Atlas2,050 of 3,915

II.C.42

m₃ = 0.75

From Li & Liao (2017)

II.C.42 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 41.205 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 50.08), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000203 of each other at a top speed of 75.1, line up 78 times a period, and the computed loop closes to 2.3×10⁻²⁴.

Measured over one period

Period: 41.20479954
Masses: 1 : 1 : 0.75
Energy: -1.63327
Angular momentum: 0
Closest approach: 2.0×10⁻⁴
Top speed: 75.13
Path length: 107.03
Alignments per period: 78
Stability: unstable (|λ|max 50.08)
Loop closure: 2.3×10⁻²⁴

Neighbours on the map

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