Atlas2,170 of 3,942

II.C.107

m₃ = 0.75

From Li & Liao (2017)

II.C.107 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 116.68 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is linearly stable (largest Floquet multiplier 1.022), so a small nudge only makes it wobble. The bodies pass within 0.000319 of each other at a top speed of 59.9, line up 162 times a period, and the computed loop closes to 1.8×10⁻²⁴.

Measured over one period

Period: 116.6820174
Masses: 1 : 1 : 0.75
Energy: -1.31503
Angular momentum: 0
Closest approach: 3.2×10⁻⁴
Top speed: 59.87
Path length: 270.09
Alignments per period: 162
Topology: ababABabaBABabaBABabaBAbabaBAbabABAbabABAbabABababABabaBABabaBABabaBABabaBAbabABAbabABAbabABAbabAB (free-group class)
Stability: stable (|λ|max 1.022)
Loop closure: 1.8×10⁻²⁴

Neighbours on the map

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