Atlas227 of 3,942

Broucke R2

From Broucke (1975)

Broucke R2 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 5.7042 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 weakly unstable (largest Floquet multiplier 8.337), so a small nudge makes it unravel over a few periods. The bodies pass within 0.476 of each other at a top speed of 1.62, line up 4 times a period, and the computed loop closes to 9.1×10⁻²⁵.

Measured over one period

Period: 5.704216286
Masses: 1 : 1 : 1
Energy: -1.62175
Angular momentum: 1.8549
Closest approach: 0.4758
Top speed: 1.622
Path length: 17.158
Alignments per period: 4
Topology: a (free-group class, read from the drawing, shape period T/2)
Stability: weakly unstable (|λ|max 8.337)
Loop closure: 9.1×10⁻²⁵

Neighbours on the map

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