Atlas3,891 of 3,942

Woven loops

(1, 0.563, 1)

From Three Body Orbits (2026)

Woven loops (1, 0.563, 1) is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 0.563 : 1 that return to their starting positions and velocities every 33.149 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 834.1), so a small nudge makes it unravel over a few periods. The bodies pass within 0.209 of each other at a top speed of 2.52, line up 18 times a period, and the computed loop closes to 1.8×10⁻²⁵. The search, its checks and the catalogue comparison are in the research note.

Measured over one period

Period: 33.14877017
Masses: 1 : 0.563 : 1
Energy: -0.660095
Angular momentum: 0
Closest approach: 0.2094
Top speed: 2.521
Path length: 65.551
Alignments per period: 18
Topology: aaaabAbaaBB (free-group class)
Stability: unstable (|λ|max 834.1)
Loop closure: 1.8×10⁻²⁵

Neighbours on the map

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