The Babylonian calendar uses days, months and years. The month begins after sunset on the evening when the lunar crescent becomes visible for the first time after New Moon.
The Babylonian day begins and ends at sunset. Observations follow a tripartite division of the night. Either they take place during "the first part of the night" beginning at sunset, later in "the middle of the night," or before sunrise during "the last part of the night."
Representations of the sky were created using TheSky astronomy software. It uses state-of-the-art routines capable of picturing the celestial sphere seen on any night by sky-watchers in Babylon.
For Babylonian astronomers, the major frames of reference were the horizon and a fixed celestial frame of some 33 bright stars. These so-called normal stars are distributed around the ecliptic within a few degrees of the paths of sun, moon and planets.
A typical Diary inscription names a celestial body, notes its position, and gives the (Babylonian) date of the observation and an indication of the time.
Diary No. -567 reads: Line 8: Month II, the 1st (of which the 30th of the preceding month), the moon became visible while the sun stood there, 4 cubits below ﬂ Geminorum; it was thick;
The observation was made the first day of Month 2, when the crescent of the moon first became visible near the western horizon at sunset. The moon was close to the normal star beta Geminorum. The lunar crescent was thicker than a sliver, and it was visible while the sun stood there above the horizon.
A Babylonian month has either 29 or 30 days. Line 8 records that the 1st day of Month 2 was on the 30th of the preceding month, which means Month 1 had only 29 days.
Around the beginning of a month, Babylonian astronomers watched at sunset to catch a glimpse of the moon, which signaled the first day of the month. If bad weather got in the way, they had methods for accurately predicting the first visibility of the lunar crescent. A full understanding of their methods eludes historians of astronomy.
The data recorded about the first day of the month includes lagtime, a measure of the time between sunset and moonset. Diary No. -567 Line 12 notes, it (the crescent) was thick; sunset to moonset: 20°.
The 20° lunar lagtime corresponds to 80 minutes (1° is equivalent to 4 minutes, 15° to an hour, 360° to a day.) Thus, according to the Diaries, the moon set 80 minutes after the sun disappeared over the horizon.
In addition to simply logging the location of a planet, Babylonian astronomers watched for and recorded distinctive patterns of the planet's motion relative to the fixed stars. The events that interested the Babylonians are today called characteristic phenomena.
For superior planets Saturn, Jupiter and Mars, the characteristic phenomena are: 1) First appearance in the East 2) First stationary point 3) Opposition 4) Second stationary point 5) Last appearance in the West.
For inferior planets Venus and Mercury, the characteristic phenomena are: 1) First appearance in the East 2) Last Appearance in the East 3) First Appearance in the West 4) Last appearance in the West.