The main purpose of creating this blog is to provide material and guidance to the students of Vedanga Jyotisha who are appearing for BA as well as MA level examinations of Kavi Kulaguru Kalidas Sanskrit University. I hope this effort will be welcomed by all the students of the Vedanga Jyotish and this effort will be useful to them. Dewavrat Buit dewavrat2000@yahoo.com

Wednesday, June 14, 2006



Let us take a look at the general definitions of the Solar, Lunar and Lunisolar calendars
before delving into the specificities of that of the Indian Calendar.

The Solar Calendar
The length of the solar month varies from 29.318 days to 31.644 days. The solar day has
a fixed number of 24 hours. Therefore, the change of date begins when the midnight
occurs. The midnight is measured with respect to the time zone of the specific country.
This calendar is fixed at 365 days for normal years and at 366 days for leap years which
occur every fourth year. A leap year is so named because the extra day causes any date
after February in a leap year to ‘leap’ over 1 day in the week and to occur 2 days later in
the week than it did in the previous year, rather than just 1 day later as in a normal year.
One anti-clockwise revolution of the Earth around the Sun is considered as one year.
Instead of visualizing the movement of the Earth around the sun, let us visualize the Earth
as an immobile body and the Sun moving around it. In other words, we are considering
the apparent motion of the Sun. The general solar year is calculated by noting the time
taken for the Sun to revolve around the Earth and return to the same reference point in the
sky. There are 2 types of solar year, the sidereal year and the solar year. The sidereal
year is the time taken by the Sun to move along the ecliptic from the starting point, which
is taken with reference to a background star, and returning to the same reference point.
Furthermore, the sidereal year takes into consideration the star which is seen just before
sunrise on the day of the equinox. This star is the reference point to which the Sun
returns to after a revolution. The Time taken for the Sun to complete its path is the
sidereal year. The tropical year is the time between two equinoctial points, usually the
March equinoxes are considered. The equinoctial point is the reference point to which
the Sun has to return to.

The Lunar Calendar
A lunar, or synodic, month is the time required for the moon to make a complete rotation
around the Earth, passing from a particular phase, such as the full moon, back to the same
phase; it averages 29.53059 days. Each lunar year is made up of 12 lunar months of about
354 days in total, making it shorter than the solar year by about 11 days. This difference
is accounted for by the addition of an extra lunar month about once every 2.5 years.

The Lunisolar Calendar
The variations among the many calendars in use have been caused by the inaccuracy of
the determinations of the duration of the year, together with the fact that a year cannot be
divided evenly by any of the other time units: days, weeks, or months. The earliest
calendars based on lunar months thus failed to agree with the seasons. A month
occasionally had to be added to reconcile lunar months with the solar year. A calendar
that makes such adjustments is a lunisolar calendar.
The Indian Solar Calendar
The Indian Solar Year
Since the Indian Solar Calendar is a type of the solar calendar, it is similar to the solar
calendar. The Indian Solar Calendar follows the same system of noting the time taken for
the Sun to apparently revolve around the Earth and return to the same reference point as
the solar calendar. The Indian Solar calendar can be calculated just as the solar calendar,
in 2 ways - the nirayana system (sidereal) and the sayana (tropical) system. The method
used is similar to that of the solar calendar mentioned earlier.
In India, the traditional calendar utilises the nirayana system. In the nirayana system, the
reference point to which the Sun has to return to is taken as the fixed point on the ecliptic
which is opposite to the bright star Chaitra. Initially, this fixed point was taken to be the
March equinoctial point as the reference point coincided with the March Equinox of
285A.D. But over centuries, due to precession, the equinoctial point (fixed point) has
moved significantly westward on the ecliptic. However, as the nirayana year follows the
Surya Siddhanta (ancient astronomical treatise), the approximation of the sidereal year,
the precession of the March equinox has no effect on the length of the Indian Solar year.
More about the Indian Solar Year:
Length: 365.258756 days
Deviation: +9min or –9min

