Atlas236 of 3,942

Broucke–Boggs S39

(0.999, 0.81, 1.191)

From Broucke & Boggs (1975)

Broucke–Boggs S39 (0.999, 0.81, 1.191) is a periodic orbit of the planar three-body problem: three masses in the ratio 0.999 : 0.81 : 1.191 that return to their starting positions and velocities every 12.566 time units, published by Broucke & Boggs (1975). Broucke and Boggs’s 1975 survey of periodic orbits at many mass ratios, most of them reported linearly stable. It is linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 1.25 of each other at a top speed of 1.06, line up 6 times a period, and the computed loop closes to 8.5×10⁻²⁷.

Measured over one period

Period: 12.56637063
Masses: 0.999 : 0.81 : 1.191
Energy: -0.850297
Angular momentum: -0.70561
Closest approach: 1.254
Top speed: 1.061
Path length: 27.820
Alignments per period: 6
Topology: a (free-group class, read from the drawing, shape period T/3)
Stability: stable (|λ|max 1.000)
Loop closure: 8.5×10⁻²⁷

Neighbours on the map

All Broucke–Boggs orbits, the families of periodic three-body orbits, or the atlas map.