Atlas238 of 3,942

Broucke–Boggs S34

(0.705, 0.3, 1.995)

From Broucke & Boggs (1975)

Broucke–Boggs S34 (0.705, 0.3, 1.995) is a periodic orbit of the planar three-body problem: three masses in the ratio 0.705 : 0.3 : 1.995 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 1.34 of each other at a top speed of 1.18, line up 6 times a period, and the computed loop closes to 6.3×10⁻²⁶.

Measured over one period

Period: 12.56637066
Masses: 0.705 : 0.3 : 1.995
Energy: -0.684063
Angular momentum: 0.26812
Closest approach: 1.340
Top speed: 1.181
Path length: 30.760
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: 6.3×10⁻²⁶

Neighbours on the map

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