Atlas3,296 of 3,915

Choreography NC.68

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

Choreography NC.68 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 241.4 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 30576422), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000124 of each other at a top speed of 90, line up 120 times a period, and the computed loop closes to 9.0×10⁻¹⁹.

Measured over one period

Period: 241.3985409
Masses: 1 : 1 : 1
Energy: -0.833818
Angular momentum: 0
Closest approach: 1.2×10⁻⁴
Top speed: 89.96
Path length: 461.53
Alignments per period: 120
Stability: unstable (|λ|max 3.1×10⁷, published)
Loop closure: 9.0×10⁻¹⁹

Neighbours on the map

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