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Free-fall F31

(1, 0.1, 0.01)

From Li & Liao (2019)

Free-fall F31 (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 8.4905 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 7694), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000201 of each other at a top speed of 99.1, line up 28 times a period, and the computed loop closes to 7.1×10⁻²⁵.

Measured over one period

Period: 8.490494918
Masses: 1 : 0.1 : 0.01
Energy: -0.117439
Angular momentum: 0
Closest approach: 2.0×10⁻⁴
Top speed: 99.14
Path length: 19.473
Alignments per period: 28
Stability: unstable (|λ|max 7694)
Loop closure: 7.1×10⁻²⁵

Neighbours on the map

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