Atlas1,503 of 3,942

II.C.48

m₃ = 0.75

From Li & Liao (2017)

II.C.48 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 101.29 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 9412), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0112 of each other at a top speed of 10.1, line up 74 times a period, and the computed loop closes to 1.1×10⁻²⁵.

Measured over one period

Period: 101.2913662
Masses: 1 : 1 : 0.75
Energy: -0.919202
Angular momentum: 0
Closest approach: 0.01121
Top speed: 10.10
Path length: 227.20
Alignments per period: 74
Topology: aaBAbabAAbabABaaBABabAAbabAAbaBABaaBAbabAAbaBAB (free-group class)
Stability: unstable (|λ|max 9412)
Loop closure: 1.1×10⁻²⁵

Neighbours on the map

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