A tropical month is the time between passages of the Moon
through the same celestial longitude. It is seven seconds shorter
than a sidereal month, the time taken being 27 days 7 hours 43
minutes 5 seconds.
The draconic or nodical month is the time that elapses between
the Moon's passages through the same node, or intersection of its
orbit with the ecliptic, the apparent pathway of the Sun and the
length of a month in this case is 27 days 5 hours 5 minutes 35.8
The calendar month
A calendar month has been based on the time that elapses between
two successive new moons or lunation.
Early man used this to mark his calendar.
It was known as the lunar calendar. Twelve lunations totaled to 354
days and was roughly calculated as one year. The modern day calendar
was later devised. Here the calculation of the year was based in
relation to the sun.
The first to be established was the Julian calendar, which was also
called the old calendar. Julius Caesar, the Roman emperor,
introduced it and hence the name. Acting on the advice of an
Alexandrian astronomer Sosigenes, Caesar made the new calendar
solar, not lunar, and he took the length of the solar year as 365
1/4 days. The year was divided into 12 months, all of which had
either 30 or 31 days except February. February had 28 days. However,
every fourth year had an additional and the extra day was tagged on
to February, the last month in the year.
However, it was later realized that Sosigenes had
overestimated the length of the year by 11 minutes 14 seconds. Its
cumulative effect began to show in due course (mid-1500s) and the
dates of seasons were shifted by ten days. Pope Gregory III made a
reformation and proclaimed the calendar to the seasonal dates of AD
325 restored. The new calendar was to be effective on October 4,
that is the day following being noted as October 15, 1582. Slowly,
the Julian calendar faded and the Gregorian came to stay.
The difference between the two
The Gregorian and the Julian calendar had only one difference.
In the Julian year, a century becomes a leap year, hundred being
divisible by four. In the Gregorian year, no century is a leap year
unless exactly divisible by 400. It is said that a further fine
tuning, that is designating years evenly divisible by 4,000 as
common (not leap) years, will keep the Gregorian calendar accurate
to within one day in 20,000 years.