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Choreography NC.45

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

Choreography NC.45 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 137.04 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 49139989), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000369 of each other at a top speed of 52.3, line up 90 times a period, and the computed loop closes to 5.2×10⁻²⁰.

Measured over one period

Period: 137.0414509
Masses: 1 : 1 : 1
Energy: -1.00367
Angular momentum: 0
Closest approach: 3.7×10⁻⁴
Top speed: 52.26
Path length: 284.19
Alignments per period: 90
Stability: unstable (|λ|max 4.9×10⁷, published)
Loop closure: 5.2×10⁻²⁰

Neighbours on the map

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