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Choreography NC.4

From Hristov, Hristova, Puzynin, Puzynina, Sharipov & Tukhliev (2024)

Choreography NC.4 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 64.639 time units, published by Hristov, Hristova, Puzynin, Puzynina, Sharipov & Tukhliev (2024). Choreographies whose knot is not a power of the figure-eight’s: three bodies on one closed curve with a topology of its own. Computed to 180 digits; all unstable. It is unstable (largest Floquet multiplier 1559883), so a small nudge makes it unravel over a few periods. The bodies pass within 0.159 of each other at a top speed of 2.84, line up 36 times a period, and the computed loop closes to 1.4×10⁻²⁵.

Measured over one period

Period: 64.63923730
Masses: 1 : 1 : 1
Energy: -0.878896
Angular momentum: 0
Closest approach: 0.1594
Top speed: 2.839
Path length: 117.87
Alignments per period: 36
Stability: unstable (|λ|max 1.6×10⁶, published)
Loop closure: 1.4×10⁻²⁵

Neighbours on the map

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