Atlas1,580 of 3,915

II.C.15

m₃ = 5

From Li & Liao (2017)

II.C.15 m₃ = 5 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 5 that return to their starting positions and velocities every 198.57 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 1.000), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000188 of each other at a top speed of 666, line up 650 times a period, and the computed loop closes to 9.4×10⁻²².

Measured over one period

Period: 198.5700199
Masses: 1 : 1 : 5
Energy: -8.49752
Angular momentum: 0
Closest approach: 1.9×10⁻⁵
Top speed: 665.8
Path length: 873.12
Alignments per period: 650
Stability: weakly unstable (|λ|max 1.000)
Loop closure: 9.4×10⁻²²

Neighbours on the map

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