Atlas2,944 of 3,942

Schubart region HS.589

From Hristov, Hristova & Tanikawa (2026)

Schubart region HS.589 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 223.94 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 0.000016 of each other at a top speed of 25, line up 442 times a period, and the computed loop closes to 5.2×10⁻²³.

Measured over one period

Period: 223.9362179
Masses: 1 : 1 : 1
Energy: -2.00781
Angular momentum: 0
Closest approach: 1.6×10⁻⁵
Top speed: 250.0
Path length: 603.44
Alignments per period: 442
Topology: ababABAbabaBABababABABababABAbabaBABababABABabaBABAbabaBABAbabABABabaBABAbabaBABababABABabaBABAbabaBABababABAbabaBABAbabaBABababABABabaBABAbabABABababABABabaBABAbabABABababABAbabaBABAbabaBABababABAbabaBABAbabABABababABAbabaBABAbabABABabaBABAbabaBABAbabABAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 5.2×10⁻²³

Neighbours on the map

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