Atlas2,098 of 3,942

II.C.237

m₃ = 0.5

From Li & Liao (2017)

II.C.237 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 191.09 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 1.032), so a small nudge only makes it wobble. The bodies pass within 0.000138 of each other at a top speed of 98.2, line up 270 times a period, and the computed loop closes to 2.5×10⁻²⁴.

Measured over one period

Period: 191.0899162
Masses: 1 : 1 : 0.5
Energy: -1.05231
Angular momentum: 0
Closest approach: 1.4×10⁻⁴
Top speed: 98.18
Path length: 457.36
Alignments per period: 270
Topology: aaBAbaBAbaBAbaBAbaBAbaBAbaBAbabABabABabABabABabABabABabABabAAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbabABabABabABabABabABabABabABabAAbaBAbaBAbaBAbaBAbaBAbaBAbaBABabABabABabABabABabABabABabAB (free-group class)
Stability: stable (|λ|max 1.032)
Loop closure: 2.5×10⁻²⁴

Neighbours on the map

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