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Schubart region HS.418

From Hristov, Hristova & Tanikawa (2026)

Schubart region HS.418 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 268.73 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 0.000125 of each other at a top speed of 89.6, line up 362 times a period, and the computed loop closes to 5.1×10⁻²⁴.

Measured over one period

Period: 268.7287513
Masses: 1 : 1 : 1
Energy: -1.59232
Angular momentum: 0
Closest approach: 1.2×10⁻⁴
Top speed: 89.58
Path length: 705.84
Alignments per period: 362
Topology: abaBAbabABAbabABAbabABabaBABabaBABabaBAbabABAbabABAbaBABabaBABabaBABabABAbabABAbabABabaBABabaBABabaBAbabABAbabABAbaBABabaBABabaBABabABAbabABAbabABAbaBABabaBABabaBAbabABAbabABAbabABabaBABabaBABabABAbabABAbabABAbaBABabaBAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 5.1×10⁻²⁴

Neighbours on the map

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