Atlas1,595 of 3,942

II.C.8

m₃ = 0.5

From Li & Liao (2017)

II.C.8 m₃ = 0.5 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 0.5 that return to their starting positions and velocities every 25.721 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is unstable (largest Floquet multiplier 4759), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000887 of each other at a top speed of 33.6, line up 26 times a period, and the computed loop closes to 2.4×10⁻²⁶.

Measured over one period

Period: 25.72122038
Masses: 1 : 1 : 0.5
Energy: -0.989900
Angular momentum: 0
Closest approach: 8.9×10⁻⁴
Top speed: 33.59
Path length: 57.106
Alignments per period: 26
Topology: aaBAbaBAbaBABabAB (free-group class)
Stability: unstable (|λ|max 4759)
Loop closure: 2.4×10⁻²⁶

Neighbours on the map

All II.C orbits, the families of periodic three-body orbits, or the atlas map.