Atlas3,343 of 3,942

Choreography NC.49

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

Choreography NC.49 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 175.66 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 6376455117), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0261 of each other at a top speed of 6.29, line up 108 times a period, and the computed loop closes to 7.2×10⁻²¹.

Measured over one period

Period: 175.6643932
Masses: 1 : 1 : 1
Energy: -0.889250
Angular momentum: 0
Closest approach: 0.02614
Top speed: 6.288
Path length: 322.36
Alignments per period: 108
Topology: aaabaBBBAbaBaBaBAbAAABabAbAbAAbaaaBAbbbaBBaBaBabABBBaBAbAbAbaBAAAbabbbAB (free-group class)
Stability: unstable (|λ|max 6.4×10⁹, published)
Loop closure: 7.2×10⁻²¹

Neighbours on the map

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