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Free-fall F40

(1, 0.1, 0.01)

From Li & Liao (2019)

Free-fall F40 (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 16.456 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 12454), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000163 of each other at a top speed of 106, line up 34 times a period, and the computed loop closes to 1.6×10⁻²⁴.

Measured over one period

Period: 16.45559945
Masses: 1 : 0.1 : 0.01
Energy: -0.113377
Angular momentum: 0
Closest approach: 1.6×10⁻⁴
Top speed: 105.7
Path length: 34.102
Alignments per period: 34
Topology: 0 (free-group class)
Stability: unstable (|λ|max 12454)
Loop closure: 1.6×10⁻²⁴

Neighbours on the map

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