Atlas204 of 3,942

Broucke A13

From Broucke (1975)

Broucke A13 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 59.716 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 unstable (largest Floquet multiplier 1002), so a small nudge makes it unravel over a few periods. The bodies pass within 1.44 of each other at a top speed of 0.829, line up 8 times a period, and the computed loop closes to 1.8×10⁻²⁸.

Measured over one period

Period: 59.71607300
Masses: 1 : 1 : 1
Energy: -0.432930
Angular momentum: 1.1635
Closest approach: 1.442
Top speed: 0.8285
Path length: 85.018
Alignments per period: 8
Topology: a (free-group class, read from the drawing, shape period T/4)
Stability: unstable (|λ|max 1002)
Loop closure: 1.8×10⁻²⁸

Neighbours on the map

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