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Free-fall F13

(1, 0.8, 0.2)

From Li & Liao (2019)

Free-fall F13 (1, 0.8, 0.2) is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 0.8 : 0.2 that return to their starting positions and velocities every 3.0179 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 224.8), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00019 of each other at a top speed of 81.9, line up 20 times a period, and the computed loop closes to 4.5×10⁻²⁵.

Measured over one period

Period: 3.017887689
Masses: 1 : 0.8 : 0.2
Energy: -1.53584
Angular momentum: 0
Closest approach: 1.9×10⁻⁴
Top speed: 81.94
Path length: 9.5554
Alignments per period: 20
Stability: unstable (|λ|max 224.8)
Loop closure: 4.5×10⁻²⁵

Neighbours on the map

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