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Free-fall F21

(1, 0.8, 0.8)

From Li & Liao (2019)

Free-fall F21 (1, 0.8, 0.8) is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 0.8 : 0.8 that return to their starting positions and velocities every 5.1792 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 35998), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00002 of each other at a top speed of 2, line up 48 times a period, and the computed loop closes to 2.5×10⁻²¹.

Measured over one period

Period: 5.179153473
Masses: 1 : 0.8 : 0.8
Energy: -4.28285
Angular momentum: 0
Closest approach: 2.0×10⁻⁵
Top speed: 199.8
Path length: 21.007
Alignments per period: 48
Stability: unstable (|λ|max 35998)
Loop closure: 2.5×10⁻²¹

Neighbours on the map

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