Atlas223 of 3,942

Broucke R13

From Broucke (1975)

Broucke R13 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 22.764 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 10931), so a small nudge makes it unravel over a few periods. The bodies pass within 0.463 of each other at a top speed of 1.67, line up 14 times a period, and the computed loop closes to 1.3×10⁻²⁷.

Measured over one period

Period: 22.76441772
Masses: 1 : 1 : 1
Energy: -1.57283
Angular momentum: 1.8421
Closest approach: 0.4629
Top speed: 1.672
Path length: 67.338
Alignments per period: 14
Topology: a (free-group class, read from the drawing, shape period T/7)
Stability: unstable (|λ|max 1.1×10⁵)
Loop closure: 1.3×10⁻²⁷

Neighbours on the map

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