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Free-fall F3

From Li & Liao (2019)

Free-fall F3 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 4.5419 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 82023), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000146 of each other at a top speed of 83.5, line up 24 times a period, and the computed loop closes to 1.4×10⁻²³.

Measured over one period

Period: 4.541912559
Masses: 1 : 1 : 1
Energy: -3.92278
Angular momentum: 0
Closest approach: 1.5×10⁻⁴
Top speed: 83.55
Path length: 16.250
Alignments per period: 24
Topology: 0 (free-group class)
Stability: unstable (|λ|max 82023)
Loop closure: 1.4×10⁻²³

Neighbours on the map

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