Atlas3,078 of 3,942

Broucke region HS.171

From Hristov, Hristova & Tanikawa (2026)

Broucke region HS.171 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 206.48 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 0.0000686 of each other at a top speed of 121, line up 234 times a period, and the computed loop closes to 1.9×10⁻²³.

Measured over one period

Period: 206.4787297
Masses: 1 : 1 : 1
Energy: -1.44462
Angular momentum: 0
Closest approach: 6.9×10⁻⁵
Top speed: 120.7
Path length: 523.25
Alignments per period: 234
Topology: aaBAbaBAbbABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABaaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbbABabAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 1.9×10⁻²³

Neighbours on the map

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