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Free-fall F52

(1, 0.8, 0.6)

From Li & Liao (2019)

Free-fall F52 (1, 0.8, 0.6) is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 0.8 : 0.6 that return to their starting positions and velocities every 3.5207 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 21342), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00000144 of each other at a top speed of 93, line up 36 times a period, and the computed loop closes to 4.2×10⁻²⁰.

Measured over one period

Period: 3.520699152
Masses: 1 : 0.8 : 0.6
Energy: -3.37585
Angular momentum: 0
Closest approach: 1.4×10⁻⁶
Top speed: 930.4
Path length: 12.445
Alignments per period: 36
Stability: unstable (|λ|max 21342)
Loop closure: 4.2×10⁻²⁰

Neighbours on the map

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