Atlas255 of 3,942

Rosette 4:7

(1.005, 0.497, 0.995)

From Three Body Orbits (2026)

Rosette 4:7 (1.005, 0.497, 0.995) is a periodic orbit of the planar three-body problem: three masses in the ratio 1.005 : 0.497 : 0.995 that return to their starting positions and velocities every 21.204 time units, published by Three Body Orbits (2026). Zero-angular-momentum relatives of Broucke’s rosettes: two equal bodies in a close binary and a lighter third body circling them the other way, its mass tuned so that the precession closes the pattern after a whole number of turns and the inner paths cross the outer one. Fourteen representatives from the site’s own September 2026 search, all linearly stable; points on a known continuous family rather than a new one. Named by the inner and outer winding counts. It is linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.426 of each other at a top speed of 1.66, line up 22 times a period, and the computed loop closes to 2.6×10⁻²⁶. The search, the verification tiers and a candid novelty assessment are in the research note.

Measured over one period

Period: 21.20370933
Masses: 1.005 : 0.497 : 0.995
Energy: -1.07496
Angular momentum: 0
Closest approach: 0.4261
Top speed: 1.657
Path length: 60.044
Alignments per period: 22
Topology: a (free-group class, shape period T/11)
Stability: stable (|λ|max 1.000)
Loop closure: 2.6×10⁻²⁶

Neighbours on the map

All Broucke-like rosettes, the families of periodic three-body orbits, or the atlas map.