Atlas205 of 3,942

Broucke A15

From Broucke (1975)

Broucke A15 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 92.056 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 17793), 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 0.826, line up 10 times a period, and the computed loop closes to 2.2×10⁻²⁷.

Measured over one period

Period: 92.05611951
Masses: 1 : 1 : 1
Energy: -0.383683
Angular momentum: 1.2972
Closest approach: 1.442
Top speed: 0.8255
Path length: 122.24
Alignments per period: 10
Topology: a (free-group class, read from the drawing, shape period T/5)
Stability: unstable (|λ|max 17793)
Loop closure: 2.2×10⁻²⁷

Neighbours on the map

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