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Free-fall F31

(1, 0.8, 0.4)

From Li & Liao (2019)

Free-fall F31 (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 4.2145 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 3259), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00000274 of each other at a top speed of 723, line up 32 times a period, and the computed loop closes to 5.7×10⁻²⁰.

Measured over one period

Period: 4.214514418
Masses: 1 : 0.8 : 0.4
Energy: -2.16216
Angular momentum: 0
Closest approach: 2.7×10⁻⁶
Top speed: 722.7
Path length: 13.463
Alignments per period: 32
Topology: 0 (free-group class)
Stability: unstable (|λ|max 3259)
Loop closure: 5.7×10⁻²⁰

Neighbours on the map

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