Atlas1,701 of 3,915

II.C.42

m₃ = 0.5

From Li & Liao (2017)

II.C.42 m₃ = 0.5 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 0.5 that return to their starting positions and velocities every 36.961 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is weakly unstable (largest Floquet multiplier 1.457), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000256 of each other at a top speed of 228, line up 72 times a period, and the computed loop closes to 1.2×10⁻¹⁶.

Measured over one period

Period: 36.96055083
Masses: 1 : 1 : 0.5
Energy: -1.29497
Angular momentum: 0
Closest approach: 2.6×10⁻⁵
Top speed: 228.3
Path length: 95.033
Alignments per period: 72
Stability: weakly unstable (|λ|max 1.457)
Loop closure: 1.2×10⁻¹⁶

Neighbours on the map

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