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kurious
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Would three galaxies, held together by dark matter, be an example of a three body problem?
Galaxies have so many bodies that they can probably be treated as a fluid dynamical problem of the non-ideal gas variety: gravity being analogous to VanderWaals forces.selfAdjoint said:No, because they are too loose constructed. The Sun, Earth, and Moon are a good three body problem. Galaxies are a many body problem.
... or dark matter concentrationsmathman said:If the galaxies are far enough apart (i.e. compared to their sizes), then their relative motions could be looked at as a three body problem, as long as there are no other galaxies nearby.
I wonder how many more schools exist down there? The University of Hell, Brimstone Technical School...Chronos said:The classic 3 body problem is the homework equivalent of violating the Geneva convention. Solving it for 3 galaxies is a physics 101 assignment at Hades University.
Jenab said:gravity being analogous to VanderWaals forces.
Jerry Abbott
tony873004 said:I know there is no solution to the 3-body problem except numeric integration. But does this just mean nobody has found the solution yet? I know many prominent mathimaticians from years ago tried to solve it. Were they wasting their time? Has it been proven that the 3-body problem has no solution? Or is it possible that I might wake tommorow to find on page 9 of my newspaper "Mathamatician solves 3-body problem".
But a computer doing this as a repetitive task is an example on a numerical integration. And numerical integrations are subject to truncation errors (if you make the time step too fast) and round-off errors.BobG said:Yes, people have solved it...
...Others can get much more difficult to do by hand, since your angles and distances are always changing, but not so much so for a computer which can do repetitive tasks very well.
BobG said:Yes, people have solved it.
I might be wrong, but I think the 2-body is also analytically solveable even if both bodies have significant mass. They would both be tracing perfect unperturbed ellipses around their barycenter. A 3rd body introduces pertubations and messes the whole thing up.enigma said:Numerically only. There aren't enough constants to solve it analytically.
The only reason we're able to solve the 2 body problem analytically is because you can make the assumption that 'body 2's mass' << 'body 1's mass'.
As long as you have more than 2 bodies, and 2 of your bodies have mass, then you have an n-body problem. In certain instances, you can treat an n-body problem like a bunch of 2 body problems and get good results, but they'll just be approximations. So a galaxy can not be considered a body because it is many bodies.Rothiemurchus said:If one of the bodies in a three body problem has a large mass - like a galaxy -
and this mass is in reality made of many masses,what determines when two much smaller masses become part of the many body probelm that the galaxy already is in its own right? Where is the borderline?
tony873004 said:I might be wrong, but I think the 2-body is also analytically solveable even if both bodies have significant mass. They would both be tracing perfect unperturbed ellipses around their barycenter. A 3rd body introduces pertubations and messes the whole thing up.
But do you know if a 3-body analytical solution is an impossiblilty, or just a solution that nobody's discovered yet?
Have you submitted your solution for publication in a peer-reviewed journal?khavel said:You can download my new e-book 'N Bodies - No Problem' at:
http://www.grevytpress.com/model.html
You can also try there n-body simulations (all done by the same program).
Unless I misunderstand you, you are wrong. all that is required for the analytic solution of any "central -force" two-body problem is to convert it to a one body problem with a fixed center (At old center of mass), and the one body with "reduced mass" equal to mM/(m+M). The potential can have any form (power) you like. Check out any high level classical mechanic book - perhaps even a google search on {"reduced mass" AND "central force"} will show you this.Haelfix said:Already the two body general solution is a horrendous chore to do, and took the work of many famous physicists to solve completely (for the case of a 1/r potential). Unfortunately the integral form is nasty (elliptical integrals), but they have been done.
Change the potential, and you can no longer get a closed form stable solution...
In an n-body gravitational system, the trajectory of anybody generally depends on the masses, positions, and velocities of all remaining bodies.
To determine the trajectories of all bodies, we set a time interval deltaT for the recalculation. Obviously, the shorter the time interval results in more precise calculation of the trajectories. At the beginning of the time interval we know the masses, positions, and velocities of all bodies. During time interval deltaT we calculate for each body the sum of accelerations imparted by gravitation of all other bodies, from their masses and positions. Then, for each body, we respectively integrate the sums of the accelerations over time interval deltaT, to obtain the increment of its velocity. We add the increment of its velocity to its previous velocity, to obtain its new velocity. Then we integrate its new velocity over time interval deltaT, to obtain the increment of its position. We add the increment of its position to its previous position, to obtain its new position. Since acceleration, velocity, and position are vectors, all calculations are done with their x and y components.
We keep repeating all calculations, over successive time intervals deltaT, using the new positions and velocities of all bodies. This method of calculation is valid for any number of bodies. Needless to say, the complexity of calculation increases with the number of bodies.
The Three Body Problem is a mathematical problem that involves predicting the motion of three celestial bodies based on their initial positions and velocities. It is a notoriously difficult problem to solve and has been a subject of study for centuries.
Dark matter is a type of matter that is thought to make up a large portion of the universe. It does not interact with light or other forms of electromagnetic radiation, making it invisible to telescopes. Its existence is inferred through its gravitational effects on visible matter.
Dark matter has a significant impact on the Three Body Problem because it adds an additional gravitational force to the system. This force can cause the trajectories of the three bodies to change, making it even more difficult to predict their movements.
One theory is that dark matter could be responsible for the chaotic and unpredictable nature of the Three Body Problem. Another theory suggests that dark matter could help stabilize the orbits of three-body systems. However, further research is needed to fully understand the role of dark matter in this problem.
Studying the Three Body Problem and dark matter allows us to better understand the fundamental laws of physics and how they apply to our universe. It also helps us to understand the formation and evolution of galaxies and other large-scale structures in the universe. Additionally, it may lead to new insights and discoveries about the nature of dark matter itself.