Atlas3,101 of 3,942

Broucke region HS.489

From Hristov, Hristova & Tanikawa (2026)

Broucke region HS.489 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 342.71 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 0.000216 of each other at a top speed of 68, line up 384 times a period, and the computed loop closes to 1.9×10⁻²⁵.

Measured over one period

Period: 342.7081228
Masses: 1 : 1 : 1
Energy: -1.43382
Angular momentum: 0
Closest approach: 2.2×10⁻⁴
Top speed: 68.02
Path length: 873.19
Alignments per period: 384
Topology: aaBAbaBAbaBBabABabAAbaBAbaBAbbABabABaaBAbaBAbbABabABabAAbaBAbaBBabABabAAbaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbaBBabABabAAbaBAbaBBabABabABaaBAbaBAbbABabAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 1.9×10⁻²⁵

Neighbours on the map

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