I wanted to write a detailed article on this some time. I snever got around to
it. Remember that ancient calenders were set around geocentric model and not
the heliocentric.
Forget your heliocentric theory for a while. Imagine earth at the center of
the universe. Imagine that moon, sun, and the planets are going around the
earth with different angular velocities. The stars don't revolver around the
earth at all. Actually the case of planets is a little complicated because
they go backwards for a while. To simplify things let us concentrate
on Sun, moon, and the stars.
As you know the sun completes one circle in 365.25 days whereas the moon
completes a circle 29.3 days. Instead of a bland measure like 360
degrees, our ancients decided to measure the angles in more colorful
terms like raaSis and stars. Under the raaSi system, 360 degrees is divided
into 12 raaSis, giving 30 degrees per raaSi. Under the star system, 360
degrees is divided into 27 stars making two and a quarter stars into
one raaSi. Apparently, raaSi system is of Western/Mesopotamian origin
whereas star system is ours. Somewhere around the 4th or 5th century they
are combined into one.
To move 30 degrees sun takes 365.25/30= 30.43 days. Unfortunately, this is
not exactly equal to 29.3 days. If they were equal, it would have been
very easy to count months from moon to moon. In the absence of clocks and
sophisticated mathematics it was difficult to keep track of precise number
of days. Moon to moon was still a very convenient way to count for a month.
But 12 moon-to-moons is still only 352(approx) days.
Here is where the term "luni-solar" comes in. Many of you might be knowing
the concept adhika maasa. When does a maasa become adhika maasa?
Approximately speaking, by the time Sun moves 30 degrees, i.e. one raaSi,
moon completes one entire revolution. So we can associate a one-to-one mapping
between a raaSi and a month. Imagine
0-30 deg chaitram
30-60 deg vaiSaakham
and so on.
Suppose, the moon and Sun start out at 0 degrees. By the time moon
completes one revolution around the earth, Sun would be near 29 degrees.
In this case we would declare chaitram as adhika maasam. However, by the
time moon completes the next revolution sun would be around 58 degrees.
So the next month would be vaishaakham. After a while there would
be another raaSi in which moon completes an entire revolution while
Sun is in the same raaSI. That would be declared an adhika maasam
again.
Unfortunately, I can't draw a picture in email. I hope if you have read till
here, you got the picture! The Indian system served the ancients very well,
with convenience moon-to-moon month at the same time synchronising it with
the more precise solar raaSIs. If there was something unfortunate, it is
that the method was purely algorithmic. Most of the pundits, who could
calculate the positions of heavenly bodies precisely with their calculations,
were incapable of identifying them in the real sky! There was a small
inaccuracy in their algorithms which accumulated to an error of 23 days
in 2000 years. As a result, Makara Sankranti (another name for
Winter Solstice -- The shortest day in the year) falls
on january 14th now which should actually fall on Dec 22nd.
Sometimes it is mistakenly said that duryOdhana didn't take adhika maasa
into account during uttara gOgrahana. The argument is illogical because
if duryOdhana did really forget adhika maasa, he should have counted
even more years! The fact of the matter is that the concept of adhika maasa
is much later than mahaabhaarata. I checked the Sanskrit maha bharata
and doesn't elaborate too much on that. I would guess that at the time
of mahabharata calendar making was a very imprecise art. More likely,
Bheeshma would have simply brushed aside duryOdhana because he was
an elderly person. Remember "Boss is not always right but boss is
always boss".
Ramana