Atlas246 of 3,942

Broucke–Boggs S4

From Broucke & Boggs (1975)

Broucke–Boggs S4 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 4.2691 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 0.321 of each other at a top speed of 2.07, line up 6 times a period, and the computed loop closes to 1.1×10⁻²⁹.

Measured over one period

Period: 4.269082056
Masses: 1 : 1 : 1
Energy: -1.72338
Angular momentum: 0.79359
Closest approach: 0.3209
Top speed: 2.067
Path length: 12.739
Alignments per period: 6
Topology: (a)³ (free-group class, read from the drawing)
Stability: stable (|λ|max 1.000)
Loop closure: 1.1×10⁻²⁹

Neighbours on the map

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