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Choreography CH.242

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

Choreography CH.242 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 541.89 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 0.481 of each other at a top speed of 1.5, line up 570 times a period, and the computed loop closes to 4.6×10⁻²⁸.

Measured over one period

Period: 541.8915667
Masses: 1 : 1 : 1
Energy: -1.37905
Angular momentum: 0
Closest approach: 0.4807
Top speed: 1.495
Path length: 1467.8
Alignments per period: 570
Topology: (abAB)⁹⁵ (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 4.6×10⁻²⁸

Neighbours on the map

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