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Choreography NC.99

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

Choreography NC.99 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 166.49 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 248582025), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0101 of each other at a top speed of 10, line up 186 times a period, and the computed loop closes to 8.2×10⁻²³.

Measured over one period

Period: 166.4891107
Masses: 1 : 1 : 1
Energy: -1.43292
Angular momentum: 0
Closest approach: 0.01008
Top speed: 10.01
Path length: 439.95
Alignments per period: 186
Stability: unstable (|λ|max 2.5×10⁸, published)
Loop closure: 8.2×10⁻²³

Neighbours on the map

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