Atlas3,883 of 3,942

AABaaBAAbaBBab

(1, 1, 1)

From Three Body Orbits (2026)

AABaaBAAbaBBab (1, 1, 1) is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 1 that return to their starting positions and velocities every 20.346 time units, published by Three Body Orbits (2026). Forty-two periodic orbits of topologies absent from the checked catalogues, found in a September 2026 search at unequal masses: the middle body lighter or heavier than the outer two, or all three different. Each is named by its free-group word, a few by a nickname; all are unstable. Candidate new families relative to the catalogues checked, not established discoveries. It is unstable (largest Floquet multiplier 11594), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0515 of each other at a top speed of 4.8, line up 24 times a period, and the computed loop closes to 8.3×10⁻²⁷. The search, its checks and the catalogue comparison are in the research note.

Measured over one period

Period: 20.34612489
Masses: 1 : 1 : 1
Energy: -1.43452
Angular momentum: 0
Closest approach: 0.05150
Top speed: 4.797
Path length: 50.232
Alignments per period: 24
Topology: aabAABabbaBAAb (free-group class)
Stability: unstable (|λ|max 11594)
Loop closure: 8.3×10⁻²⁷

Neighbours on the map

All New unequal-mass families, the families of periodic three-body orbits, or the atlas map.