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Free-fall F45

(1, 0.8, 0.6)

From Li & Liao (2019)

Free-fall F45 (1, 0.8, 0.6) is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 0.8 : 0.6 that return to their starting positions and velocities every 5.746 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 1871), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00455 of each other at a top speed of 13.7, line up 30 times a period, and the computed loop closes to 4.3×10⁻²⁷.

Measured over one period

Period: 5.746014092
Masses: 1 : 0.8 : 0.6
Energy: -2.54142
Angular momentum: 0
Closest approach: 0.004549
Top speed: 13.66
Path length: 20.739
Alignments per period: 30
Topology: 0 (free-group class)
Stability: unstable (|λ|max 1871)
Loop closure: 4.3×10⁻²⁷

Neighbours on the map

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