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Free-fall F34

(1, 0.8, 0.4)

From Li & Liao (2019)

Free-fall F34 (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 5.0904 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 35611), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00000123 of each other at a top speed of 1076, line up 32 times a period, and the computed loop closes to 1.1×10⁻¹⁷.

Measured over one period

Period: 5.090385830
Masses: 1 : 0.8 : 0.4
Energy: -1.89906
Angular momentum: 0
Closest approach: 1.2×10⁻⁶
Top speed: 1076
Path length: 15.083
Alignments per period: 32
Stability: unstable (|λ|max 35611)
Loop closure: 1.1×10⁻¹⁷

Neighbours on the map

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