Atlas2,197 of 3,942

II.C.110

m₃ = 0.5

From Li & Liao (2017)

II.C.110 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 111.48 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 69.57), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000686 of each other at a top speed of 139, line up 150 times a period, and the computed loop closes to 2.4×10⁻²⁴.

Measured over one period

Period: 111.4832388
Masses: 1 : 1 : 0.5
Energy: -1.01183
Angular momentum: 0
Closest approach: 6.9×10⁻⁵
Top speed: 139.4
Path length: 256.60
Alignments per period: 150
Topology: aabAbaBABaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBBaaBAbbAABaBB (free-group class)
Stability: unstable (|λ|max 69.57)
Loop closure: 2.4×10⁻²⁴

Neighbours on the map

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