Atlas1,791 of 3,942

II.C.251

m₃ = 0.5

From Li & Liao (2017)

II.C.251 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 154.57 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is unstable (largest Floquet multiplier 25.29), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000193 of each other at a top speed of 83.1, line up 336 times a period, and the computed loop closes to 2.7×10⁻²³.

Measured over one period

Period: 154.5748576
Masses: 1 : 1 : 0.5
Energy: -1.39417
Angular momentum: 0
Closest approach: 1.9×10⁻⁴
Top speed: 83.06
Path length: 402.55
Alignments per period: 336
Topology: aabAbaBAbaBAbaBBaabAbbAABaBAbaBAbaBAbbAABaBBaabAbaBAbaBAbaBBaabAbbAABaBAbaBAbaBAbbAABaBBaabAbaBAbbAABaBBaabAbaBAbaBAbaBBaabAbbAABaBAbaBAbaBAbbAABaBBaabAbaBAbbAABaBBaabAbaBAbaBAbaBBaabAbbAABaBAbaBAbaBAbbAABaBBaabAbaBAbbAABaBB (free-group class)
Stability: unstable (|λ|max 25.29)
Loop closure: 2.7×10⁻²³

Neighbours on the map

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