Atlas222 of 3,942

Broucke R7

From Broucke (1975)

Broucke R7 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 5.0886 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 0.271 of each other at a top speed of 1.88, line up 14 times a period, and the computed loop closes to 1.4×10⁻²⁹.

Measured over one period

Period: 5.088609448
Masses: 1 : 1 : 1
Energy: -2.62657
Angular momentum: 1.6691
Closest approach: 0.2712
Top speed: 1.884
Path length: 19.518
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: 1.4×10⁻²⁹

Neighbours on the map

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