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Broucke region HS.178

From Hristov, Hristova & Tanikawa (2026)

Broucke region HS.178 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 209.69 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 0.000214 of each other at a top speed of 68.3, line up 240 times a period, and the computed loop closes to 2.0×10⁻²⁴.

Measured over one period

Period: 209.6896836
Masses: 1 : 1 : 1
Energy: -1.45433
Angular momentum: 0
Closest approach: 2.1×10⁻⁴
Top speed: 68.33
Path length: 539.92
Alignments per period: 240
Topology: aaBAbaBAbaBBabABabAAbaBAbaBAbbABabABaaBAbaBAbaBBabABabAAbaBAbaBAbbABabABaaBAbaBAbaBBabABabAAbaBAbaBAbbABabABaaBAbaBAbbABabABabAAbaBAbaBBabABabABaaBAbaBAbbABabAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 2.0×10⁻²⁴

Neighbours on the map

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