Hindu, Muslim and Christian festivals have in many cases obvious astronomical connection

1. Astronomical basis of Indian
festivals
Rajesh Kochhar
President IAU Commission 41: History of Astronomy
Indian Institute of Science Education and Research, Sector 81, Mohali,
rkochhar2000@yahoo.com
Panchkula 5 January 2013

2. • Festivals and commemorations are
an important part of a culture.
• Although they are celebrated variously,
it is instructive to note that many of
them have an astronomical basis.

3. • Keeping track of passage of time has been one of
the greatest intellectual challenges human beings
had set before themselves.
• We know much less about the visible sky than our
ancestors did.
• To know what time of the year it is, we look at the
calendar.
• To know what time of the day it is, we look at the
clock.
• We often forget that there was a time when one
had to turn to the sky to know the time.

4. Geo-centric model universe
The model of the Universe that remained in
vogue till the work of Copernicus, Kepler and
Galileo is this:
• The Earth was at the centre of the Universe.
Moon, Mercury, Venus, Sun, Mars, Jupiter
and Saturn went around the Earth.
• These were the seven (geo-centric) planets
which, through their predictable behavior,
represented divine order.

5. • In contrast, unpredictable events like comets
and meteors, and eclipses (till 500 CE in
India) were the utpata , or calamities; they
represented divine wrath.
• The un-moving stars merely constituted a
backdrop for planetary motions.
• Ritual was an important part of ancient life.
It was seen as a means of securing divine
approval, support or forgiveness for
terrestrial actions.

6. • To be efficacious, the ritual had to be elaborate
and well-timed, so that a careful distinction was
made between auspicious and inauspicious times.
• Interest in time keeping thus went beyond mere
functional needs.
• Nature has provided us with three convenient
keepers:
1.Spin of the Earth defines the day;
2.Moon’s orbit around the Earth defines a month;
3.The Sun’s apparent orbit around the Earth
defines a year.

7. • We can use the term lunation, or chandramasa
to denote the period from one new ( or full)
Moon to the next.
• All lunar months are not equal; the duration
can vary from 29d 5h to 29d 19h. A lunar
month on an average comprises about 29 and a
half days.
• The path of the Sun around the Earth is called
the ecliptic. Any point on the ecliptic can be
taken to be the reference point for beginning
the year.

8. • There are four important imaginary points on
the ecliptic which were recognized in very
ancient times. The dates given are for the Northern Hemisphere
(i) Spring Equinox ( 20- 21 March) when day
and night are equal.
(ii) Summer Solstice ( 20-21 June) when the day
is the longest;
(iii) Autumn Equinox ( 22- 23 September) when
day and night are again equal;
(iv) Winter Solstice ( 21-22 December) when
the night is the longest.

9. • Spring Equinox and Winter Solstice are the
two most common starting points for
tracking the Sun's apparent orbit.
• Later the concept of zodiacal signs would be
introduced and merged with knowledge
about cardinal points.

10. • In early times, equinoxes and solstices were
determined not by the time duration, but
from the direction of the sunrise. Get up
before sunrise, stick two poles in the ground
to mark the sunrise. Do it day after day for a
year.
• Sun rises exactly due East on Spring Equinox
day. The sunrise point progressively shifts
northwards with respect to distant stars till
it reaches the northern most point on Summer
Solstice.

11. • The sunrise point reverses its direction till
on Autumn Equinox, the Sun again rises
exactly due East. The Sun reaches its
Southern most point on Winter Solstice.
• It was customary to divide the year into two
parts:
1.Uttarayana (from Winter to Summer
Solstice, when Sun moves northwards)
2. Dakshinayana ( from Summer Solstice to
Winter Solstice, when Sun moves
southwards).

12. • Winter Solstice was often taken as the
starting point for a new year; the Sun is
weakest at this time and can only become
stronger. (The same philosophy operates
for starting a lunar month with the ending
moments of amavasya.)
• The Sun takes about 365 and a quarter days
from say one spring equinox to the next,
while 12 lunation's comprise only 354 days.
If the solar year had exactly coincided with
a “lunar year”, we would have had a very
simple universal calendar.

