solving a system of non-linear differential equations.
Yes, the Three-Body Problem can be solved in the same plane. This means that the three bodies are moving in a two-dimensional plane and their motions can be described using two-dimensional coordinates. However, it is important to note that this is a simplified version of the problem, as in reality, the three bodies may be moving in three-dimensional space.
Yes, numerical methods are often used to solve the Three-Body Problem. These methods involve using computers to simulate the motions of the three bodies over time. While this approach may not provide an analytical solution, it can give accurate results and allow for the exploration of different scenarios and initial conditions.
Yes, chaos can arise in the Three-Body Problem. Chaos refers to the unpredictable and seemingly random behavior of a system, even though it follows deterministic rules. In the Three-Body Problem, small changes in the initial conditions can lead to drastically different outcomes, making it difficult to predict the long-term behavior of the system.
The Three-Body Problem has connections to various areas of science, including physics, mathematics, and astronomy. It has been studied to understand the behavior of celestial bodies, such as planets and moons, in our solar system. The insights gained from studying the Three-Body Problem have also been applied in other fields, such as fluid dynamics and chaos theory.