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Free-fall F12

(1, 0.8, 0.8)

From Li & Liao (2019)

Free-fall F12 (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 5.5848 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 1432), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000168 of each other at a top speed of 69.3, line up 30 times a period, and the computed loop closes to 8.6×10⁻²⁵.

Measured over one period

Period: 5.584793134
Masses: 1 : 0.8 : 0.8
Energy: -3.00259
Angular momentum: 0
Closest approach: 1.7×10⁻⁴
Top speed: 69.31
Path length: 20.907
Alignments per period: 30
Topology: 0 (free-group class)
Stability: unstable (|λ|max 1432)
Loop closure: 8.6×10⁻²⁵

Neighbours on the map

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