Atlas230 of 3,942

Broucke R12

From Broucke (1975)

Broucke R12 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 17.021 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 0.47 of each other at a top speed of 1.6, line up 14 times a period, and the computed loop closes to 6.5×10⁻³⁰.

Measured over one period

Period: 17.02060228
Masses: 1 : 1 : 1
Energy: -1.69277
Angular momentum: 1.8502
Closest approach: 0.4699
Top speed: 1.602
Path length: 52.354
Alignments per period: 14
Topology: a (free-group class, read from the drawing, shape period T/7)
Stability: stable (|λ|max 1.000)
Loop closure: 6.5×10⁻³⁰

Neighbours on the map

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