Atlas1,798 of 3,942

II.C.21

m₃ = 0.75

From Li & Liao (2017)

II.C.21 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 21.442 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 111.2), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00125 of each other at a top speed of 30.1, line up 52 times a period, and the computed loop closes to 1.2×10⁻²⁵.

Measured over one period

Period: 21.44167614
Masses: 1 : 1 : 0.75
Energy: -1.92743
Angular momentum: 0
Closest approach: 0.001253
Top speed: 30.11
Path length: 60.463
Alignments per period: 52
Topology: ababAbabaBababABAbaBABabABAbaBAB (free-group class)
Stability: unstable (|λ|max 111.2)
Loop closure: 1.2×10⁻²⁵

Neighbours on the map

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