Atlas1,562 of 3,942

II.C.12

m₃ = 0.75

From Li & Liao (2017)

II.C.12 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 27.478 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 395.2), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000512 of each other at a top speed of 47.1, line up 30 times a period, and the computed loop closes to 6.0×10⁻²⁵.

Measured over one period

Period: 27.47772522
Masses: 1 : 1 : 0.75
Energy: -1.20039
Angular momentum: 0
Closest approach: 5.1×10⁻⁴
Top speed: 47.13
Path length: 69.458
Alignments per period: 30
Topology: aabABaaBABabAABabAB (free-group class)
Stability: unstable (|λ|max 395.2)
Loop closure: 6.0×10⁻²⁵

Neighbours on the map

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