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Free-fall F12

(1, 0.1, 0.01)

From Li & Liao (2019)

Free-fall F12 (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 4.0684 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 460.3), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000157 of each other at a top speed of 129, line up 28 times a period, and the computed loop closes to 2.0×10⁻²¹.

Measured over one period

Period: 4.068377595
Masses: 1 : 0.1 : 0.01
Energy: -0.119522
Angular momentum: 0
Closest approach: 1.6×10⁻⁵
Top speed: 129.1
Path length: 9.0095
Alignments per period: 28
Topology: 0 (free-group class)
Stability: unstable (|λ|max 460.3)
Loop closure: 2.0×10⁻²¹

Neighbours on the map

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