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Choreography CH.331

From Hristov, Hristova, Puzynin, Puzynina, Sharipov & Tukhliev (2023)

Choreography CH.331 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 685.79 time units, published by Hristov, Hristova, Puzynin, Puzynina, Sharipov & Tukhliev (2023). All three bodies follow one closed curve, each a third of a period behind the next. Every one here is linearly stable. It is linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.399 of each other at a top speed of 1.64, line up 780 times a period, and the computed loop closes to 7.3×10⁻²⁸.

Measured over one period

Period: 685.7917610
Masses: 1 : 1 : 1
Energy: -1.45278
Angular momentum: 0
Closest approach: 0.3990
Top speed: 1.636
Path length: 1899.7
Alignments per period: 780
Topology: (abAB)¹³⁰ (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 7.3×10⁻²⁸

Neighbours on the map

All Choreographies, the families of periodic three-body orbits, or the atlas map.