"It's green!"
Now we know the secret to Captain Kirk's success in space!
-PJ
Posted on 01/04/2022 12:20:44 PM PST by Red Badger
A physics problem that has plagued science since the days of Isaac Newton is closer to being solved, say a pair of Israeli researchers. The duo used "the drunkard's walk" to calculate the outcome of a cosmic dance between three massive objects, or the so-called three-body problem.
For physicists, predicting the motion of two massive objects, like a pair of stars, is a piece of cake. But when a third object enters the picture, the problem becomes unsolvable. That's because when two massive objects get close to each other, their gravitational attraction influences the paths they take in a way that can be described by a simple mathematical formula. But adding a third object isn't so simple: Suddenly, the interactions between the three objects become chaotic. Instead of following a predictable path defined by a mathematical formula, the behavior of the three objects becomes sensitive to what scientists call "initial conditions" — that is, whatever speed and position they were in previously. Any slight difference in those initial conditions changes their future behavior drastically, and because there's always some uncertainty in what we know about those conditions, their behavior is impossible to calculate far out into the future. In one scenario, two of the objects might orbit each other closely while the third is flung into a wide orbit; in another, the third object might be ejected from the other two, never to return, and so on.
CLOSE In a paper published in the journal Physical Review X, scientists used the frustrating unpredictability of the three-body problem to their advantage.
"[The three-body problem] depends very, very sensitively on initial conditions, so essentially it means that the outcome is basically random," said Yonadav Barry Ginat, a doctoral student at Technion-Israel Institute of Technology who co-authored the paper
(Excerpt) Read more at livescience.com ...
Solved? Can they make predictions?
Somehow I doubt this. Will be interesting to see how things go with this.
"It's green!"
Now we know the secret to Captain Kirk's success in space!
-PJ
Has it been shown there is no closed form solution (e.g. like it’s been shown that an angle can’t be trisected using only a compass and straight edge) or is this still an open problem like the Reimann Hypothesis?
Close enough for government work...................
That’s silly.
Frankly, there were no French in Julius Caesar’s time, just Bois and Gauls.................
True about the probabilities... physical tolerances are defined so the product will assemble and function properly.
One of the most interesting manufacturing challenges I had was to grind a hemispherical shell of ceramic to the tightest tolerance I could. That included concentric position of the inner and outer hemisphere. Our CMM was a Zeiss with about a 3 micron accuracy and it showed everything spot on. The customer bought 4 of the grinders and had us build 2 frames so they could convert them to CMM’s. Fun project. the hemispheres were about 20” or 500mm across.
We will DEFINITELY be a LOT closer to solving it when we receive our new grant money!
Kevin, you may want to jump in here.
Or not...
We can thank our lucky stars that a FOURTH body hasn’t said, “Hello...”
The web can show us many images of three bodies solving a particular problem, even when the initial conditions are unknown.
See!
But it IS one of the four possible starting positions.
I wink in your direction, ma’am.
L
There are now mathematical solutions being worked out on computers that could never be approached using humans, pen and paper. But this particular problem doesn’t look like they generated a real solution. This is a well known issue in mathematics, similar to a prior issue in math where it didn’t seem possible to calculate the area under a curve with any precision until Liebniz and Newton developed calculus. I think that this particular problem will generate its own new mathematical flourish similar to calculus.
They got the idea from watching Joe Buy-Dung. Thanks Red Badger. Another three-fer!
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You need a nice, hot cup of tea /Hitchhikers’ Guide To The Galaxy>
If one of the bodies is mine and the other two are attractive nubile females I’d have no difficulty solving this problem.
It would take repeated efforts and long term study, of course.
L
= = = = = = = = =
Doubtless your solution would include simple hormonic motion and the presence of degenerate modes...
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