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Free-fall F42

(1, 0.1, 0.01)

From Li & Liao (2019)

Free-fall F42 (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 16.043 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 15101), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000218 of each other at a top speed of 91.3, line up 40 times a period, and the computed loop closes to 4.4×10⁻²⁵.

Measured over one period

Period: 16.04263118
Masses: 1 : 0.1 : 0.01
Energy: -0.114233
Angular momentum: 0
Closest approach: 2.2×10⁻⁴
Top speed: 91.30
Path length: 32.136
Alignments per period: 40
Topology: 0 (free-group class)
Stability: unstable (|λ|max 15101)
Loop closure: 4.4×10⁻²⁵

Neighbours on the map

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