Atlas208 of 3,942

Broucke A7

From Broucke (1975)

Broucke A7 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 12.056 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 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 0.991, line up 4 times a period, and the computed loop closes to 1.2×10⁻²⁵.

Measured over one period

Period: 12.05586586
Masses: 1 : 1 : 1
Energy: -0.717522
Angular momentum: 0.92529
Closest approach: 1.442
Top speed: 0.9913
Path length: 23.351
Alignments per period: 4
Topology: a (free-group class, read from the drawing, shape period T/2)
Stability: stable (|λ|max 1.000)
Loop closure: 1.2×10⁻²⁵

Neighbours on the map

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