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Free-fall F13

(1, 0.412, 0.267)

From Li & Liao (2019)

Free-fall F13 (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 2.527 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 3077), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00000197 of each other at a top speed of 504, line up 32 times a period, and the computed loop closes to 1.2×10⁻¹⁸.

Measured over one period

Period: 2.526991829
Masses: 1 : 0.412 : 0.267
Energy: -1.46731
Angular momentum: 0
Closest approach: 2.0×10⁻⁶
Top speed: 504.0
Path length: 8.2168
Alignments per period: 32
Stability: unstable (|λ|max 3077)
Loop closure: 1.2×10⁻¹⁸

Neighbours on the map

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