Atlas231 of 3,942

Broucke R9

From Broucke (1975)

Broucke R9 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 11.296 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 0.462 of each other at a top speed of 1.6, line up 10 times a period, and the computed loop closes to 4.5×10⁻³⁰.

Measured over one period

Period: 11.29559525
Masses: 1 : 1 : 1
Energy: -1.72950
Angular momentum: 1.8436
Closest approach: 0.4622
Top speed: 1.602
Path length: 35.132
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: 4.5×10⁻³⁰

Neighbours on the map

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