Atlas1,671 of 3,942

II.C.15

m₃ = 0.75

From Li & Liao (2017)

II.C.15 m₃ = 0.75 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 0.75 that return to their starting positions and velocities every 41.246 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 2418), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0234 of each other at a top speed of 7.07, line up 42 times a period, and the computed loop closes to 2.8×10⁻²⁵.

Measured over one period

Period: 41.24625738
Masses: 1 : 1 : 0.75
Energy: -1.11980
Angular momentum: 0
Closest approach: 0.02345
Top speed: 7.065
Path length: 98.427
Alignments per period: 42
Topology: aaBAbaBAbaBAbaBabaBAbaBAbaBB (free-group class)
Stability: unstable (|λ|max 2418)
Loop closure: 2.8×10⁻²⁵

Neighbours on the map

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