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Free-fall F13

(1, 0.1, 0.01)

From Li & Liao (2019)

Free-fall F13 (1, 0.1, 0.01) is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 0.1 : 0.01 that return to their starting positions and velocities every 4.3023 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 306), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00000835 of each other at a top speed of 325, line up 28 times a period, and the computed loop closes to 1.2×10⁻²².

Measured over one period

Period: 4.302294565
Masses: 1 : 0.1 : 0.01
Energy: -0.115019
Angular momentum: 0
Closest approach: 8.3×10⁻⁶
Top speed: 324.8
Path length: 9.4291
Alignments per period: 28
Stability: unstable (|λ|max 3060)
Loop closure: 1.2×10⁻²²

Neighbours on the map

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