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Free-fall F13

(0.393, 0.288, 0.662)

From Li & Liao (2019)

Free-fall F13 (0.393, 0.288, 0.662) is a periodic orbit of the planar three-body problem: three masses in the ratio 0.393 : 0.288 : 0.662 that return to their starting positions and velocities every 5.3628 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 13648), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000327 of each other at a top speed of 168, line up 30 times a period, and the computed loop closes to 2.4×10⁻²³.

Measured over one period

Period: 5.362824890
Masses: 0.393 : 0.288 : 0.662
Energy: -0.998886
Angular momentum: 0
Closest approach: 3.3×10⁻⁵
Top speed: 167.9
Path length: 14.106
Alignments per period: 30
Topology: 0 (free-group class)
Stability: unstable (|λ|max 13648)
Loop closure: 2.4×10⁻²³

Neighbours on the map

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