Atlas2,216 of 3,942

II.C.107

m₃ = 0.5

From Li & Liao (2017)

II.C.107 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 122.66 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 123.2), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00111 of each other at a top speed of 34.6, line up 146 times a period, and the computed loop closes to 4.8×10⁻²⁵.

Measured over one period

Period: 122.6577743
Masses: 1 : 1 : 0.5
Energy: -0.936569
Angular momentum: 0
Closest approach: 0.001109
Top speed: 34.63
Path length: 269.07
Alignments per period: 146
Topology: aabAbaBABaBAbaBAbaBAbaBABaBAbabABaBABabABabABabABabABabABaaBBabAAbaBBaaBAbaBAbaBAbaBBaaBAbbAABaBB (free-group class)
Stability: unstable (|λ|max 123.2)
Loop closure: 4.8×10⁻²⁵

Neighbours on the map

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