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Free-fall F6

(1, 0.412, 0.267)

From Li & Liao (2019)

Free-fall F6 (1, 0.412, 0.267) is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 0.412 : 0.267 that return to their starting positions and velocities every 2.7027 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 weakly unstable (largest Floquet multiplier 6.263), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000719 of each other at a top speed of 83.3, line up 20 times a period, and the computed loop closes to 8.1×10⁻²⁵.

Measured over one period

Period: 2.702691816
Masses: 1 : 0.412 : 0.267
Energy: -1.21567
Angular momentum: 0
Closest approach: 7.2×10⁻⁵
Top speed: 83.28
Path length: 8.1137
Alignments per period: 20
Stability: weakly unstable (|λ|max 6.263)
Loop closure: 8.1×10⁻²⁵

Neighbours on the map

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