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Broucke region HS.500

From Hristov, Hristova & Tanikawa (2026)

Broucke region HS.500 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 346.54 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 0.0000453 of each other at a top speed of 149, line up 390 times a period, and the computed loop closes to 4.4×10⁻²³.

Measured over one period

Period: 346.5363009
Masses: 1 : 1 : 1
Energy: -1.43796
Angular momentum: 0
Closest approach: 4.5×10⁻⁵
Top speed: 148.6
Path length: 880.37
Alignments per period: 390
Topology: aaBAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbbABabAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 4.4×10⁻²³

Neighbours on the map

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