Atlas1,770 of 3,942

II.C.207

m₃ = 0.5

From Li & Liao (2017)

II.C.207 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 134.04 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 75.3), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000152 of each other at a top speed of 93.6, line up 240 times a period, and the computed loop closes to 7.7×10⁻²⁴.

Measured over one period

Period: 134.0444643
Masses: 1 : 1 : 0.5
Energy: -1.23350
Angular momentum: 0
Closest approach: 1.5×10⁻⁴
Top speed: 93.61
Path length: 338.54
Alignments per period: 240
Topology: aabAbaBABabAbabABaBABabAbaaBBabAAbaBBaaBAbbAAbaBAbabAbaBABaBAbabABaBABabAbabABabAAbbABaaBBabAAbaBBaaBAbbAAbaBAbabAbaBABaBAbabABaBAAbbABaaBBabAAbbABaaBAbbAABaBB (free-group class)
Stability: unstable (|λ|max 75.30)
Loop closure: 7.7×10⁻²⁴

Neighbours on the map

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