Atlas1,896 of 3,942

II.C.216

m₃ = 0.5

From Li & Liao (2017)

II.C.216 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 183.58 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 1.036), so a small nudge only makes it wobble. The bodies pass within 0.0000255 of each other at a top speed of 229, line up 236 times a period, and the computed loop closes to 2.0×10⁻²³.

Measured over one period

Period: 183.5801830
Masses: 1 : 1 : 0.5
Energy: -1.00571
Angular momentum: 0
Closest approach: 2.5×10⁻⁵
Top speed: 228.8
Path length: 440.60
Alignments per period: 236
Topology: aaBAbaBAbabABabAAbaBAbaBABabABaaBAbaBAbabABabAAbaBAbaBABabABabAAbaBAbabABabABaaBAbaBABabABabAAbaBAbaBABabABaaBAbaBAbabABabABaaBAbaBABabABabAAbaBAbabABabAB (free-group class)
Stability: stable (|λ|max 1.036)
Loop closure: 2.0×10⁻²³

Neighbours on the map

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