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Free-fall F9

From Li & Liao (2019)

Free-fall F9 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 5.2 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 59138), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000176 of each other at a top speed of 239, line up 28 times a period, and the computed loop closes to 1.3×10⁻²¹.

Measured over one period

Period: 5.199975681
Masses: 1 : 1 : 1
Energy: -3.86196
Angular momentum: 0
Closest approach: 1.8×10⁻⁵
Top speed: 239.3
Path length: 18.048
Alignments per period: 28
Stability: unstable (|λ|max 59138)
Loop closure: 1.3×10⁻²¹

Neighbours on the map

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