Atlas206 of 3,942

Broucke A2

From Broucke (1975)

Broucke A2 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 7.7024 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 0.434 of each other at a top speed of 1.53, line up 14 times a period, and the computed loop closes to 1.2×10⁻²⁹.

Measured over one period

Period: 7.702403002
Masses: 1 : 1 : 1
Energy: -1.75108
Angular momentum: 1.0306
Closest approach: 0.4339
Top speed: 1.532
Path length: 24.143
Alignments per period: 14
Topology: a (free-group class, read from the drawing, shape period T/7)
Stability: stable (|λ|max 1.000)
Loop closure: 1.2×10⁻²⁹

Neighbours on the map

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