Questions tagged [three-body-problem]
95 questions
54
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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…
Emilio Pisanty
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2 answers
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…
dotancohen
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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…
Noldorin
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2 answers
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?
DannyH
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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…
HeeysamH
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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…
user196574
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$N$-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…
Marton Trencseni
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13
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5 answers
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…
Maurice Mizrahi
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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…
Loïc Poncin
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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"…
Mr Chikn
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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
7
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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…
7
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1 answer
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?
Anixx
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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.…
Hamed.Begloo
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