Atlas211 of 3,942

Broucke A3

From Broucke (1975)

Broucke A3 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 7.9103 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 0.497 of each other at a top speed of 1.46, line up 12 times a period, and the computed loop closes to 8.4×10⁻³⁰.

Measured over one period

Period: 7.910269763
Masses: 1 : 1 : 1
Energy: -1.59209
Angular momentum: 1.0142
Closest approach: 0.4974
Top speed: 1.460
Path length: 23.637
Alignments per period: 12
Topology: a (free-group class, read from the drawing, shape period T/6)
Stability: stable (|λ|max 1.000)
Loop closure: 8.4×10⁻³⁰

Neighbours on the map

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