Atlas3,904 of 3,942

SN.13

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

SN.13 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 7.1716 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 unstable (largest Floquet multiplier 36.17), so a small nudge makes it unravel over a few periods. The bodies pass within 0.172 of each other at a top speed of 2.38, line up 12 times a period, and the computed loop closes to 1.5×10⁻²⁹.

Measured over one period

Period: 7.171575055
Masses: 1 : 1 : 1
Energy: -1.85094
Angular momentum: -0.20452
Closest approach: 0.1715
Top speed: 2.376
Path length: 21.745
Alignments per period: 12
Topology: aaBB (free-group class, read from the drawing, shape period T/2)
Stability: unstable (|λ|max 36.17)
Loop closure: 1.5×10⁻²⁹

Neighbours on the map

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