Atlas2,176 of 3,915

II.C.80

m₃ = 0.5

From Li & Liao (2017)

II.C.80 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 75.786 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 8.356), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00012 of each other at a top speed of 105, line up 116 times a period, and the computed loop closes to 2.1×10⁻¹⁷.

Measured over one period

Period: 75.78557825
Masses: 1 : 1 : 0.5
Energy: -1.10831
Angular momentum: 0
Closest approach: 1.2×10⁻⁴
Top speed: 105.3
Path length: 185.57
Alignments per period: 116
Stability: weakly unstable (|λ|max 8.356)
Loop closure: 2.1×10⁻¹⁷

Neighbours on the map

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