Atlas831 of 3,942

I.B.68

m₃ = 0.75

From Li & Liao (2017)

I.B.68 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 86.677 time units, published by Li & Liao (2017). Class I.B orbits, for equal and unequal masses. It is linearly stable (largest Floquet multiplier 1.007), so a small nudge only makes it wobble. The bodies pass within 0.0000503 of each other at a top speed of 151, line up 184 times a period, and the computed loop closes to 8.9×10⁻¹⁷.

Measured over one period

Period: 86.67657321
Masses: 1 : 1 : 0.75
Energy: -1.73276
Angular momentum: 0
Closest approach: 5.0×10⁻⁵
Top speed: 150.7
Path length: 220.49
Alignments per period: 184
Topology: ababABabaBABAbabABAbabABAbabABABabaBAbabaBABabABABabABAbabaBAbabABABabaBABabaBABabaBABAbabABababABAbaBABAbaBAB (free-group class)
Stability: stable (|λ|max 1.007)
Loop closure: 8.9×10⁻¹⁷

Neighbours on the map

All I.B orbits, the families of periodic three-body orbits, or the atlas map.