13. • The mismatch has been dealt
variously, giving rise to three
main annual calendars:
1.Purely Solar
2.Purely Lunar
3.Luni-Solar

14. Solar Calendar 1
• The most commonly used calendar in the
world is the Gregorian calendar. It has a
very accurate year length. In it the year has
either 365 or 366 days.
• For convenience the year is sub-divided
into 12 months. Although January,
February, etc., are called months, they have
nothing to do with the Moon. That is why a
month can have 28, 29, 30 or 31 days.

15. • Even if the Moon did not exist the calendar
would function in exactly the same way as
now. Incidentally, this calendar originated
in ancient Egypt and was introduced into
Europe in Cleopatra’s time.
The names September, October,
November, December refer to numbers 7, 8,
9, 10. At one time, the calendar started in
March, the Spring month.
•

16. Solar Calendar 2
• We can construct a solar calendar in another
way, where the month is still decoupled
from the Moon but now has astronomical
significance.
• The ecliptic has been divided into 12 equal
parts, called zodiacal signs or rashis. Sun's
entry into a rashi is called samkranti, which
can take place at any time during day or
night.

17. Solar Calendar 2
• We can construct a solar calendar in another
way, where the month is still decoupled
from the Moon but now has astronomical
significance.
• The ecliptic has been divided into 12 equal
parts, called zodiacal signs or rashis. Sun's
entry into a rashi is called samkranti, which
can take place at any time during day or
night.

18. • The time taken by the Sun to move from
one samkranti to the next is called a solar
month or a sauramasa.
• The solar year would then comprise 12 solar
months. These months are of different
durations.
• They would have been equal had the
Earth’s orbit around the Sun been exactly
circular.

19. • Since the orbit is elliptical, the distance
between the Sun and Earth varies. When the
Sun is at perigee ( nearest to the Earth),
which happen on 3 or 4 July, its angular
velocity is the largest.
• As a result transit through Dhanur
(Sagittarius) constitutes the shortest solar
month, with duration of 29 days and 7
hours.

20. • Six months later (around 2 or 3 January) the
Sun is at apogee (farthest from the Earth).
• Its angular velocity is the smallest with the
result that the Mithuna (Gemini) month at
31 days and 15 hours is the longest.
• It is important to keep in mind that the time
span between two samkrantis can be longer
or shorter than a lunation.

21. • The problem with solar years is that the new
month and therefore the new year begin
stealthily.
• We can indeed construct a calendar which
does not use the orbit of the Sun at all.
• The Sun of course remains in the picture as
the cause of lunar phases.

22. Lunar Calendar
• The Hijri calendar, which fixes Muslim
festivals, is a purely lunar calendar. In it, the
year uniformly consists of 12 lunations.
• Muslim festivals are therefore independent
of seasons; they slide through the solar
year.
• This calendar is the youngest of the three.

23. • It was introduced as a reaction to the
complex luni-solar calendar in use
previously as an import from ancient Iraq.
• The luni-solar calendar required complex
calculations and therefore bestowed unusual
power on the calendar experts.
• Hijri calendar in contrast depends on
simple observations.

24. Luni-Solar Calendar
• The luni-solar calendar was introduced into
India about 100 CE. Subsequently, it came
to be known as the Vikrami calendar, with a
back-dated zero year.
• It insists on using the Moon to define a
month and at the same time remains
anchored to the Sun.
• That is why it is so complex.

25. • Like the Hijri calendar, the Vikrami
calendar also has a lunar month, which
begins, let us say, with (the ending moment
of) amavasya. ( Alternatively , the month
can begin with purnima .)
• But while the Hijri year sticks to 12
lunations, the Vikrami year can have either
12 or 13 lunations.

