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Broucke region HS.540

From Hristov, Hristova & Tanikawa (2026)

Broucke region HS.540 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 360.21 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 0.0000434 of each other at a top speed of 152, line up 402 times a period, and the computed loop closes to 4.4×10⁻²².

Measured over one period

Period: 360.2114970
Masses: 1 : 1 : 1
Energy: -1.42997
Angular momentum: 0
Closest approach: 4.3×10⁻⁵
Top speed: 151.9
Path length: 915.45
Alignments per period: 402
Topology: aaBAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbbABabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabABaaBAbaBAbbABabABaaBAbaBAbbABabAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 4.4×10⁻²²

Neighbours on the map

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