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Nested crossings

(1.25, 1.134, 0.75)

From Three Body Orbits (2026)

Nested crossings (1.25, 1.134, 0.75) is a periodic orbit of the planar three-body problem: three masses in the ratio 1.25 : 1.134 : 0.75 that return to their starting positions and velocities every 10.45 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 122), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0762 of each other at a top speed of 4.54, line up 10 times a period, and the computed loop closes to 8.1×10⁻²⁶. The search, its checks and the catalogue comparison are in the research note.

Measured over one period

Period: 10.45022203
Masses: 1.25 : 1.134 : 0.75
Energy: -1.34700
Angular momentum: 0
Closest approach: 0.07621
Top speed: 4.540
Path length: 26.202
Alignments per period: 10
Topology: aaaBAB (free-group class)
Stability: unstable (|λ|max 122.0)
Loop closure: 8.1×10⁻²⁶

Neighbours on the map

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