Atlas215 of 3,942

Broucke A6

From Broucke (1975)

Broucke A6 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 9.5933 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 1.01 of each other at a top speed of 1.16, line up 6 times a period, and the computed loop closes to 1.8×10⁻³⁰.

Measured over one period

Period: 9.593324634
Masses: 1 : 1 : 1
Energy: -1.00402
Angular momentum: 0.93958
Closest approach: 1.012
Top speed: 1.158
Path length: 22.491
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: 1.8×10⁻³⁰

Neighbours on the map

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