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Free-fall F3

(1, 0.8, 0.8)

From Li & Liao (2019)

Free-fall F3 (1, 0.8, 0.8) is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 0.8 : 0.8 that return to their starting positions and velocities every 2.5505 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 11419), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000129 of each other at a top speed of 79.1, line up 18 times a period, and the computed loop closes to 1.3×10⁻²².

Measured over one period

Period: 2.550461135
Masses: 1 : 0.8 : 0.8
Energy: -3.45768
Angular momentum: 0
Closest approach: 1.3×10⁻⁴
Top speed: 79.06
Path length: 8.9154
Alignments per period: 18
Stability: unstable (|λ|max 11419)
Loop closure: 1.3×10⁻²²

Neighbours on the map

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