Atlas212 of 3,942

Broucke A12

From Broucke (1975)

Broucke A12 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 42.823 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 1.44 of each other at a top speed of 0.917, line up 10 times a period, and the computed loop closes to 2.1×10⁻²⁹.

Measured over one period

Period: 42.82322171
Masses: 1 : 1 : 1
Energy: -0.592114
Angular momentum: 0.96370
Closest approach: 1.442
Top speed: 0.9174
Path length: 73.914
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: 2.1×10⁻²⁹

Neighbours on the map

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