Atlas245 of 3,942

Broucke–Boggs S33

(0.6, 0.3, 2.1)

From Broucke & Boggs (1975)

Broucke–Boggs S33 (0.6, 0.3, 2.1) is a periodic orbit of the planar three-body problem: three masses in the ratio 0.6 : 0.3 : 2.1 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 1.29 of each other at a top speed of 1.24, line up 6 times a period, and the computed loop closes to 1.2×10⁻²⁵.

Measured over one period

Period: 12.56637056
Masses: 0.6 : 0.3 : 2.1
Energy: -0.631274
Angular momentum: 0.16573
Closest approach: 1.286
Top speed: 1.240
Path length: 30.757
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: 1.2×10⁻²⁵

Neighbours on the map

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