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Broucke region HS.581

From Hristov, Hristova & Tanikawa (2026)

Broucke region HS.581 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 345.13 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 0.0000112 of each other at a top speed of 299, line up 414 times a period, and the computed loop closes to 7.7×10⁻²².

Measured over one period

Period: 345.1274118
Masses: 1 : 1 : 1
Energy: -1.50042
Angular momentum: 0
Closest approach: 1.1×10⁻⁵
Top speed: 298.7
Path length: 882.75
Alignments per period: 414
Topology: aaBAbaBAbaBBabABaaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbbABabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabABaaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbbABabAAbaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbbABabAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 7.7×10⁻²²

Neighbours on the map

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