Atlas1,796 of 3,942

II.C.60

m₃ = 0.75

From Li & Liao (2017)

II.C.60 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 40.388 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 267.7), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000579 of each other at a top speed of 44.4, line up 98 times a period, and the computed loop closes to 4.5×10⁻²⁵.

Measured over one period

Period: 40.38823831
Masses: 1 : 1 : 0.75
Energy: -1.92197
Angular momentum: 0
Closest approach: 5.8×10⁻⁴
Top speed: 44.35
Path length: 113.97
Alignments per period: 98
Topology: ababAbabaBababABAbaBABabABABabABAbabABabaBABabABABabABAbaBAB (free-group class)
Stability: unstable (|λ|max 267.7)
Loop closure: 4.5×10⁻²⁵

Neighbours on the map

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