Atlas1,850 of 3,942

II.C.40

m₃ = 2

From Li & Liao (2017)

II.C.40 m₃ = 2 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 2 that return to their starting positions and velocities every 84.184 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 6.176), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00000211 of each other at a top speed of 1123, line up 234 times a period, and the computed loop closes to 1.1×10⁻²⁰.

Measured over one period

Period: 84.18419679
Masses: 1 : 1 : 2
Energy: -4.03973
Angular momentum: 0
Closest approach: 2.1×10⁻⁶
Top speed: 1123
Path length: 267.96
Alignments per period: 234
Topology: 0 (free-group class)
Stability: weakly unstable (|λ|max 6.176)
Loop closure: 1.1×10⁻²⁰

Neighbours on the map

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