Science behind Indian festivals

Chief guest’s address delivered at Pushpa Gujral Science City, Kapurthala

  on National  Science Day, 28 February 2009


Science behind Indian festivals


Rajesh Kochhar

CSIR Emeritus Scientist

Indian Institute of Science Education and Research Mohali

 MG SIPA Complex,  Sector 26, Chandigarh 160019

[email protected]



The year 2009 has been declared by the United Nations as the International Year of Astronomy. The declaration is in honour of the first ever astronomical use of telescope by Galileo exactly 400 years ago. The telescope changed the human perception of their natural environment for all times to come. Telescope and microscope permitted human beings to see things   which were not part of every day experience. Astronomy today is a child of high technology. The Universe has been reduced to a mere ensemble of objects which we study with a view to discovering laws of nature and testing our theories.


 But the sky was not always like that. In the ancient past sky was viewed with awe and respect. Attempts were made to discover patterns  in it so that its wrath could be averted and its goodwill earned. Till relatively recent times, the driving force for human interest in the study of the Cosmos has been fear; first the fear of the celestial gods and then the fear of the waters. Onwards from the 15th century when European sailors took to oceanic navigation, they only had stars for company and guidance, the study of which therefore became a matter of life and death.  Curiosity- driven astronomy is thus only a few centuries old.

Our interest this evening is in that phase of human culture when propitiating the celestial gods and negotiating with them for their benevolence  were matters of the highest priority. A clear distinction was made between what was auspicious ( shubh) and what was inauspicious ( ashubh), and the  shubh times were assiduously worked out. This ritualistic sophistication was an extension of a very practical need, that is to keep track  of the passage of time. Time was cyclic; the Moon went through its phases and  seasons changed and returned.  But time passed and never returned . Understanding the complexity of time and pondering over its nature constituted the earliest philosophical and intellectual exercise undertaken by human beings.


Such a study has a contemporary significance also, because many of our extant cultural and social practices are a continuation of the times long gone by. Paradoxically while these days we are very knowledgeable about the celestial objects and the Universe as a whole, we know much less about the  tapestry of the visible sky than our ancestors did. Today when we want to know what time of the year it is, we look at the calendar. When we want to know what time of the day it is, we look at the clock. We  often forget  that  there was a time when you had to turn to the sky to  know the time.


Let us look at our watches and clocks and  construct a simple clock . This clock will have only one hand  (sui) instead of two or three. It does have a dial , but only with a single mark or digit, say at the location of 12.When the hand is in front of the digit, the counting starts. When the hand returns to the digi, we say that one unit of time has passed. ( In your real watch the time elapsed will be 12 hours.)


We have two famous natural clocks. In the first case, the Moon is the clock hand and the Sun the digit on the dial. When  the Moon is in front of the Sun, it is  New Moon ( Amavasya). When the Moon returns to the Sun , a month has passed. When the Moon is opposite the Sun , it is full Moon  , or Poornima. Since these days the word month is used independently of the Moon , we can use the term lunar month or better still lunation.  A lunation is the period from one Amavasya to the next , or what is the same thing, from one Poornima to the next. A lunation comprises about 29  and a half days.


In the second natural clock, the Sun itself acts as the clock hand. There is no obvious dial digit now. We have to create an imaginary one. The Sun appears to go around the  Earth. This path is called the ecliptic. Any point on the ecliptic can be taken to be the dial digit provided we remember  that we must  return to  the very same point. There are four important points on the ecliptic: (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; and (iv) Winter Solstice ( 21-22 December)  when the night is the longest. Note that these dates are   for the  present epoch and the northern hemisphere. In the southern hemisphere dates remain the same but seasons are reversed. Spring Equinox and Winter Solstice are the two most common starting points for tracking the Sun’s apparent  orbit. The Sun takes  about 365 and a quarter days   from say one Spring Equinox to the next.


Gregorian calendar 

Let us now look at the  most  commonly used calendar in the world. According to it today is 28th February 2009.This calendar is so popular that on 1 January we wish one another Happy New Year as if it was THE new year. We forget that there are many other calendars in the world which start their new year  on  other days. This calendar is some times called the Christian calendar. It is however better to use a neutral term like Gregorian calendar after Pope Gregory who reformed it. This calendar has a very accurate  year length. In it the year has either 365 or 366 days. Although January, February, etc., are called months they have nothing to do with the Moon. That is why the month can have 28, 29, 30 or 31 days.


In this calendar to keep track of the passage of time we must actually count the number of days. For convenience the year is sub-divided into 12 months, but their length is arbitrary. We could have had a month of 36 days if we so wished. As far as the Gregorian calendar is concerned, the Moon is totally irrelevant. Even if the Moon did not exist the calendar would function in exactly the same way as now. Gregorian calendar is  (purely) a solar calendar. 

We can construct a solar calendar in another way, where the month is still decoupled fro the moon but now has astronomical significance. Divide the ecliptic into 12 equal parts. Each is called a zodiacal sign or rashi. Sun’s entry into a rashi is called Samkranti. The solar year would then comprise 12 Samkranti months. 