26. • 1A1 l unar year falls short of a solar years by
days. Within three years the shortfall will be
sufficient to permit addition of an extra
month.
• The prescription for this addition is quite
remarkable.
• The basic principle of the calendar will be
discussed in next slides.

27. • The basic principle of the calendar is this.
Identify the Spring Equinox. In about 600
CE, Spring Equinox occurred when the Sun
was near the nakshatra Revati, or on the
verge of entering the Mesha rashi. This was
taken as the beginning of first point of
Aries, or the beginning of the rashi system.
• Identify the New Moon preceding this.
Start the new year from this New Moon so
that the Spring Equinox falls in the first
month.

28. • Monitor the samkrantis and New Moons.
If there are two New Moons in a solar
month, repeat the lunar month.
• If no New Moon occurs in the solar month,
delete that lunar month.
• The cycle will be completed in 19 years: If
you preserve the Vikrami calendar of this
year, you can use it again 19 years later.
• You will find that in this period you have
had a mixture of 12 years of 12 lunar months,
and seven years of 13 lunar months.

29. • The Siddhantic length of the tropical year,
from Spring Equinox to the next, is very
inaccurate. It is 0.1656 days too long. This
is a large error, amounting to three days in
200 years.
• The error gets added up year after year, so
that the start of the year is pushed to later
and later dates. We have documentary
evidence that in 1763, following Ahmad
Shah Abdali’s invasion, Baisakhi was
celebrated on 10 April.

30. • It now falls on 14 April; there is thus an
accumulated error of 23 days. In future, it
will be occurring still later.
• We celebrate Baisakhi with great fervor as
the harvesting festival. But, the crops
respond to onset of Spring , not to a
Panchang.
• Note that even when the year has 13 months,
there are only 12 month names. A name will
therefore have to be repeated.

31. • Vikrami calendar is a twin-track calendar. It
keeps track of the samkrantis as well as the
New and Full Moons. Normally between
two samkrantis there would occur an
amavasya.
• Conversely, a samkranti will fall within a
lunar month. Sometimes it happens that
between two neighbouring samkrantis there
are two amavasyas instead of one.

32. • We then count the lunar month twice. The
first one is called adhik masa ( extra month)
and the second shuddha or nija (pure).
• Alternatively the shuddha masa is split into
two, and the adhika masa sandwiched in
between.
• Celebrations are reserved for the shuddha
one which includes a samkranti. On very
rare occasions there will be no amavasya
between two samkrantis .

33. • This month is then deleted as kshaya masa
(decayed month). A Vikrami year cannot
have less than 12 months. Therefore, if one
month is deleted, some other(s) must be
repeated.
• Kshaya masa is a rarity. Successive kshaya
masa occurred/ will occur in 1823, 1964,
1983, 2124; that is after 141 and 19 years

34. Festivals
• For ease of calculations, a lunation is divided
into 30 parts called tithis. They are of unequal
duration. A tithi can begin at any time.
• While, calculations are carried out in terms of
tithi, a festival must be assigned to a civil day
beginning with sunrise.
• Connecting a tithi to a civil day is a complex
affair.

35. • That is why at times there is controversy
whether the festival is today or tomorrow.
• There is a Hindi phrase, meen mekh
nikalana; meen here is Mina rashi and
mekh the Mesha rashi.
• The phrase depicts the common perception
about the disagreement among astronomers or
astrologers in fixing astronomical timings.

36. • A lunation is divided into two parts, called
pakshas
1.The period from amavasya to purnima is
called shukla ( bright) paksha, because the
Moon becomes brighter night after night.
2. The period from purnima to amavasya is
called krishna ( dark) paksha.

37. • Vikrami new year starts with the ending
moments of the amavasya preceding the
(theoretical) Spring Equinox.
• The first nine tithis of the first month,
collectively known as Navaratri (nine
nights), are earmarked for piety, worship
and restrained behaviour.
• This is in contrast to the Gregorian New
Year which is often ushered in with revelry
and hang-over.

