Atlas1,959 of 3,942

II.C.137

m₃ = 0.75

From Li & Liao (2017)

II.C.137 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 162.74 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 69.99), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000708 of each other at a top speed of 40.1, line up 222 times a period, and the computed loop closes to 3.5×10⁻²⁵.

Measured over one period

Period: 162.7392471
Masses: 1 : 1 : 0.75
Energy: -1.31956
Angular momentum: 0
Closest approach: 7.1×10⁻⁴
Top speed: 40.15
Path length: 396.72
Alignments per period: 222
Topology: abaBAbabABabaBAbabABabaBAbabABabaBAbabABabaBAbabABabaBAbabABAbaBABabaBAbabABabaBABabABAbaBABabABAbaBABabABAbaBABabABAbabABabaBAbabABAbaBAB (free-group class)
Stability: unstable (|λ|max 69.99)
Loop closure: 3.5×10⁻²⁵

Neighbours on the map

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