Atlas3,707 of 3,942

Split figure-8 SE.87

m₃ = 0.87

From Titov (2012)

Split figure-8 SE.87 m₃ = 0.87 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 0.87 that return to their starting positions and velocities every 6.2832 time units, published by Titov (2012). Titov’s continuations of the figure-eight to a lighter third body, where the curve splits into two lobes. It is weakly unstable (largest Floquet multiplier 5.183), so a small nudge makes it unravel over a few periods. The bodies pass within 0.355 of each other at a top speed of 1.68, line up 6 times a period, and the computed loop closes to 8.4×10⁻²⁵.

Measured over one period

Period: 6.283185307
Masses: 1 : 1 : 0.87
Energy: -1.18586
Angular momentum: 0
Closest approach: 0.3551
Top speed: 1.677
Path length: 15.560
Alignments per period: 6
Topology: abAB (free-group class)
Stability: weakly unstable (|λ|max 5.183)
Loop closure: 8.4×10⁻²⁵

Neighbours on the map

All Split figure-eights, the families of periodic three-body orbits, or the atlas map.