Atlas2,110 of 3,942

II.C.213

m₃ = 0.5

From Li & Liao (2017)

II.C.213 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 152.55 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 1172), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000365 of each other at a top speed of 60.4, line up 244 times a period, and the computed loop closes to 1.2×10⁻²³.

Measured over one period

Period: 152.5491452
Masses: 1 : 1 : 0.5
Energy: -1.14111
Angular momentum: 0
Closest approach: 3.6×10⁻⁴
Top speed: 60.44
Path length: 375.05
Alignments per period: 244
Topology: aabAbaBABabAbabABaBABabABabABabABabABabABabABabABabABabABabABaaBBabAAbbABaaBAbbAABaBAbabAbaBABaBAbabABabABabABabABabABabABabABabABabABabABabABabAAbaBBaaBAbbAAbaBB (free-group class)
Stability: unstable (|λ|max 1172)
Loop closure: 1.2×10⁻²³

Neighbours on the map

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