Atlas3,094 of 3,942

Broucke region HS.677

From Hristov, Hristova & Tanikawa (2026)

Broucke region HS.677 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 402.51 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 0.0000178 of each other at a top speed of 237, line up 444 times a period, and the computed loop closes to 7.4×10⁻²².

Measured over one period

Period: 402.5053067
Masses: 1 : 1 : 1
Energy: -1.41920
Angular momentum: 0
Closest approach: 1.8×10⁻⁵
Top speed: 237.1
Path length: 1033.2
Alignments per period: 444
Topology: aaBAbaBAbaBBabABabAAbaBAbaBAbbABabABabAAbaBAbaBAbbABabABabAAbaBAbaBAbbABabABabAAbaBAbaBAbbABabABabAAbaBAbaBAbbABabABabAAbaBAbaBAbbABabABabAAbaBAbaBAbbABabABabAAbaBAbaBBabABabABaaBAbaBAbaBBabABabABaaBAbaBAbaBBabABabABaaBAbaBAbaBBabABabABaaBAbaBAbaBBabABabABaaBAbaBAbaBBabABabABaaBAbaBAbaBBabABabAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 7.4×10⁻²²

Neighbours on the map

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