Atlas228 of 3,942

Broucke R8

From Broucke (1975)

Broucke R8 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 11.225 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 unstable (largest Floquet multiplier 35711), so a small nudge makes it unravel over a few periods. The bodies pass within 0.419 of each other at a top speed of 1.79, line up 6 times a period, and the computed loop closes to 2.5×10⁻²⁷.

Measured over one period

Period: 11.22484551
Masses: 1 : 1 : 1
Energy: -1.53187
Angular momentum: 1.7997
Closest approach: 0.4190
Top speed: 1.787
Path length: 32.658
Alignments per period: 6
Topology: a (free-group class, read from the drawing, shape period T/3)
Stability: unstable (|λ|max 35711)
Loop closure: 2.5×10⁻²⁷

Neighbours on the map

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