Atlas257 of 3,942

Rosette 7:13

(1, 0.497, 1)

From Three Body Orbits (2026)

Rosette 7:13 (1, 0.497, 1) is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 0.497 : 1 that return to their starting positions and velocities every 36.463 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 0.38 of each other at a top speed of 1.76, line up 40 times a period, and the computed loop closes to 7.4×10⁻²⁸. The search, the verification tiers and a candid novelty assessment are in the research note.

Measured over one period

Period: 36.46321045
Masses: 1 : 0.497 : 1
Energy: -1.11613
Angular momentum: 0
Closest approach: 0.3804
Top speed: 1.757
Path length: 105.00
Alignments per period: 40
Topology: (a)¹⁰ (free-group class, shape period T/2)
Stability: stable (|λ|max 1.000)
Loop closure: 7.4×10⁻²⁸

Neighbours on the map

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