Atlas224 of 3,942

Broucke R10

From Broucke (1975)

Broucke R10 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 10.948 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 0.404 of each other at a top speed of 1.65, line up 14 times a period, and the computed loop closes to 5.8×10⁻³⁰.

Measured over one period

Period: 10.94827766
Masses: 1 : 1 : 1
Energy: -1.94866
Angular momentum: 1.7927
Closest approach: 0.4043
Top speed: 1.649
Path length: 36.192
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: 5.8×10⁻³⁰

Neighbours on the map

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