Gfyuki

It always was interesting for me to understand the answer for the question:

What's the reason that we have different quantities of days each month?

If the month is fixed on the time that the moon circles the earth, then the time of the circling isn't equal each month? And if the month fixed by the time that the earth circles the sun and then divided by 12 (365:12=30.4), why one month has more days and the other month has less days?

Before desktop computers, how did astronomers handle calculations of dates and times accurately, for example two plates taken decades apart, how would an astronomer calculate the time difference precisely?

You make a great point. The reason behind the discrepancy between the dates is due to a complicated history behind it.

The calendar is based on the calendar created by ancient Romans, which is based on one Moon cycle. One lunar cycle is

29.53 days.

www.universetoday.com/20620/lunar-year/

which does not evenly divide into the 365.25 days of the year.

Note: The Romans borrowed the calendar from the ancient Greeks to develop the idea of a 10-month calendar that left approximately 60 days unaccounted for.

Consequently, the earliest ancient Roman calendars had months that were either 29 or 30 days to account for this discrepancy.

The Romans started using the 10-month calendar in 738 B.C. that included Martius[March], Aprilis[April], Maius[May], Junius[June], Quintilis[July, quin- meaning "5"], Sextilis[August, sex- meaning "6"], September, October, November, and December.

To account for the remaining $pm60$ days, Januarius[January] was added to the beginning of the year and Februarius[February] to the end of the year during Numa's reign around 700 B.C with a leap year every 4 years. The calendar stayed in that order until 452 B.C. when a small council of Romans, called the Decemvirs, moved February to follow January.

However, people began adding a leap year every three years, so that caused a big problem. In fact, by the start of the reign of Julius Caesar, the previous calendar was off by a whole week!

Julius Caesar noticed this and thus modified the Roman calendar in 46 B.C. to make each month have either 30 or 31 days, with the exception of Februarius[February], which had 29 days, with the three year leap year fixed into a four year leap year, along with the nullification of a leap year when the year number is a multiple of 100. Quintilis[July] was later renamed Julius[July] in his honor. Likewise, Sextilis[August] later became Augustus[August] to honor Augustus Caesar, Julius' Aunt. Augustus[August] was also given an extra day (taken away from Februarius[February]), so that Augustus and Julius would have an equal number of days, representing their equal power.

This calendar was extremely accurate, but was still off as thousands of years later it was off by a day or so. Then a pope named Pope Gregory XIII modified the Julian calendar again in October 1582. This is the currently used Gregorian calendar. He made it so that

Every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100, but these centurial years are leap years if they are exactly divisible by 400.

https://en.wikipedia.org/wiki/Gregorian_calendar

This calendar is the most accurate calendar there is, and won't be a single day off until the year of $pm 3500$ AD.