Atlas265 of 3,942

Rosette 35:49

(1, 0.484, 1)

From Three Body Orbits (2026)

Rosette 35:49 (1, 0.484, 1) is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 0.484 : 1 that return to their starting positions and velocities every 225.17 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 0.479 of each other at a top speed of 1.59, line up 168 times a period, and the computed loop closes to 1.2×10⁻²⁷. The search, the verification tiers and a candid novelty assessment are in the research note.

Measured over one period

Period: 225.1695006
Masses: 1 : 0.484 : 1
Energy: -0.851227
Angular momentum: 0
Closest approach: 0.4792
Top speed: 1.592
Path length: 572.68
Alignments per period: 168
Topology: (a)⁷ (free-group class, shape period T/12)
Stability: stable (|λ|max 1.000)
Loop closure: 1.2×10⁻²⁷

Neighbours on the map

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