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Astronomical basis of Indian 
festivals 
Rajesh Kochhar 
President IAU Commission 41: History of Astronomy 
Indian Institu...
• Festivals and commemorations are 
an important part of a culture. 
• Although they are celebrated variously, 
it is inst...
• Keeping track of passage of time has been one of 
the greatest intellectual challenges human beings 
had set before them...
Geo-centric model universe 
The model of the Universe that remained in 
vogue till the work of Copernicus, Kepler and 
Gal...
• In contrast, unpredictable events like comets 
and meteors, and eclipses (till 500 CE in 
India) were the utpata , or ca...
• To be efficacious, the ritual had to be elaborate 
and well-timed, so that a careful distinction was 
made between auspi...
• We can use the term lunation, or chandramasa 
to denote the period from one new ( or full) 
Moon to the next. 
• All lun...
• There are four important imaginary points on 
the ecliptic which were recognized in very 
ancient times. The dates given...
• Spring Equinox and Winter Solstice are the 
two most common starting points for 
tracking the Sun's apparent orbit. 
• L...
• In early times, equinoxes and solstices were 
determined not by the time duration, but 
from the direction of the sunris...
• The sunrise point reverses its direction till 
on Autumn Equinox, the Sun again rises 
exactly due East. The Sun reaches...
• Winter Solstice was often taken as the 
starting point for a new year; the Sun is 
weakest at this time and can only bec...
• The mismatch has been dealt 
variously, giving rise to three 
main annual calendars: 
1.Purely Solar 
2.Purely Lunar 
3....
Solar Calendar 1 
• The most commonly used calendar in the 
world is the Gregorian calendar. It has a 
very accurate year ...
• Even if the Moon did not exist the calendar 
would function in exactly the same way as 
now. Incidentally, this calendar...
Solar Calendar 2 
• We can construct a solar calendar in another 
way, where the month is still decoupled 
from the Moon b...
Solar Calendar 2 
• We can construct a solar calendar in another 
way, where the month is still decoupled 
from the Moon b...
• The time taken by the Sun to move from 
one samkranti to the next is called a solar 
month or a sauramasa. 
• The solar ...
• Since the orbit is elliptical, the distance 
between the Sun and Earth varies. When the 
Sun is at perigee ( nearest to ...
• Six months later (around 2 or 3 January) the 
Sun is at apogee (farthest from the Earth). 
• Its angular velocity is the...
• The problem with solar years is that the new 
month and therefore the new year begin 
stealthily. 
• We can indeed const...
Lunar Calendar 
• The Hijri calendar, which fixes Muslim 
festivals, is a purely lunar calendar. In it, the 
year uniforml...
• It was introduced as a reaction to the 
complex luni-solar calendar in use 
previously as an import from ancient Iraq. 
...
Luni-Solar Calendar 
• The luni-solar calendar was introduced into 
India about 100 CE. Subsequently, it came 
to be known...
• Like the Hijri calendar, the Vikrami 
calendar also has a lunar month, which 
begins, let us say, with (the ending momen...
• 1A1 l unar year falls short of a solar years by 
days. Within three years the shortfall will be 
sufficient to permit ad...
• The basic principle of the calendar is this. 
Identify the Spring Equinox. In about 600 
CE, Spring Equinox occurred whe...
• Monitor the samkrantis and New Moons. 
If there are two New Moons in a solar 
month, repeat the lunar month. 
• If no Ne...
• The Siddhantic length of the tropical year, 
from Spring Equinox to the next, is very 
inaccurate. It is 0.1656 days too...
• It now falls on 14 April; there is thus an 
accumulated error of 23 days. In future, it 
will be occurring still later. ...
• Vikrami calendar is a twin-track calendar. It 
keeps track of the samkrantis as well as the 
New and Full Moons. Normall...
• We then count the lunar month twice. The 
first one is called adhik masa ( extra month) 
and the second shuddha or nija ...
• This month is then deleted as kshaya masa 
(decayed month). A Vikrami year cannot 
have less than 12 months. Therefore, ...
Festivals 
• For ease of calculations, a lunation is divided 
into 30 parts called tithis. They are of unequal 
duration. ...
• That is why at times there is controversy 
whether the festival is today or tomorrow. 
• There is a Hindi phrase, meen m...
• A lunation is divided into two parts, called 
pakshas 
1.The period from amavasya to purnima is 
called shukla ( bright)...
• Vikrami new year starts with the ending 
moments of the amavasya preceding the 
(theoretical) Spring Equinox. 
• The fir...
• Each of the nine tithis is addressed to a 
different deity. In particular the ninth tithi is 
celebrated as Ramanavami. ...
• Since both Good Friday (just preceding 
Easter) and Ramanavami are related to the 
Spring Equinox, the two holidays occu...
• The eighth tithi of the new month is devoted 
to Durga. After the Navaratri is over, the 
next day Vijayadashami is cele...
• The purnima following Deepavali is 
celebrated as Guru Nanak Jayanti. 
• Note that Buddha Jayanti also falls on a 
purni...
• The last Shivaratri of the year would of 
course be a tithi before the first Navaratri. 
The one prior to this, that is ...
To sum up 
• Mahashivaratri is related to the last but one 
amavasya of the Vikrami year. 
• A fortnight later comes Holi,...
• Six or seven lunations later comes the 
Ashvina amavasya which marks the 
beginning of Autumn Navaratri. (*2012, eg, 
ha...
• Independently of the festivals associated 
with lunar phases, Mesha samkranti 
(Baisakhi) is celebrated as Spring Equino...
• So far we have spoken about the Sun and the 
Moon. In passing we may note a festival 
associated with Jupiter. 
• Its en...
• There are in all four Jupiter-related celebrations, 
three rashis apart. 
Place Jupiter in Sun and Moon in 
Hardwar 11. ...
• The seasonal festivals are all associated with 
the astronomical position of the Sun. The 
unstated assumption was that ...
• As pointed above, the Vikrami calendar 
today has an accumulated error of 23 days. 
There is need to rectify it to bring...
Conclusion 
Traditional festivities and commemorations 
are a multi-dimensional thing. My aim has 
been to draw attention ...
Thanks
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Astronomical basis of Indian festivals

  1. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 13. • The mismatch has been dealt variously, giving rise to three main annual calendars: 1.Purely Solar 2.Purely Lunar 3.Luni-Solar
  14. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 51. Thanks
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Hindu, Muslim and Christian festivals have in many cases obvious astronomical connection

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