Atlas3,894 of 3,942

Near-equal-mass weave

(1, 1.023, 1)

From Three Body Orbits (2026)

Near-equal-mass weave (1, 1.023, 1) is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1.023 : 1 that return to their starting positions and velocities every 33.83 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 weakly unstable (largest Floquet multiplier 1.577), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00473 of each other at a top speed of 14.8, line up 54 times a period, and the computed loop closes to 3.5×10⁻²⁶. The search, its checks and the catalogue comparison are in the research note.

Measured over one period

Period: 33.82994070
Masses: 1 : 1.023 : 1
Energy: -1.83135
Angular momentum: 0
Closest approach: 0.004735
Top speed: 14.78
Path length: 98.415
Alignments per period: 54
Topology: abaBAbabABabaBAbaBABabABAbaBABabAB (free-group class)
Stability: weakly unstable (|λ|max 1.577)
Loop closure: 3.5×10⁻²⁶

Neighbours on the map

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