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Choreography NC.153

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

Choreography NC.153 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 212.41 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 417901465164), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000000457 of each other at a top speed of 1479, line up 270 times a period, and the computed loop closes to 2.4×10⁻¹⁰.

Measured over one period

Period: 212.4115018
Masses: 1 : 1 : 1
Energy: -1.56031
Angular momentum: 0
Closest approach: 4.6×10⁻⁷
Top speed: 1479
Path length: 571.66
Alignments per period: 270
Stability: unstable (|λ|max 4.2×10¹¹, published)
Loop closure: 2.4×10⁻¹⁰

Neighbours on the map

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