I'm a bit confused as to what the three body problem is. Why is it impossible to predict the motions of three bodies in orbit around eachother?
mathematicians are too dumb
There are ten constants of motion:
Three position co-ordinates for the centre of mass of the system
Three velocity co-ordinates for the centre of mass of the system
Three vector components for the angular momentum of the system
Total energy of the system
There are 18 unknowns in the system
Three position co-ordinates for each body (nine in total)
Three velocity co-ordinates for each body (nine in total)
Try to solve a linear system of 10 equations and 18 unknowns. Can't be done.
>>7653929
>Try to solve a linear system of 10 equations and 18 unknowns. Can't be done.
Oh so that's why the double slit experiment gives unpredictable results!
>>7654062
>What is quantum mechanics
Stochastic and chaotic
>>7654065
My understanding is that it's a mathematical formalism for which no coherent explanation has yet been offered.
>>7654062
What? No.
>>7653929
>Try to solve a linear system of 10 equations and 18 unknowns. Can't be done.
I bet it can if the system is linearly dependent
>>7653883
because we're still waiting on captain autismo to solve that problem
>>7653883
It's absolutely solvable, and is solved all the time. It's just not exactly solvable analytically, and numerical methods use more computing power.
Most three-body situations lead to motion that is chaotic and nonrepeating, and so no simple finite function can express the entire history of the system from t=0 to t=infinity - which is what finding an analytical solution would mean.
>>7654095
No. That makes no sense.
There are some numerical methods that can be applied to yield good approximations, particularly so for sparse matrices. However, this system is unsolvable explicitly with 10 equations and 18 unknows
>>7654095
>tfw you live in the kernel of a rank 8 map
>>7653883
I believe it has to do with chaos theory. A modeled equation could theoretically be worked out, but if your measurements are off in the slightest you will get starkly different results.
Think this can maybe be worked around by treating a system of two of the bodies as a single body and using their approximate center of mass as the point in space for a hypothetical body and reducing it to a 2 body problem but a lot is lost in translation.
I'm drunk and probably wrong, I'll stick around until someone calls me a retard and corrects my verbal diarrhea.
>>7653883
OP, don't listen to anybody here. Everybody is stupid and/or talking out of his ass. Of course there are analytical solutions, the system is integrable. Here:
Three-body problem: https://en.wikipedia.org/wiki/Three-body_problem#Sundman.27s_theorem
n-body problem: https://en.wikipedia.org/wiki/N-body_problem#Power_series_solution
>>7656698
>Infinite series solution is an analytical solution
I wish this meme would die. By that logic any numerical simulation (ie. a series) of a system is an analytical solution.
>>7656704
>By that logic any numerical simulation of a system is an analytical solution.
No.
Just because it isn't expressible as an algebraic combination of simple functions it doesn't mean is not analytical.
>>7656728
>No.
It's proven that an infinite series any integrator is an exact solution.
Just because it isn't expressible as an algebraic combination of simple functions it doesn't mean is not analytical.
