Atlas3,081 of 3,942

Broucke region HS.658

From Hristov, Hristova & Tanikawa (2026)

Broucke region HS.658 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 389.04 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 0.0000381 of each other at a top speed of 162, line up 438 times a period, and the computed loop closes to 8.8×10⁻²³.

Measured over one period

Period: 389.0351134
Masses: 1 : 1 : 1
Energy: -1.43834
Angular momentum: 0
Closest approach: 3.8×10⁻⁵
Top speed: 162.1
Path length: 988.28
Alignments per period: 438
Topology: aaBAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbbABabAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 8.8×10⁻²³

Neighbours on the map

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