Atlas1,657 of 3,942

II.C.21

m₃ = 0.5

From Li & Liao (2017)

II.C.21 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 21.079 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 9.983), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000379 of each other at a top speed of 59.3, line up 44 times a period, and the computed loop closes to 4.8×10⁻²⁵.

Measured over one period

Period: 21.07860487
Masses: 1 : 1 : 0.5
Energy: -1.37482
Angular momentum: 0
Closest approach: 3.8×10⁻⁴
Top speed: 59.30
Path length: 57.070
Alignments per period: 44
Topology: aabAbbAABabAbabABabABabAAbbAB (free-group class)
Stability: weakly unstable (|λ|max 9.983)
Loop closure: 4.8×10⁻²⁵

Neighbours on the map

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