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Free-fall F12

(1, 0.8, 0.6)

From Li & Liao (2019)

Free-fall F12 (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 3.6751 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 3058), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000244 of each other at a top speed of 226, line up 20 times a period, and the computed loop closes to 2.0×10⁻²³.

Measured over one period

Period: 3.675095483
Masses: 1 : 0.8 : 0.6
Energy: -2.46576
Angular momentum: 0
Closest approach: 2.4×10⁻⁵
Top speed: 226.1
Path length: 11.707
Alignments per period: 20
Stability: unstable (|λ|max 3058)
Loop closure: 2.0×10⁻²³

Neighbours on the map

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