Atlas209 of 3,942

Broucke A4

From Broucke (1975)

Broucke A4 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 8.2116 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 0.589 of each other at a top speed of 1.38, line up 10 times a period, and the computed loop closes to 6.7×10⁻³⁰.

Measured over one period

Period: 8.211605747
Masses: 1 : 1 : 1
Energy: -1.41941
Angular momentum: 0.99435
Closest approach: 0.5893
Top speed: 1.377
Path length: 23.140
Alignments per period: 10
Topology: a (free-group class, read from the drawing, shape period T/5)
Stability: stable (|λ|max 1.000)
Loop closure: 6.7×10⁻³⁰

Neighbours on the map

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