Atlas1,358 of 3,942

II.B.4

m₃ = 0.5

From Li, Jing & Liao (2018)

II.B.4 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 191.89 time units, published by Li, Jing & Liao (2018). Class II.B orbits, mostly long-period. It is linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.0000196 of each other at a top speed of 261, line up 240 times a period, and the computed loop closes to 5.1×10⁻²³.

Measured over one period

Period: 191.8933812
Masses: 1 : 1 : 0.5
Energy: -0.984827
Angular momentum: 0
Closest approach: 2.0×10⁻⁵
Top speed: 260.8
Path length: 454.22
Alignments per period: 240
Topology: aaBAbaBAbabABabABaaBAbaBAbabABabABaaBAbaBAbabABabABaaBAbaBAbabABabABaaBAbaBAbaBABabABabAAbaBAbaBABabABabAAbaBAbaBABabABabAAbaBAbaBABabABabAAbaBAbaBABabABabAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 5.1×10⁻²³

Neighbours on the map

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