Atlas1,966 of 3,942

II.C.175

m₃ = 0.5

From Li & Liao (2017)

II.C.175 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 158.57 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 1.278), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000106 of each other at a top speed of 112, line up 202 times a period, and the computed loop closes to 3.4×10⁻²⁴.

Measured over one period

Period: 158.5701926
Masses: 1 : 1 : 0.5
Energy: -1.00608
Angular momentum: 0
Closest approach: 1.1×10⁻⁴
Top speed: 112.4
Path length: 383.50
Alignments per period: 202
Topology: aaBAbabABabAAbaBAbabABaaBAbaBABabABaaBAbaBABabAAbaBAbabABabAAbaBAbabABaaBAbaBABabABaaBAbaBABabAAbaBAbabABabAAbaBABabABaaBAbaBABabAB (free-group class)
Stability: weakly unstable (|λ|max 1.278)
Loop closure: 3.4×10⁻²⁴

Neighbours on the map

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