The three-body problem is a well-known challenge in the field of astronomy, partly because it has inspired one of the most significant science fiction sagas in recent years, Liu Cixin’s Remembrance of Earth’s Past. This problem has fascinated physicists around the world for centuries. Although a definitive solution remains elusive, a team of researchers has recently discovered an important new clue.
Islands of stability. The team has found evidence of “islands of regularity” (regular trajectories) in how groups of three astronomical objects interact gravitationally. The findings were published in the journal Astronomy & Astrophysics.
Understanding the three-body problem. To put this into context, the three-body problem refers to the difficulty of calculating the orbital motions of three objects orbiting each other. Three centuries ago, the discovery of gravity and the underlying mathematics allowed scientists to mathematically describe the motion of two objects based on their gravitational interaction.
These motions are relatively simple, enabling regular interactions such as the orbiting of planets around a star. Thanks to this knowledge, astronomers can, for instance, predict with great accuracy when a comet will pass by or determine the distance between the Earth and the Sun in four and a half years.
However, the situation becomes much more complicated when a third body is introduced into the equation. This simple addition can derail any hope of calculating long-term interactions. This is because the system becomes chaotic, meaning that small changes in the initial conditions can lead to significant differences in the outcomes, much like with double pendulums.
From statistics to simulations. When three objects interact gravitationally, achieving a stable equilibrium is rare. Typically, one (or more) of the objects is ejected from the system. To navigate this complexity, physicists often rely on statistical methods to avoid the costly deterministic calculations needed to determine if one body will eventually be expelled. Essentially, they simplify the three-body problem by eliminating one object from consideration.
Recently, the research group mentioned earlier faced an issue. When comparing their statistical models with computer simulations, they noticed significant discrepancies in the results. In their experiments, physicists started with a binary system consisting of two bodies orbiting each other. They then simulated the approach of a third object from random positions in space and studied the system’s evolution over time until one of the objects was ejected.
Regular trajectories. Researchers identified a series of “regular trajectories,” which are paths that the objects followed without exhibiting chaotic behavior. This regularity doesn’t imply stable equilibria but instead signifies non-chaotic trajectories that are easier to predict. In this context, these predictable paths lead to the expulsion of one object more quickly and directly.
By creating a graph based on the system’s initial conditions, they discovered clusters of similar conditions that yielded comparable outcomes. These clusters are referred to as “islands of regularity.”
Progress and setbacks. The result of the study represents a breakthrough, providing deeper insights into the complex three-body problem. However, it also reveals a setback. Navigating the chaotic nature of this problem is proving to be more challenging than previously anticipated.
According to the research team, the interaction between chaotic and predictable behaviors is more intricate than the dominance of chaos alone. As a result, the calculations involved become even more complex.
Image | Alessandro Alberto Trani
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