38. • Each of the nine tithis is addressed to a
different deity. In particular the ninth tithi is
celebrated as Ramanavami.
• Easter is a Christian festival (the same as
the Jewish Passover) still connected to the
Moon.
• Easter falls on the Sunday that comes after
the calculated full Moon on or after the
Spring Equinox.

39. • Since both Good Friday (just preceding
Easter) and Ramanavami are related to the
Spring Equinox, the two holidays occur
close together.
• Six months after the spring equinox comes
the Autumn Equinox. The lunar month
Containing the autumn equinox again
begins with Navaratri.
• Before this, homage is paid to the departed
ancestors in a ceremony called Shraadh.

40. • The eighth tithi of the new month is devoted
to Durga. After the Navaratri is over, the
next day Vijayadashami is celebrated with
great enthusiasm and fun.
• Note that if Vijayadashami were part of
Navaratri, it will have to be a very solemn
affair. About 20 days after Dussehra comes
amavasya which is celebrated as Deepavali.

41. • The purnima following Deepavali is
celebrated as Guru Nanak Jayanti.
• Note that Buddha Jayanti also falls on a
purnima
• We may now take note of two festivals
towards the close of the Vikrami year. A
night before amavasya the Moon appears to
be very thin. It is termed Shivaratri.

42. • The last Shivaratri of the year would of
course be a tithi before the first Navaratri.
The one prior to this, that is in the 11th
month, is celebrated as Mahashivaratri.
• The purnima after this is Holi; it is the last
purnima of the year. With the amavasya
after this begins the New Year.

43. To sum up
• Mahashivaratri is related to the last but one
amavasya of the Vikrami year.
• A fortnight later comes Holi, the last
purnima of the year.
• The new year (1st of Chaitra) begins on
New Moon a fortnight later.
• Ramanavami is the last of the nine-tithi
celebration.

44. • Six or seven lunations later comes the
Ashvina amavasya which marks the
beginning of Autumn Navaratri. (*2012, eg,
had an adhik Bhadrapada (Aug.-Sep.)
• The next amavasya is Divali.
• The purnima immediately after this is
Nanak Jayanti.

45. • Independently of the festivals associated
with lunar phases, Mesha samkranti
(Baisakhi) is celebrated as Spring Equinox,
and Makar samkranti ( Lohri) as Winter
Solstice.
• It is not a coincidence that Christmas,
(Gregorian) New Year Day, and Lohri all
come so close together; they all
commemorate Winter Solstice.

46. • So far we have spoken about the Sun and the
Moon. In passing we may note a festival
associated with Jupiter.
• Its entry into the Kumbha rashi (Aquarius)
is celebrated as the main Kumbha mela in
Hardwar.
• Since Jupiter’s orbital period is about 12
years, the main Kumbha celebration returns
after this period.

47. • There are in all four Jupiter-related celebrations,
three rashis apart.
Place Jupiter in Sun and Moon in
Hardwar 11. Kumbha 1. Mesha
Ujjain 8. Vrishchik 7. Tula
Nasik 5. Simha 4. Karka
Prayag 2. Vrishabh 10. Makar
• Since Jupiter’s period is not exactly 12 years but
slightly less, Jupiter is actually not in Aquarius at the
time of Hardwar Kumbh,

48. • The seasonal festivals are all associated with
the astronomical position of the Sun. The
unstated assumption was that Earth’s
climate plays no role.
• This was true in the past when human beings
lived in harmony with nature.

49. • As pointed above, the Vikrami calendar
today has an accumulated error of 23 days.
There is need to rectify it to bring it in line
with the actual, observed sky.
• Two steps are needed:
1.A very accurate year length should be used
as an input for panchanga making.
2.To remove the 23-day accumulated error,
by a diktat the next Baisakhi should be
celebrated on the actual Spring Equinox day
and Lohri on the actual Winter Solstice day.

50. Conclusion
Traditional festivities and commemorations
are a multi-dimensional thing. My aim has
been to draw attention to the underlying
astronomical principles of some of the world
festivals.

51. Thanks