Atlas1,769 of 3,942

II.C.252

m₃ = 0.5

From Li & Liao (2017)

II.C.252 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 164.23 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 21.21), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000248 of each other at a top speed of 73.3, line up 344 times a period, and the computed loop closes to 2.9×10⁻²⁴.

Measured over one period

Period: 164.2313983
Masses: 1 : 1 : 0.5
Energy: -1.36907
Angular momentum: 0
Closest approach: 2.5×10⁻⁴
Top speed: 73.35
Path length: 438.33
Alignments per period: 344
Topology: aabAbaBABaBAbabAbabABaBAAbbAbaaBBabAAbbAAbaBBaaBAbbAABaBAbabAbaBABaBABabAbabABaBAAbbAbaaBBabAAbbAAbaBBaaBAbbAABaBAbabAbaBABaBABabAbabABaBAAbbAbaaBBabAAbbABaaBBaaBAbbAAbaBBaabAbaBABaBAbabAbabABaBAAbbAbaaBBabAAbbABaaBBaaBAbbAAbaBB (free-group class)
Stability: unstable (|λ|max 21.21)
Loop closure: 2.9×10⁻²⁴

Neighbours on the map

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