Atlas2,219 of 3,915

II.C.20

m₃ = 0.5

From Li & Liao (2017)

II.C.20 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 35.775 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is weakly unstable (largest Floquet multiplier 2.454), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00188 of each other at a top speed of 26.6, line up 42 times a period, and the computed loop closes to 1.8×10⁻²⁵.

Measured over one period

Period: 35.77536770
Masses: 1 : 1 : 0.5
Energy: -0.924249
Angular momentum: 0
Closest approach: 0.001876
Top speed: 26.61
Path length: 77.058
Alignments per period: 42
Stability: weakly unstable (|λ|max 2.454)
Loop closure: 1.8×10⁻²⁵

Neighbours on the map

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