Questions tagged [three-body-problem]

95 questions
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Can we infer the existence of periodic solutions to the three-body problem from numerical evidence?

I recently found out about the discovery of 13 beautiful periodic solutions to the three-body problem, described in the paper Three Classes of Newtonian Three-Body Planar Periodic Orbits. Milovan Šuvakov and V. Dmitrašinović. Phys. Rev. Lett. 110…
39
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The impossibility (or possibility) of solving $N$-Body problem

One can obtain the solution to a $2$-Body problem analytically. However, I understand that obtaining a general solution to a $N$-body problem is impossible. Is there a proof somewhere that shows this possibility/impossibility? Edit: I am looking to…
Graviton
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Might a planet perform figure-8 orbits around two stars?

Might a planet perform figure-8 orbits around two stars? I'm thinking that if the two stars were equal mass (and not orbiting each other) then a planet that were to go right between them would continue in a straight line, with no preference for…
31
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5 answers

What are the primary obstacles to solve the many-body problem in quantum mechanics?

(This is a simple question, with likely a rather involved answer.) What are the primary obstacles to solve the many-body problem in quantum mechanics? Specifically, if we have a Hamiltonian for a number of interdependent particles, why is solving…
28
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If the 3-Body force problem hasn't been solved, how do rocket scientists plan orbits of spacecraft?

What methods would they use to predict what would happen in a situation when a probe is being acted upon by the gravity of two stars, say?
23
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5 answers

How do computers "solve" the three-body-problem?

I've done a bit of research, and have learned that computers "solve" the three-body-problem by using "Numerical methods for ordinary differential equations", but I can't really find anything about it other then Wikipedia. Does anyone have any good…
14
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1 answer

Explicit form of Sundman's general solution of three-body problem

I recently heard from a couple astronomy graduate students that Sundman solved the entire three-body problem of Newtonian gravity over a century ago, for generic initial conditions with non-vanishing angular momentum. This sounds almost too good to…
14
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2 answers

$N$-body simulation in General Relativity

How would one perform an $N$-body simulation in General Relativity (GR) for something like galaxy formation or galactic dynamics? Suppose one wants to simulate the rotation curve $v(r)$ for galaxies with an $N$-body simulation, and wants to do it in…
13
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Why does chaos preclude exact solutions?

It is sometimes said that the n-body problem (using the initial positions and velocities of n point masses to calculate their future paths) has no general closed-form solution because the system is chaotic: A small change in the initial conditions…
11
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Are there aspects of General Relativity that have yet to be tested?

Good evening everyone, I am new in the field of General Relativity and I have been reading and learning about the subject in recent months. For example, I read several articles about experiments designed to test the Principle of Equivalence and…
10
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1 answer

Why does the three-body problem have no solution?

Why does the three-body problem have no solution? Nothing is wrong with not having found a solution yet, but I've heard that we've proven that there is no solution. I know that it is chaotic, but is it just that we have formulas to predict "perfect"…
10
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Making new sense of the three-body problem in the light of Maryam Mirzakhani math contributions

I am unfamiliar with moduli spaces and ergodic theory which appear to be essential in Maryam Mirzakhani's math contributions which won her the Fields Medal. However, I am well conversant in essential topology, general relativity, Hamilton–Jacobi…
user56963
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1 answer

Does the Taylor series for the $N$-Body Problem converge?

So I am doing a Presentation on the $N$-Body Problem for my Physics final (12th grade) and the main content of the Presentation is going to be the comparison between an analytical and a numerical approach to solve the problem. I chose the "$N$-Body…
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Quantum $n$-body problem

Is the quantum $n$-body problem as difficult as the classical $n$-body problem? Or quantum mechanics allows to get a simpler exact solution? Suppose there are 3 particles with uniform potential field. Can their wave functions be found exactly?
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Proof of unsolvability of $n$-body problem for $n\geqslant 3$ in general

We know there are general solutions for the 1-body problem and 2-body problem and also we know in some "special cases" there are some possible solutions for $n$-body problem for $n \geqslant 3$. There might not be a general solution to this problem.…
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