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Free-fall F9

(1, 0.8, 0.4)

From Li & Liao (2019)

Free-fall F9 (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 3.7613 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 8368), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000331 of each other at a top speed of 208, line up 20 times a period, and the computed loop closes to 3.7×10⁻²⁴.

Measured over one period

Period: 3.761258655
Masses: 1 : 0.8 : 0.4
Energy: -1.88558
Angular momentum: 0
Closest approach: 3.3×10⁻⁵
Top speed: 207.6
Path length: 11.473
Alignments per period: 20
Stability: unstable (|λ|max 8368)
Loop closure: 3.7×10⁻²⁴

Neighbours on the map

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