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Choreography NC.121

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

Choreography NC.121 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 162.15 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 23558867964), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00698 of each other at a top speed of 12, line up 204 times a period, and the computed loop closes to 6.2×10⁻²².

Measured over one period

Period: 162.1503859
Masses: 1 : 1 : 1
Energy: -1.55103
Angular momentum: 0
Closest approach: 0.006982
Top speed: 11.98
Path length: 438.23
Alignments per period: 204
Stability: unstable (|λ|max 2.4×10¹⁰, published)
Loop closure: 6.2×10⁻²²

Neighbours on the map

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