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Free-fall F53

(1, 0.8, 0.6)

From Li & Liao (2019)

Free-fall F53 (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 5.259 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 690), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00152 of each other at a top speed of 24.3, line up 34 times a period, and the computed loop closes to 5.7×10⁻²⁵.

Measured over one period

Period: 5.259018987
Masses: 1 : 0.8 : 0.6
Energy: -2.87107
Angular momentum: 0
Closest approach: 0.001517
Top speed: 24.25
Path length: 20.455
Alignments per period: 34
Topology: 0 (free-group class)
Stability: unstable (|λ|max 690.0)
Loop closure: 5.7×10⁻²⁵

Neighbours on the map

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