(Newswire.net — September 24, 2020) — For centuries, the three-body problem has been a fixture of conversations between scientists, a hot topic of discussion in any mathematics seminar, and a challenge that kept the brightest minds puzzled to no end. Over the years, new solutions cropped up, but this mathematical problem still defies Newton’s laws as much as it taunts logical thought.
Commodities specialist, Turab Musayev of London, England, has always found the three-body problem a worthy challenge. With various degrees in business administration and a long career in the energy industry with companies like BP and Merrill Lynch in London, mathematics has always been an integral part of his studies and career. “The three-body mathematical problem,” he explains, “is one of the most exciting puzzles that has been around for the last 300 years and still demands a fully satisfying solution. What I find intriguing about it is that every new solution sheds new light on the problem and offers new insights that have applications in day-to-day life.”
What is the Three-Body Problem?
Put simply, the three-body problem tries to predict the motion of three bodies in space given their initial position and velocity. According to Turab Musayev, this simple problem soon develops into a veritable Gordian knot when Newton’s laws of physics are applied. The main issue, he says, is when you try to use both Newton’s law of universal gravitation and laws of motion to solve it. That’s because you cannot predict the orbit of any of the three bodies or the impact each one has over the other bodies.
The laws of classical mechanics and physics stipulate that if the starting point and momenta or velocity of a body are determined, then its orbit and movement can be predicted. But the orbits in the three-body problem, and most n-body problems for that matter, soon become too chaotic. Even worse, it’s hard to tell if the bodies will follow the same pattern, stay bound within their orbits, or simply fly everywhere.
A Long-winded History
It’s not unusual for mathematical problems to taunt the brightest minds for years. Hilbert’s problems remain mostly unsolved. But the three-body problem has been around for longer than Hilbert’s problems or many of the other unresolved mathematical problems.
According to Turab Musayev, the first time this problem was proposed was in 1687. It was Isaac Newton who first discussed it in his book Principia. Newton was concerned with the gravitational attractions among three massive celestial bodies and how it would affect their movement. In particular, he was thinking about the gravitational influence of the earth and sun over the movement of the moon.
But the roots of the problem in physics can be traced back to Galileo Galilei and Amerigo Vespucci, an Italian navigator, which puts the origin of this puzzle right around the turn of the 15th century. Over the years, scientists gave it their best shot. From French mathematician Henri Poincaré to Joseph-Louis Lagrange, the Italian astronomer, new solutions to the problem appeared over time. But as Poincaré soon realized, the general laws of dynamics made it almost impossible to know exactly which direction any of the celestial bodies would take or whether the orbits would be repeated.
Turab Musayev on Solutions to the Three-Body Problem
Since the three-body problem is not a purely mathematical one, instead, touching on many other fields including dynamics, geometry, and topology among others, a binary solution is not possible. This made it necessary to simplify the problem which led to what is known as special case solutions.
One such solution involves three objects charting various paths down an eight-shaped course. Turab Musayev considers this a breakthrough in this centuries-old stubborn problem. This is not about three massive celestial bodies of different mass each going in a random direction. Rather, these three small bodies are of the same mass and their orbits are limited to the eight-shaped figure.
Other purely numerical solutions appeared recently. In theory at least, it’s possible to define the motion of one body if the position of the other two bodies is known. However, since each body has a gravitational force that impacts the orbit of the other bodies, it becomes clear how complicated a general analytical solution can be.
Applications
The three-body problem has been used to explain natural phenomena, especially those pertaining to the laws of physics. According to Turab Musayev, the gravitational forces of the sun and moon and their impact on our planet can explain the tidal distortions once we apply the insights and solutions of the three-body problem. Even with the incomplete solutions or special case ones, we can better understand the tides and movements of the oceans much better now than we did a century or so ago. These solutions were also pivotal in the study of binary stars and planetary satellites.