An unsolved three-body issue has been solved using the drunkard's walk method of physics

pixabay.com

It's been a problem for scientists since Isaac Newton.

According to a pair of Israeli scientists, a physics problem that has troubled science since the days of Isaac Newton may be closer to an answer than previously thought. Three-body problem was solved using "the drunkard's walk" to determine what would happen in a cosmic dance between three huge objects.

Calculating the velocity of two large objects, such as stars, is second nature to physicists. However, the issue becomes insoluble when a third object is introduced. This is because the gravitational attraction between two huge objects alters their courses in a way that can be explained mathematically. Adding a third object is not as easy as one might think. The three things begin to interact in a disorderly manner. Scientists term this phenomenon "starting conditions," which refers to the earlier speed and position of the three objects rather than a mathematical formula-defined path. It's hard to predict how they'll act in the future because the original conditions are always subject to change. The third object may be thrown into a wide orbit while the other two remain in close orbit, or it could be expelled from the other two and never return, and so on.

Physical Review magazine released a research report in which scientists exploited the three-body problem's annoying unpredictability to their advantage.

According to Yonadav Ginat, a doctorate student at Technion-Israel Institute of Technology who co-authored the study with physicist Hagai Perets, "basically, the outcome is practically random" since the three-body problem "depends very, very sensitively on initial conditions." That doesn't mean we can't determine each occurrence's likelihood.

They used a theory known as "the drunkard's walk" called the theory of random walks to accomplish this. If you imagine a drunkard wandering, every step he takes has the same chance of going right as it does going left. You can compute the likelihood of a drunken person showing up at a specific location later if you know those probabilities.

Ginat and Perets, on the other hand, studied three-body systems where the third object approaches a pair of orbiting bodies. Each of the drunkard's "steps" correlates to the third object's velocity about the other two in their solution.

For instance, Ginat explained that the final probability of what will happen to the three-body system a long time from now could be found by calculating probabilities for each of the possible speeds of the third body and then composing all of those steps and probabilities. This includes whether the third object will be flung out for good or whether it might return.

On the other hand, scientists have come up with a more comprehensive solution. Virtually all three-body problem simulations use so-called "ideal particles," which have no intrinsic features. However, the relationships between the stars and planets are more nuanced: Consider how the moon's gravity pulls on Earth, causing the tides to rise and fall. The relationship between the two bodies is altered because of the tidal forces, which take energy away from them.

This approach can account for these additional forces because it calculates the likelihood of each "step" in the three-body interaction.

The three-body problem has taken a giant stride forward, but Ginat maintains it's far from solved. What happens if all three bodies are placed on a flat surface? That's what the researchers are hoping to discover. Another challenge is to investigate if these ideas can be applied to four different bodies.

Many unanswered questions remain, Ginat noted.

Reference : https://www.livescience.com/three-body-problem-solution

Image source : https://pixabay.com/id/vectors/tabung-reaksi-kimia-hijau-biru-2235388/