Atlas1,894 of 3,942

II.C.94

m₃ = 0.5

From Li & Liao (2017)

II.C.94 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 105.61 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 3.930), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000524 of each other at a top speed of 16, line up 128 times a period, and the computed loop closes to 1.6×10⁻²³.

Measured over one period

Period: 105.6095850
Masses: 1 : 1 : 0.5
Energy: -0.973354
Angular momentum: 0
Closest approach: 5.2×10⁻⁵
Top speed: 159.5
Path length: 251.26
Alignments per period: 128
Topology: aaBAbabABabAAbaBAbabABabAAbaBABabABaaBAbabABabAAbaBAbabABabAAbaBABabABaaBAbaBABabAB (free-group class)
Stability: weakly unstable (|λ|max 3.930)
Loop closure: 1.6×10⁻²³

Neighbours on the map

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