Atlas3,906 of 3,942

SN.21

From Šuvakov (2026). Thirteen equal-mass orbits with angular momentum from Milovan Šuvakov’s own searches, shared with this atlas.

SN.21 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 7.1618 time units. Thirteen equal-mass orbits with angular momentum from Milovan Šuvakov’s own searches, shared with this atlas in September 2026. Seven are the figure-eight carried to nonzero angular momentum, its 1/5 to 2/3 resonances, all linearly stable; four lie on a branch that ends, at zero angular momentum, in Broucke’s isosceles collision orbit; two branch off Broucke’s A family. Numbered as in his file. It is linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.155 of each other at a top speed of 2.49, line up 12 times a period, and the computed loop closes to 6.6×10⁻²⁹.

Measured over one period

Period: 7.161820669
Masses: 1 : 1 : 1
Energy: -1.85633
Angular momentum: -0.18025
Closest approach: 0.1551
Top speed: 2.494
Path length: 21.348
Alignments per period: 12
Topology: abAB (free-group class, read from the drawing, shape period T/2)
Stability: stable (|λ|max 1.000)
Loop closure: 6.6×10⁻²⁹

Neighbours on the map

All Šuvakov’s other orbits, the families of periodic three-body orbits, or the atlas map.