Atlas226 of 3,942

Broucke R3

From Broucke (1975)

Broucke R3 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 5.5608 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 linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.434 of each other at a top speed of 1.62, line up 6 times a period, and the computed loop closes to 5.6×10⁻²⁵.

Measured over one period

Period: 5.560806790
Masses: 1 : 1 : 1
Energy: -1.83994
Angular momentum: 1.8187
Closest approach: 0.4337
Top speed: 1.619
Path length: 17.853
Alignments per period: 6
Topology: a (free-group class, read from the drawing, shape period T/3)
Stability: stable (|λ|max 1.000)
Loop closure: 5.6×10⁻²⁵

Neighbours on the map

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