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Free-fall F40

(1, 0.8, 0.4)

From Li & Liao (2019)

Free-fall F40 (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 3.3349 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 5824), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00000222 of each other at a top speed of 777, line up 40 times a period, and the computed loop closes to 4.1×10⁻¹⁹.

Measured over one period

Period: 3.334888105
Masses: 1 : 0.8 : 0.4
Energy: -2.78291
Angular momentum: 0
Closest approach: 2.2×10⁻⁶
Top speed: 777.3
Path length: 11.987
Alignments per period: 40
Stability: unstable (|λ|max 5824)
Loop closure: 4.1×10⁻¹⁹

Neighbours on the map

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