Atlas3,260 of 3,915

Choreography NC.98

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

Choreography NC.98 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 153.33 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 0.00955 of each other at a top speed of 10.3, line up 186 times a period, and the computed loop closes to 3.2×10⁻²².

Measured over one period

Period: 153.3257322
Masses: 1 : 1 : 1
Energy: -1.51380
Angular momentum: 0
Closest approach: 0.009546
Top speed: 10.29
Path length: 416.45
Alignments per period: 186
Stability: unstable (|λ|max 2.5×10⁸, published)
Loop closure: 3.2×10⁻²²

Neighbours on the map

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