Atlas1,935 of 3,942

II.C.182

m₃ = 0.5

From Li & Liao (2017)

II.C.182 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 104.04 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is linearly stable (largest Floquet multiplier 1.023), so a small nudge only makes it wobble. The bodies pass within 0.00000277 of each other at a top speed of 694, line up 224 times a period, and the computed loop closes to 8.8×10⁻²⁰.

Measured over one period

Period: 104.0378908
Masses: 1 : 1 : 0.5
Energy: -1.36520
Angular momentum: 0
Closest approach: 2.8×10⁻⁶
Top speed: 693.8
Path length: 260.61
Alignments per period: 224
Topology: ababAbabABaBABabABAbaBAbaBAbabAbabABabABAbABabaBabaBAbABAbaBABabAbabABabaBabABAbaBABaBAbabAbabABaBABabABabaBabaBAbaBAbaBABabABAbABabaBababAbABABaB (free-group class)
Stability: stable (|λ|max 1.023)
Loop closure: 8.8×10⁻²⁰

Neighbours on the map

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