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Broucke–Boggs S122

From Broucke & Boggs (1975)

Broucke–Boggs S122 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 8.7497 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 unstable (largest Floquet multiplier 17.82), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0473 of each other at a top speed of 4.78, line up 10 times a period, and the computed loop closes to 6.8×10⁻²⁵.

Measured over one period

Period: 8.749669031
Masses: 1 : 1 : 1
Energy: -1.36710
Angular momentum: 1.8311
Closest approach: 0.04726
Top speed: 4.779
Path length: 21.256
Alignments per period: 10
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: unstable (|λ|max 17.82)
Loop closure: 6.8×10⁻²⁵

Neighbours on the map

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