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Free-fall F33

(1, 0.8, 0.6)

From Li & Liao (2019)

Free-fall F33 (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 4.3424 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 473.7), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0003 of each other at a top speed of 55.2, line up 30 times a period, and the computed loop closes to 7.6×10⁻²⁶.

Measured over one period

Period: 4.342378325
Masses: 1 : 0.8 : 0.6
Energy: -2.90011
Angular momentum: 0
Closest approach: 3.0×10⁻⁴
Top speed: 55.20
Path length: 15.277
Alignments per period: 30
Stability: unstable (|λ|max 473.7)
Loop closure: 7.6×10⁻²⁶

Neighbours on the map

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