Atlas1,735 of 3,915

II.C.47

m₃ = 0.75

From Li & Liao (2017)

II.C.47 m₃ = 0.75 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 0.75 that return to their starting positions and velocities every 49.744 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 25.8), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00224 of each other at a top speed of 22.7, line up 84 times a period, and the computed loop closes to 1.1×10⁻²⁵.

Measured over one period

Period: 49.74394318
Masses: 1 : 1 : 0.75
Energy: -1.54611
Angular momentum: 0
Closest approach: 0.002237
Top speed: 22.69
Path length: 136.81
Alignments per period: 84
Stability: unstable (|λ|max 25.80)
Loop closure: 1.1×10⁻²⁵

Neighbours on the map

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