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Schubart region HS.75

From Hristov, Hristova & Tanikawa (2026)

Schubart region HS.75 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 80.302 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 0.000676 of each other at a top speed of 38.5, line up 152 times a period, and the computed loop closes to 9.2×10⁻²⁵.

Measured over one period

Period: 80.30201418
Masses: 1 : 1 : 1
Energy: -1.97548
Angular momentum: 0
Closest approach: 6.8×10⁻⁴
Top speed: 38.50
Path length: 226.60
Alignments per period: 152
Topology: ababABAbabABAbabaBABabaBABabaBABAbabABAbabABAbabaBABabaBABababABAbabABAbabABABabaBABabaBAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 9.2×10⁻²⁵

Neighbours on the map

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