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Choreography NC.140

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

Choreography NC.140 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 244.29 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 11494884045), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00932 of each other at a top speed of 10.4, line up 240 times a period, and the computed loop closes to 4.9×10⁻²¹.

Measured over one period

Period: 244.2867361
Masses: 1 : 1 : 1
Energy: -1.31591
Angular momentum: 0
Closest approach: 0.009315
Top speed: 10.38
Path length: 629.67
Alignments per period: 240
Stability: unstable (|λ|max 1.1×10¹⁰, published)
Loop closure: 4.9×10⁻²¹

Neighbours on the map

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