Atlas3,011 of 3,942

Schubart region HS.539

From Hristov, Hristova & Tanikawa (2026)

Schubart region HS.539 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 233.88 time units, published by Hristov, Hristova & Tanikawa (2026). Stable orbits that pass extremely close to a binary collision, descended from Schubart’s rectilinear orbit. They needed 100-digit arithmetic to find. It is linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.0000796 of each other at a top speed of 112, line up 422 times a period, and the computed loop closes to 5.9×10⁻²⁴.

Measured over one period

Period: 233.8838159
Masses: 1 : 1 : 1
Energy: -1.90623
Angular momentum: 0
Closest approach: 8.0×10⁻⁵
Top speed: 112.1
Path length: 638.47
Alignments per period: 422
Topology: ababABAbabaBABabaBABababABAbabaBABabaBABAbabABAbabaBABabaBABAbabABAbabaBABabaBABAbabABAbabaBABababABAbabABAbabaBABababABAbabABABabaBABAbabABAbabABABabaBABAbabABAbabaBABabaBABAbabABAbabaBABabaBABAbabABAbabaBABabaBABAbabABABabaBABabaBABAbabABABabaBAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 5.9×10⁻²⁴

Neighbours on the map

All Schubart region, the families of periodic three-body orbits, or the atlas map.