Atlas210 of 3,942

Broucke A5

From Broucke (1975)

Broucke A5 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 8.6891 time units, published by Broucke (1975). Broucke’s 1975 retrograde family: a binary and a third body circling it, the binary turning one way and the third body’s orbit the other; several are linearly stable. It is linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.736 of each other at a top speed of 1.28, line up 8 times a period, and the computed loop closes to 1.4×10⁻²⁵.

Measured over one period

Period: 8.689119976
Masses: 1 : 1 : 1
Energy: -1.22751
Angular momentum: 0.96956
Closest approach: 0.7356
Top speed: 1.280
Path length: 22.699
Alignments per period: 8
Topology: a (free-group class, read from the drawing, shape period T/4)
Stability: stable (|λ|max 1.000)
Loop closure: 1.4×10⁻²⁵

Neighbours on the map

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