A physics problem that has plagued science since the days of IsaacNewton is close to being solved, say a pair of Israeli researchers. The duo used "the drunkard's walk" to calculate the outcome of a dance between three massive objects.
Predicting the motion of a pair of stars is a piece of cake for physicists. The problem becomes unsolvable when a third object enters the picture. The paths that two massive objects take in a way that can be described by a simple mathematical formula are influenced by the attraction of the objects. Adding a third object isn't easy: Suddenly, the interactions between the three objects become chaotic. The behavior of the three objects becomes sensitive to what scientists call "initial conditions", that is, whatever speed and position they were in before. 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 may be in close proximity to each other, while the third may be flung into a wide circle, never to return, and so on.
What is the story behind the stars?
Scientists used the unpredictability of the three-body problem to their advantage in a paper published in the journal Physical Review X.
The outcome of the three-body problem is basically random because it depends very, very sensitively on initial conditions, according to a paper co-authored by a PhD student. "That doesn't mean that we can't calculate the probability of each outcome."
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The theory of random walks was used to do that. The idea is that a drunk can walk in random directions with the same chance of taking a step to the right as a step to the left. You can calculate the probability of a drunkard ending up in any given spot if you know those chances.
The three-body problem has been a problem for scientists for a long time. There are three objects in the sky with a galaxy behind them. The image is from the Israel Institute of Technology.
Ginat and Perets looked at the systems of three bodies, where the third object approaches a pair of objects. The drunkard's steps correspond to the velocities of the other two objects.
The final probability of what's going to happen to the three-body system in a long time from now can be found by calculating the probabilities for each of the possible speeds of the third body.
The scientists' solution goes further than that. The three objects are treated as ideal particles in most simulations of the three-body problem. Think about how the moon's gravity tugs on the Earth to produce the tides. The way each body moves is affected by the way the tidal forces steal energy from the two bodies.
The solution calculates the probability of each step of the interaction and can account for the additional forces to calculate the outcome.
Ginat says it's not the end for the three-body problem. The researchers hope to figure out what happens when the three bodies are in different configurations. They have to see if they can generalize these ideas to four bodies.
Ginat said there were quite a few open questions.
Live Science published the original article.
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