New approach to centuries-old 'three-body problem'
The “three-body problem,” the term coined for predicting the motion of three gravitating bodies in space, is essential for understanding a variety of astrophysical processes as well as a large class of mechanical problems, and has occupied some of the world’s best physicists, astronomers and mathematicians for over three centuries. Their attempts have led to the discovery of several important fields of science; yet its solution remained a mystery.
At the end of the 17th century, Sir Isaac Newton succeeded in explaining the motion of the planets around the sun through a law of universal gravitation. He also sought to explain the motion of the moon. Since both the earth and the sun determine the motion of the moon, Newton became interested in the problem of predicting the motion of three bodies moving in space under the influence of their mutual gravitational attraction (see attached illustration), a problem that later became known as “the three-body problem.”
However, unlike the two-body problem, Newton was unable to obtain a general mathematical solution for it. Indeed, the three-body problem proved easy to define, yet difficult to solve.
New research, led by Professor Barak Kol at Hebrew University of Jerusalem’s Racah Institute of Physics, adds a step to this scientific journey that began with Newton, touching on the limits of scientific prediction and the role of chaos in it.
The theoretical study presents a novel and exact reduction of the problem, enabled by a re-examination of the basic concepts that underlie previous theories. It allows for a precise prediction of the probability for each of the three bodies to escape the system.
Following Newton and two centuries of fruitful research in the field including by Euler, Lagrange and Jacobi, by the late 19th century the mathematician Poincare discovered that the problem exhibits extreme sensitivity to the bodies’ initial positions and velocities. This sensitivity, which later became known as chaos, has far-reaching implications — it indicates that there is no deterministic solution in closed-form to the three-body problem. More