The Indian Solar Month
The nirayana year consists of 12 months and these are related to the 12 rasis (zodiacs).
The ecliptic lies in the middle of the zodiac stars and these stars act as landmarks which
signify the different months. The 12 rasis divide the ecliptic into 12 equal parts as shown
in the diagram below. This division starts from the fixed point on the ecliptic which acts
as the reference point when observing the sidereal year. In this case the division starts
from Mesha (Aries) rasi. Hence, the Indian solar calendar starts from zodiac zone Mesha
and ends at the zodiac zone Mina (Pisces).
Samkranti is the movement of the Sun into a rasi arc (zodiac zone). Hence, the length of
the month is the time taken for the sun to travel through one rasi arc and it usually is
about 30-31 days.
The samkranti may take place at any time of the day or night and this gives rise to the
four schools of the Indian Solar Calendar.4 different Schools of the Indian Solar Calendar:

1. Orissa School
The panchang* day and the start of a month is the day when the sun first enters a rasi arc.
In other words the month starts on the day of samkranti. In this system the time of the
day is insignificant. This system is used in Punjab, Haryana and Orissa.
When sun enters a
zodiac arc, that day
is the panchang day

2. Tamil School
If samkranti happens before sunset, the month begins on the same day. If it happens after
sunset, the panchang day occurs the next day. Hence the time of the day is of great
importance in the system. This calendar is followed by the people of Tamil Nadu.

3. Malayali School
This school not only takes samkranti into account but also takes aparahna into account.
Aparahna is 3/5th duration of the time taken from sunrise to sunset. In the system, if the
samkranti occurs before aparahna, the panchang is on that day. If it occurs after
aparahna, the panchang is on the next day. This calendar is used mainly in Kerala.

4. Bengal School
When the samkranti takes place between sunrise and the following midnight, the solar
month starts the next day. If it begins after midnight, the panchang is on the following
day. The rule is generally utilised in Assam, Bengal and Tripura.

The Indian Lunar Calendar
The Hindu lunar day is known usually begins at the sunrise and the length of the day is
usually measured by the time elapsed between the 2 successive sunrises. The lunar day is
known as the ‘Tithi’. The length of the day varies between 22-26 hours. This number of
hours is based on the angular rotation of the moon around the Earth in its elliptical orbit.
As the moon revolves around the Earth, the angular distance between the sun and the
moon change from 00 to 3600. When the angular distance returns to 0, it represent the
birth of the new lunar month.
The Hindu lunar month is calculated on the basis that the moon revolution around the
Earth. Therefore, one lunar month equals to one complete revolution of the moon around
the Earth. The rotation period of the moon around the sun varies so this in turns affect the
duration of the lunar month. The length of the Hindu lunar month therefore varies from
the period of 29.305 to 29.812.
The Hindu lunar year is based on the Earth revolution of the Earth around the sun. In the
lunar year, there is generally about 12 lunar months which equates to about 354 days.
This male it 1 days shorter that the solar year. Therefore, the only way to reduce this
difference is to add an extra lunar month about once every 2.5 years. This extra month is
referred as "Adhik Mas" which means extra month.
The Hindu synodic month takes the motion of the sun into the account where it takes the
mean time between new months. The length with respect of the Hindu synodic month is

The mean time for the sunrise is 6a.m. However, it is being affected by 4 factors:
• The latitude of the location affects the time of the sunrise which also is in turn
dependant on the season.
• There is also the ¼ time difference between the sidereal day and the solar day.
• The equation of time will give the difference between the local and the civil
midnight. This is caused by the uneven motion of the sun throughout the seasons.
For the different locations, the difference in the longitude affects the local time of
astronomical events by 4 minutes for every degree of longitude.
The Indian Lunisolar calendar
Amanta is a lunar month which starts from a new moon to another new moon. While
purnimanta is the month begins from one full month to another. The lunar calendar using
these months are called amanta calendar and purnimanta calendar respectively.
Since the solar calendar is longer than the lunar calendar, it is kept adjusted to the earlier
by adding intercalary months at intervals. The first day of the lunar year will change from
one year to another and will fall between March and April. This is due to the fact that
Chaitra, the first month of Indian Calendar, generally take place from 15th March to 13th

Amanta Lunisolar Calendar
The amanta lunisolar calendar is called mukhyamana, where mukhya means primary.
This is an important calendar as the days of festival is fixed based on it even if the
purnimanta calendar is followed.
This amanta calendar begins from the Chaitra. The solar months in which the new moon
of the lunar month occurs is used to name the months of this calendar. The months of this
amanta calendar can be grouped into two, the Sukla paksha, which means the bright half
of the month, and Krishna paksha, which means the dark half of the month. Sukla paksha
occupy the period of time from new moon to the coming full moon where as Krishna
paksha covers the time period from the full moon where Sukla paksha stops to the next
new moon.

