Atlas3,865 of 3,942

AAAAAAAAAAAABaaB

(1, 1.268, 1)

From Three Body Orbits (2026)

AAAAAAAAAAAABaaB (1, 1.268, 1) is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1.268 : 1 that return to their starting positions and velocities every 30.182 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 21873), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0381 of each other at a top speed of 6.65, line up 30 times a period, and the computed loop closes to 4.6×10⁻²⁷. The search, its checks and the catalogue comparison are in the research note.

Measured over one period

Period: 30.18196013
Masses: 1 : 1.268 : 1
Energy: -1.29790
Angular momentum: 0
Closest approach: 0.03814
Top speed: 6.652
Path length: 68.598
Alignments per period: 30
Topology: aaaaaaaaaaaaBAAB (free-group class)
Stability: unstable (|λ|max 2.2×10⁵)
Loop closure: 4.6×10⁻²⁷

Neighbours on the map

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