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Free-fall F12

(1, 0.8, 0.2)

From Li & Liao (2019)

Free-fall F12 (1, 0.8, 0.2) is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 0.8 : 0.2 that return to their starting positions and velocities every 2.7646 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 2806), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00025 of each other at a top speed of 71.3, line up 18 times a period, and the computed loop closes to 1.2×10⁻²⁵.

Measured over one period

Period: 2.764613582
Masses: 1 : 0.8 : 0.2
Energy: -1.58492
Angular momentum: 0
Closest approach: 2.5×10⁻⁴
Top speed: 71.33
Path length: 9.1862
Alignments per period: 18
Stability: unstable (|λ|max 2806)
Loop closure: 1.2×10⁻²⁵

Neighbours on the map

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