Purnimanta Lunisolar calendar
This calendar takes place from the time when a full moon starts to another. It is named
after amanta month that occurs two weeks later. The purnimanta lunisolar month starts a
fortnight before the first new moon of an amanta month and ends in the middle of that
same amanta month.
While an amanta month can occur totally outside the solar month it is named after, this
purnimanta month will always occupy half or more of the solar month.
Note: we realized that the first month, Chaitra, of the year in Indian Calendar and the year
does not begin in the same time and day. The year begins in the middle, that is, about the
15th day of the first lunar month (Chaitra) leading in counting the Krushna paksha of
Chaitra in the previous year. The year begins with the start of Sukla paksha of Chaitra.

The lunar cycle begins with the new month and then it enters to a crescent phase and ends
with the full moon. This whole cycle will lasts for approximately 15 days. After the 15
days, the moon will reach the waning phase before it enters the new moon phase.
According to the Hindu lunar calendar, the crescent lunar phase fortnight is called the
"Shukla Paksha". The waning phase is known as "Krushna Paksha". "Shukla Paksha"
changes from 00 to 1800 and the "Krushna Paksha" changes from 1800 to 00. Therefore, if
we divide the 1800 to 15 parts in which 1 part represent to 1 day, each part represent 120.
This 120 portion represent the angular distance between the moon and the sun. Hence, 1
lunar day is 120. However, it must be noted that according to Kepler’s Law, the angular
velocity of moon in its elliptical orbit around the Earth continuously varies, the length a
lunar day or tithi also varies accordingly. Hence, the tithi can extend over one day or it
can be skipped of two tithis happened one day.

It is the traditional 5 part Hindu calendar compromising for civil day, day of the week,
stellar position of the moon, yoga and karana which is based on the lunar phase.
Panchang literally means "five parts". "Panch" means five while "ang" means parts. It is
the traditional 5 part Hindu calendar compromising for civil day, day of the week, stellar
position of the moon, yoga and karana which is based on the lunar phase.
The people in India have always measure time using the scientific and spiritual calendar
Panchang. The Panchang determines festivals that celebrate and honour the legends and
gods of India. It evokes the universe using mathematical calculations which can predict
weather, epidemics, personal fortune and events.
The Panchang uses lunar month to calculate and measure time. The lunar months used
have their names reveal the secret path of constellations and stars. The face of Aamvasya,
the new moon, ushers in a new month.
For Hindus, Panchang is more, much more than determining time in India. It is essential
for their religion and lives. The Panchang is used to forecast the spiritual way of a person
on his journey towards god.
The 60 year cycle and the Jovian periods in the Tamil calendar
The Tamil calendar follows a sixty year cycle which is similar to the sixty year cycle in
the Chinese calendar. The ancient Indian astronomers, through many years of
observation, found out that Jupiter actually took twelve years to revolve around the sun.

They also observed that in the course of the twelve years, Jupiter passed in the same
sequence through the same zodiacal constellations as the sun did in a twelve month cycle.
Actually, Jupiter did not take exactly twelve years to revolve around the sun. Jupiter only
takes about 11.86 years to revolve around the sun. Therefore, twelve years was actually
an approximation rather than a precise figure. However, although twelve years is not the
precise duration of time it took for Jupiter to revolve round the sun once, ancient Indian
astronomers use this approximated value to extend to a unit of five cycles, also known as
the sixty year cycle of Jupiter. The ancient Indian astronomers thought that Jupiter takes
about sixty years (5 revolutions around the sun) to come back to its original position
(relative to the zodiacal constellations). Thus, they formulated the sixty year cycle in that
after each period of sixty years, they would start with the same naming of the year again,
just as the way Jupiter returns to the same position (relative to the zodiacal constellations)
as it first started out. This sixty year cycle system was used in Indian calendars from the
6th century AD onwards. Each revolution of Jupiter around the sun was also known as
one Jovian period (1 Jovian period = 12 years) and therefore there are actually five Jovian
periods in a sixty year cycle. However, in actual fact, it takes Jupiter about 83.02 years to
return to its original position, that is, about 7 revolutions around the sun (11.86 X 7 =
83.02 years)


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