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Choreography NC.136

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

Choreography NC.136 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 265.97 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 1263421), so a small nudge makes it unravel over a few periods. The bodies pass within 0.029 of each other at a top speed of 5.88, line up 240 times a period, and the computed loop closes to 7.8×10⁻²⁵.

Measured over one period

Period: 265.9714355
Masses: 1 : 1 : 1
Energy: -1.24331
Angular momentum: 0
Closest approach: 0.02904
Top speed: 5.878
Path length: 667.97
Alignments per period: 240
Stability: unstable (|λ|max 1.3×10⁶, published)
Loop closure: 7.8×10⁻²⁵

Neighbours on the map

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