Atlas1,569 of 3,915

II.C.4

m₃ = 0.5

From Li & Liao (2017)

II.C.4 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 8.8878 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 546.6), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0057 of each other at a top speed of 15.5, line up 18 times a period, and the computed loop closes to 1.1×10⁻²⁶.

Measured over one period

Period: 8.887818364
Masses: 1 : 1 : 0.5
Energy: -1.47027
Angular momentum: 0
Closest approach: 0.005700
Top speed: 15.49
Path length: 25.060
Alignments per period: 18
Stability: unstable (|λ|max 546.6)
Loop closure: 1.1×10⁻²⁶

Neighbours on the map

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