Atlas221 of 3,942

Broucke R5

From Broucke (1975)

Broucke R5 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 5.2669 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 0.333 of each other at a top speed of 1.75, line up 10 times a period, and the computed loop closes to 1.9×10⁻²⁶.

Measured over one period

Period: 5.266917857
Masses: 1 : 1 : 1
Energy: -2.25597
Angular momentum: 1.7280
Closest approach: 0.3330
Top speed: 1.754
Path length: 18.741
Alignments per period: 10
Topology: a (free-group class, read from the drawing, shape period T/5)
Stability: stable (|λ|max 1.000)
Loop closure: 1.9×10⁻²⁶

Neighbours on the map

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