Atlas1,699 of 3,915

II.C.67

m₃ = 0.5

From Li & Liao (2017)

II.C.67 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 48.484 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 28.12), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000697 of each other at a top speed of 43.7, line up 100 times a period, and the computed loop closes to 4.4×10⁻²⁵.

Measured over one period

Period: 48.48397173
Masses: 1 : 1 : 0.5
Energy: -1.36135
Angular momentum: 0
Closest approach: 7.0×10⁻⁴
Top speed: 43.72
Path length: 131.69
Alignments per period: 100
Stability: unstable (|λ|max 28.12)
Loop closure: 4.4×10⁻²⁵

Neighbours on the map

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