Atlas217 of 3,942

Broucke A10

From Broucke (1975)

Broucke A10 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 32.611 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 11.89), 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 0.875, line up 6 times a period, and the computed loop closes to 8.1×10⁻²⁵.

Measured over one period

Period: 32.61094691
Masses: 1 : 1 : 1
Energy: -0.518353
Angular momentum: 1.0242
Closest approach: 1.442
Top speed: 0.8750
Path length: 51.862
Alignments per period: 6
Topology: a (free-group class, read from the drawing, shape period T/3)
Stability: unstable (|λ|max 11.89)
Loop closure: 8.1×10⁻²⁵

Neighbours on the map

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