Atlas225 of 3,942

Broucke R4

From Broucke (1975)

Broucke R4 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 5.3958 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 0.378 of each other at a top speed of 1.68, line up 8 times a period, and the computed loop closes to 3.7×10⁻³⁰.

Measured over one period

Period: 5.395834177
Masses: 1 : 1 : 1
Energy: -2.05434
Angular momentum: 1.7687
Closest approach: 0.3775
Top speed: 1.683
Path length: 18.320
Alignments per period: 8
Topology: a (free-group class, read from the drawing, shape period T/4)
Stability: stable (|λ|max 1.000)
Loop closure: 3.7×10⁻³⁰

Neighbours on the map

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