Atlas1,694 of 3,915

II.C.12

m₃ = 0.5

From Li & Liao (2017)

II.C.12 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 40.602 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 444.3), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0373 of each other at a top speed of 5.16, line up 28 times a period, and the computed loop closes to 1.5×10⁻²⁷.

Measured over one period

Period: 40.60152433
Masses: 1 : 1 : 0.5
Energy: -0.751890
Angular momentum: 0
Closest approach: 0.03732
Top speed: 5.164
Path length: 79.094
Alignments per period: 28
Stability: unstable (|λ|max 444.3)
Loop closure: 1.5×10⁻²⁷

Neighbours on the map

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