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Free-fall F22

(1, 0.8, 0.8)

From Li & Liao (2019)

Free-fall F22 (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 7.5383 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 22762), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000716 of each other at a top speed of 39.6, line up 54 times a period, and the computed loop closes to 4.2×10⁻²³.

Measured over one period

Period: 7.538254071
Masses: 1 : 0.8 : 0.8
Energy: -3.67788
Angular momentum: 0
Closest approach: 7.2×10⁻⁴
Top speed: 39.59
Path length: 28.873
Alignments per period: 54
Topology: 0 (free-group class)
Stability: unstable (|λ|max 2.3×10⁵)
Loop closure: 4.2×10⁻²³

Neighbours on the map

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