Atlas1,828 of 3,942

II.C.77

m₃ = 0.75

From Li & Liao (2017)

II.C.77 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 75.153 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 22.62), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000924 of each other at a top speed of 35.1, line up 112 times a period, and the computed loop closes to 8.2×10⁻²⁵.

Measured over one period

Period: 75.15301706
Masses: 1 : 1 : 0.75
Energy: -1.42250
Angular momentum: 0
Closest approach: 9.2×10⁻⁴
Top speed: 35.08
Path length: 199.01
Alignments per period: 112
Topology: ababAbabABabaBabaBAbabAbabABabABabaBAbaBAbabABabABabaBabaBAbabAbabABabaB (free-group class)
Stability: unstable (|λ|max 22.62)
Loop closure: 8.2×10⁻²⁵

Neighbours on the map

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