Atlas1,958 of 3,942

II.C.155

m₃ = 0.75

From Li & Liao (2017)

II.C.155 m₃ = 0.75 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 0.75 that return to their starting positions and velocities every 198.55 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is weakly unstable (largest Floquet multiplier 9.872), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000963 of each other at a top speed of 109, line up 280 times a period, and the computed loop closes to 2.1×10⁻¹⁸.

Measured over one period

Period: 198.5463548
Masses: 1 : 1 : 0.75
Energy: -1.34890
Angular momentum: 0
Closest approach: 9.6×10⁻⁵
Top speed: 108.9
Path length: 488.93
Alignments per period: 280
Topology: abaBAbabABabaBAbabABabaBAbabABabaBAbabABabaBAbabABAbaBABabaBAbabABabaBAbabABAbaBABabABAbaBABabABAbaBABabABAbabABabaBABabABAbaBABabABAbaBABabABAbaBABabaBAbabABabaBAbabABAbaBAB (free-group class)
Stability: weakly unstable (|λ|max 9.872)
Loop closure: 2.1×10⁻¹⁸

Neighbours on the map

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