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I've come across this passage:
Diese Zahl variierte zudem erstaunlich, je nach dem Stand von Ebbe und Flut, die wiederum je nach den Positionen von Sonne, Mond und Erde selbst erheblich unterschiedlich ausfielen.
According to every dictionary that I've checked, 'ausfallen' means 'to fall apart' or other meanings in that sense; It seems to have another meaning in this context.
I suggest to bookmark for DWDS. Meaning 3 is the appropriate one, translating to English turn out.
Since Duden also lists it as meaning two, I'm somewhat puzzled, what apparently poor references you may have used.
So a translation would be
The number varied to an amazing degree depending on the tides, which due to the positions of sun, moon and earth themselves turned out differently.
The second meaning in Duden is correct: http://www.duden.de/rechtschreibung/ausfallen#Bedeutung2.
ausfallen in this meaning is very common with clothing, e.g.:
Das Kleid fällt größer aus als angegeben.
