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Choreography CH.417

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

Choreography CH.417 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 851.31 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 0.429 of each other at a top speed of 1.6, line up 948 times a period, and the computed loop closes to 1.0×10⁻²⁷.

Measured over one period

Period: 851.3127521
Masses: 1 : 1 : 1
Energy: -1.43245
Angular momentum: 0
Closest approach: 0.4290
Top speed: 1.597
Path length: 2345.1
Alignments per period: 948
Topology: (abAB)¹⁵⁸ (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 1.0×10⁻²⁷

Neighbours on the map

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