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Free-fall F42

(1, 0.8, 0.6)

From Li & Liao (2019)

Free-fall F42 (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 5.7507 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 41299), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000334 of each other at a top speed of 165, line up 32 times a period, and the computed loop closes to 7.0×10⁻²⁴.

Measured over one period

Period: 5.750665281
Masses: 1 : 0.8 : 0.6
Energy: -2.53660
Angular momentum: 0
Closest approach: 3.3×10⁻⁵
Top speed: 165.4
Path length: 19.503
Alignments per period: 32
Stability: unstable (|λ|max 41299)
Loop closure: 7.0×10⁻²⁴

Neighbours on the map

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