Atlas219 of 3,942

Broucke R1

From Broucke (1975)

Broucke R1 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 5.2266 time units, published by Broucke (1975). The prograde counterpart of the A family: the binary and the third body’s orbit turn the same way. It is unstable (largest Floquet multiplier 72.52), so a small nudge makes it unravel over a few periods. The bodies pass within 0.182 of each other at a top speed of 2.72, line up 2 times a period, and the computed loop closes to 1.5×10⁻²⁸.

Measured over one period

Period: 5.226591279
Masses: 1 : 1 : 1
Energy: -1.46495
Angular momentum: 1.6061
Closest approach: 0.1825
Top speed: 2.717
Path length: 14.468
Alignments per period: 2
Topology: a (free-group class, read from the drawing)
Stability: unstable (|λ|max 72.52)
Loop closure: 1.5×10⁻²⁸

Neighbours on the map

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