Atlas3,099 of 3,942

Broucke region HS.186

From Hristov, Hristova & Tanikawa (2026)

Broucke region HS.186 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 219.13 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 0.00011 of each other at a top speed of 95.2, line up 246 times a period, and the computed loop closes to 2.0×10⁻²³.

Measured over one period

Period: 219.1308468
Masses: 1 : 1 : 1
Energy: -1.43558
Angular momentum: 0
Closest approach: 1.1×10⁻⁴
Top speed: 95.20
Path length: 556.79
Alignments per period: 246
Topology: aaBAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbbABabAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 2.0×10⁻²³

Neighbours on the map

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