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Free-fall F33

(1, 0.1, 0.01)

From Li & Liao (2019)

Free-fall F33 (1, 0.1, 0.01) is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 0.1 : 0.01 that return to their starting positions and velocities every 8.3297 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 273.6), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000852 of each other at a top speed of 48.2, line up 28 times a period, and the computed loop closes to 6.6×10⁻²⁶.

Measured over one period

Period: 8.329719528
Masses: 1 : 0.1 : 0.01
Energy: -0.118934
Angular momentum: 0
Closest approach: 8.5×10⁻⁴
Top speed: 48.17
Path length: 18.605
Alignments per period: 28
Topology: 0 (free-group class)
Stability: unstable (|λ|max 273.6)
Loop closure: 6.6×10⁻²⁶

Neighbours on the map

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