There is a good reason why a solar year has 12 months even if these months are independent of the Moon. Seasons return with the solar year ( 365 days). During this period there occur 12  lunations (  that is 12 Amavasya’s or Poornima’s)

 The problem with solar year is that the new month and therefore the new year begins Chori Chori Chupke Chupke. The fact that the word month comes from the Moon tells us that originally the Moon  was the month-maker. We can indeed  construct a calendar which dispenses with the Sun as the clock hand and instead utilizes the Moon. The Sun of course remains in the picture as the digit on the dial.


Hijri calendar


Hijri calendar is a purely lunar calendar. Muslim festivals are fixed according to it. The year  uniformly consists of 12 lunations  adding up to  354 days. The Hijri year is decoupled from the Sun. That is why Muslim festivals systematically slide through seasons.


Vikrami calendar


The Gregorian and the Hijri calendars achieve their simplicity by using  either  the Sun or  the   Moon  as the colck hand. The Vikrami calendar on the other hand insists on employing both. That is why it is complex and can be very confusing to a layperson. 

Like the Hijri calendar the Vikrami calendar also has a lunar month, which  begins with (the  ending moment of) Amavasya. But while the Hijri year consists uniformly of 12 lunations, the Vikrami calendar some times makes the year of 13 lunations. The  festivals therefore show deviation from seasons  but it will  always be less than a lunation ( 29 days). Christmas  falls on a fixed day of the Gregorian calendar ; Eid can come any time in a year  while Divali  falls within a narrow range of days.

 The  solar reference point for the Vikrami calendar is the Spring Equinox, which  currently occurs on  20-21 March. Because of wrong year length, the Vikrami calendar  at the present epoch nominally considers 14 April to be the Spring Equinox. The first month of the Vikrami year must begin before this date , on   New Moon. As already noted the year can consist of 12 or 13 lunations. There is a prescription for doing so. Also note that even when the year has 13 months there are only 12 month names. A name will therefore have to be repeated.

 Vikrami calendar is a twin-track calendar.  It keeps track of the Samkranti’s as well as   Amavasya’s and Poornima’s. Samkranti’s are the more important because they are directly related to seasons. Normally between two Samkranti’s there would occur an Amavasya. Some times it happens that  between two neighbouring  Samkranti’s  there are two  Amavasya’s instead of one.  We then count the lunar month twice; the first  one  is called Adhik Masa, pronounce Maas ( extra month). Conventionally  celebrations are reserved for the latter one, which includes a Samkranti . On very  rare occasions there will be  no Amavasya between two Samkranti’s . This month is  then  deleted as Kshaya Masa ( decayed month). A Vikrami year cannot have less than 12 months. If one month is deleted, some other must be repeated.




For ease of calculations, a lunation is divided into 30 parts known as tithi’s. They are of unequal duration. Assigning a civil day to a festival calculated for a  tithi is based on a complicated prescription  A lunation is broken into two parts, called Paksha’s The period from Amavasya to Poornima is called Shukla ( bright) Paksha, because the Moon becomes brighter night after night. The period from Poornima to Amavasya is called Krishna ( dark) Paksha


A Vikrami new year starts with Amavasya preceding the  Spring Equinox theoretically taken to occur on 14 April. The first nine days of the first month ( strictly speaking the 9 tithi’s) , 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. Each of the nine tithi’s is addressed to a different deity. In particular the ninth tithi is celebrated as Ramanavami. Easter is a Christian festival still connected to the Moon. Easter falls on the Sunday that comes after the calculated Full Moon  on or after the Spring Equinox.  Since both Easter and Ramanavami are related to the Spring Equinox, they 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 Shradha, pronounced Shraadh. The eighth tithi of the new month is devoted to Durga. After the Navaratri is over, the next day  Dussehra or Vijayadashmi is celebrated with great enthusiasm and fun. Note that if Dussehra 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 or Divali. The Poornima following Deepavali is celebrated as Guru Nanak Jayanti. Note that Buddha Jayanti also falls on a Poornima. Deepavali is probably the only festival associated with New Moon. 

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. This day is devoted to Shivaratri. The  last Shivaratri of the year would of course be the one just before Navaratri.The one prior to this is celebrated as Mahashivaratri. The Poornima  after this is Holi; it is the last Poornima of the year. With the Amavasya after this begins the new year.The astronomical context of these festivals is obvious. It would be interesting to learn about the fixation of  the tithi’s of other festivals like Gansh Chaturthi, Krishnashtami,etc. 

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 Kumbha mela. Since  Jupiter’s orbital period is  about 12 years, the main Kumbha  celebration returns after this period.

 Finally we may make two observations. The seasonal festivals are all associated with the astronomical position of the Sun. The assumption is that Earth’s climate plays no role. This was true in the past when human beings lived in harmony with nature.. Not any more. Man made activities are now profoundly influencing the environment. 

 As  pointed above that the Vikrami calendar  has an accumulated error of  23 days. Lohri should fall on about 22 December and Baisakhi on 23 March. There is urgent need to apply corrections to the Vikrami calendar to  make it agree with the actual, observed, sky.

( Spelling of Sanskrit words employed  here does not follow any consistent pattern. An apostrophe has been added in the plurals of Sanskrit words so that the original word can be identified unambiguously. )


















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