"חלק", being a 1/1080 part of an hour, is used in calculating the New Moon.
Rambam in הלכות קידוש החודש mentions that the original tradition of calculating the New Moon was forgotten and the system our Sages used ever since the Babylon exile was the Greek's. In those calculations, the phrase "our Sages divided an hour into 1080 parts" appears in many sources.
However, I could not understand whether this unit of measure was used by the Sages as a unit of time, prior to calculating the New Moon, or it was copied from the Greek's sixty-base system for those calculations only.
Are there other practical Halachot that this measure of time is used?