Atlas233 of 3,942

Broucke–Boggs S37

(0.999, 0.45, 1.551)

From Broucke & Boggs (1975)

Broucke–Boggs S37 (0.999, 0.45, 1.551) is a periodic orbit of the planar three-body problem: three masses in the ratio 0.999 : 0.45 : 1.551 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 1.33 of each other at a top speed of 1.04, line up 6 times a period, and the computed loop closes to 2.1×10⁻²⁵.

Measured over one period

Period: 12.56637063
Masses: 0.999 : 0.45 : 1.551
Energy: -0.821105
Angular momentum: 0.078390
Closest approach: 1.334
Top speed: 1.037
Path length: 29.832
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: 2.1×10⁻²⁵

Neighbours on the map

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