Atlas3,915 of 3,942

SN.12

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

SN.12 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 9.3876 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 62.48), so a small nudge makes it unravel over a few periods. The bodies pass within 0.06 of each other at a top speed of 4.07, line up 18 times a period, and the computed loop closes to 1.1×10⁻²⁸.

Measured over one period

Period: 9.387609750
Masses: 1 : 1 : 1
Energy: -2.04230
Angular momentum: -0.092283
Closest approach: 0.06004
Top speed: 4.074
Path length: 29.084
Alignments per period: 18
Topology: aaBB (free-group class, read from the drawing, shape period T/3)
Stability: unstable (|λ|max 62.48)
Loop closure: 1.1×10⁻²⁸

Neighbours on the map

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