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Free-fall F33

(1, 0.8, 0.4)

From Li & Liao (2019)

Free-fall F33 (1, 0.8, 0.4) is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 0.8 : 0.4 that return to their starting positions and velocities every 2.7778 time units, published by Li & Liao (2019). Three bodies released from rest fall together, swing past each other and return to rest exactly where they started. It is unstable (largest Floquet multiplier 7951), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00000276 of each other at a top speed of 622, line up 32 times a period, and the computed loop closes to 1.9×10⁻¹⁹.

Measured over one period

Period: 2.777799978
Masses: 1 : 0.8 : 0.4
Energy: -2.80465
Angular momentum: 0
Closest approach: 2.8×10⁻⁶
Top speed: 621.5
Path length: 10.143
Alignments per period: 32
Stability: unstable (|λ|max 7951)
Loop closure: 1.9×10⁻¹⁹

Neighbours on the map

All Free-fall orbits, the families of periodic three-body orbits, or the atlas map.