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(Image
credit: Adrienne Bresnahan/Getty Images) |
It has been a source of consternation for scientists since the time of Isaac Newton.
According
to a pair of Israeli researchers, a physics problem that has plagued science
since the days of Isaac Newton is getting closer to being solved. To compute
the outcome of a cosmic dance between three huge objects, or the so-called
three-body problem, the duo used "the drunkard's stroll".
Predicting
the motion of two large objects, such as a pair of stars, is a piece of cake
for physicists. However, when a third object is introduced, the problem becomes
insoluble. Because when two huge objects approach one other, their
gravitational attraction alters their courses in a way that can be explained by
a simple mathematical formula. However, adding a third object is more
difficult: The interactions between the three objects have suddenly become
chaotic. Instead of following a predictable course determined by a mathematical
formula, the three objects' behaviour becomes sensitive to what scientists
refer to as "initial circumstances," or their past speed and
position. Any small change in those initial conditions has a significant impact
on their future behaviour, and because what we know about those settings is
always unpredictable, their behaviour is impossible to predict far into the
future. In one scenario, two of the objects may orbit close together while the
third is launched into a broad orbit; in another, the third object may be
ejected from the other two, never to return, and so on.
"[The
three-body problem] is very, very sensitive to initial conditions," said
Yonadav Barry Ginat, a PhD student at Technion-Israel Institute of Technology
who co-authored the article with Hagai Perets, a physicist at the same institution.
"However, this does not rule out the possibility of calculating the
likelihood of each outcome."
They used
the theory of random walks, popularly known as "the drunkard's walk,"
to accomplish this. The premise is that a drunken person walks in random directions,
with the equal possibility of taking a step to the right or left. You can
compute the likelihood of the drunkard showing up in any particular location at
a later time if you know those odds.
(Image
credit: Technion - Israel Institute of Technology) |
Ginat and
Perets investigated three-body systems in which the third object approaches a
pair of orbiting objects in their new study. Each of the drunkard's
"steps" corresponds to the velocity of the third object in relation
to the other two in their solution.
"You
can calculate the probabilities for each of those possible speeds of the third
body, and then you can combine all of those steps and probabilities to find the
final probability of what's going to happen to the three-body system in a long
time from now," Ginat said, referring to whether the third object will be
flung out for good or whether it might return.
However,
the scientists' solution goes even further. The three objects are considered as
so-called ideal particles in most simulations of the three-body problem, with
no intrinsic attributes at play. Stars and planets, on the other hand, interact
in more sophisticated ways: Consider how the moon's gravity pulls on the Earth
to create the tides. The interaction between the two bodies loses some energy
due to the tidal forces, which modifies the way each body moves.
Because
this approach assesses the likelihood of each "step" of the
three-body interaction, it can take these additional forces into account and
calculate the result more precisely.
Although
this is a significant step forward for the three-body problem, Ginat believes
it is far from the finish. The researchers are now trying to figure out what
happens when the three bodies are arranged in unusual ways, such as all three
on a flat plane. Another test will be to determine if they can apply these concepts
to four bodies.
"There
are still a lot of unanswered questions," Ginat remarked.
References:
Analytical,
Statistical Approximate Solution of Dissipative and Nondissipative Binary-Single
Stellar Encounters Yonadav Barry Ginat and Hagai B. Perets Phys. Rev. X 11,
031020
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