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Schubart region HS.781

From Hristov, Hristova & Tanikawa (2026)

Schubart region HS.781 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 320.14 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 0.0000628 of each other at a top speed of 126, line up 490 times a period, and the computed loop closes to 4.5×10⁻²³.

Measured over one period

Period: 320.1356146
Masses: 1 : 1 : 1
Energy: -1.71975
Angular momentum: 0
Closest approach: 6.3×10⁻⁵
Top speed: 126.2
Path length: 852.15
Alignments per period: 490
Topology: ababABAbabABAbabABAbabABAbabABAbabaBABabaBABabaBABabaBABabaBABAbabABAbabABAbabABAbabABAbabaBABabaBABabaBABabaBABabaBABababABAbabABAbabABAbabABAbabABABabaBABabaBABabaBABabaBABabaBABAbabABAbabABAbabABAbabABAbabaBABabaBABabaBABabaBABabaBABAbabABAbabABAbabABAbabABAbabABABabaBABabaBABabaBABabaBAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 4.5×10⁻²³

Neighbours on the map

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