Dating days of the week
The Earth revolves around the sun in about 365¼ days, that is, about 12.4 lunar months.The civil calendar used by most of the world has abandoned any correlation between the moon cycles and the month, arbitrarily setting the length of months to 28, 30 or 31 days.In ancient times, the new months used to be determined by observation.
A day is added to the month of Cheshvan or subtracted from the month of Kislev of the previous year to prevent these things from happening. The "first month" of the Jewish calendar is the month of Nissan, in the spring, when Passover occurs.
When the Sanhedrin heard testimony from two independent, reliable eyewitnesses that the new moon occurred on a certain date, they would declare the rosh chodesh (first of the month) and send out messengers to tell people when the month began.
The problem with strictly lunar calendars is that there are approximately 12.4 lunar months in every solar year, so a 12-month lunar calendar is about 11 days shorter than a solar year and a 13-month lunar is about 19 longer than a solar year.
These three phenomena are independent of each other, so there is no direct correlation between them.
On average, the moon revolves around the Earth in about 29½ days.