Atlas1,824 of 3,942

II.C.99

m₃ = 0.75

From Li & Liao (2017)

II.C.99 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 165.8 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 36.02), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00411 of each other at a top speed of 16.7, line up 126 times a period, and the computed loop closes to 4.4×10⁻²⁶.

Measured over one period

Period: 165.7961205
Masses: 1 : 1 : 0.75
Energy: -0.948276
Angular momentum: 0
Closest approach: 0.004110
Top speed: 16.68
Path length: 362.68
Alignments per period: 126
Topology: aaBAbabAAbaBAbabABaaBABabAAbaBAbabAAbaBABabABaaBAbabAAbaBABabABaaBAbabAAbaBABabAB (free-group class)
Stability: unstable (|λ|max 36.02)
Loop closure: 4.4×10⁻²⁶

Neighbours on the map

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