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Broucke region HS.451

From Hristov, Hristova & Tanikawa (2026)

Broucke region HS.451 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 348.7 time units, published by Hristov, Hristova & Tanikawa (2026). Stable orbits related to Broucke’s isosceles orbit, with one body swinging through the other two. It is linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.000198 of each other at a top speed of 71.1, line up 366 times a period, and the computed loop closes to 7.1×10⁻²⁴.

Measured over one period

Period: 348.7043554
Masses: 1 : 1 : 1
Energy: -1.37398
Angular momentum: 0
Closest approach: 2.0×10⁻⁴
Top speed: 71.06
Path length: 902.82
Alignments per period: 366
Topology: aaBAbaBAbaBAbaBAbbABabABabABabAAbaBAbaBAbaBAbaBBabABabABabABaaBAbaBAbaBAbaBAbbABabABabABabABaaBAbaBAbaBAbaBBabABabABabABabAAbaBAbaBAbaBAbaBBabABabABabABaaBAbaBAbaBAbaBAbbABabABabABabAAbaBAbaBAbaBAbaBBabABabABabABabAAbaBAbaBAbaBAbbABabABabABabAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 7.1×10⁻²⁴

Neighbours on the map

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