The Dance of Three Bodies: New Orbits in Chaos ⚡ экспресс
Using a high-precision numerical approach, 10,059 three-dimensional periodic orbits were discovered in the general three-body problem for masses $$m_1=m_2=1$$ and $$m_3=0.1n$$, where $$1\leq n\leq 20$$. Of these, 1,996 (about 20%) turned out to be linearly stable. The method is applicable for an arbitrary value of $$m_3$$, allowing theoretically to obtain arbitrarily many three-dimensional periodic orbits. In the case of three equal masses, 21 choreographic orbits were found with all bodies moving along the same closed curve. For two equal masses, 273 orbits of the 'piano trio' type were identified: two bodies with $$m_1=m_2=1$$ revolve along a common orbit, while the third ($$m_3\neq 1$$) moves along a separate one. All orbits are new and deepen the understanding of the chaotic properties of the three-body problem, which, in Poincaré's words, opens access to previously inaccessible regions.
Three bodies in space under the influence of gravity usually dance wildly, like strangers on a dance floor. But occasionally their dance becomes strict — the figure closes and repeats for eternity. These periodic orbits were sought by Newton long ago, and today's scientists have managed to find thousands.
For two massive bodies and one light one, they collected 10,059 three-dimensional steps. Contrary to chaos, nearly 20% are stable: a nudge doesn't break the rhythm — the orbit would survive even a passing rogue star. Such high stability surprised even skeptics: it seemed triple systems should be chaotic from birth. Three equal bodies circle in 21 round dances, following a single curve. There are also 273 duets with a solo: two as a pair, the third on its own, but together they return. Such figures hide in any galaxy, even where black holes lurk. This is the key to why triple stars don't fly apart: they simply dance a perfect dance.
🎯 Stable triple star systems are rare, but one of them — Alpha Centauri — is our neighbor, though its dance is not so elaborate.
🎬 The unpredictability of three bodies inspired Liu Cixin's novel 'The Three-Body Problem,' where a civilization's survival hinges on the chaos of the gravitational dance.