 As I mentioned that first few minutes I will use the software with me for explaining the ideas of positional astronomy. What I will show you that the real sky as you see observed from Kanpur campus at different times how it was 46,000 years back, how it will be tomorrow all these things you can get. So I think then after those ideas of movement of the sun, planet and the stars clear we will move on to the topic. Say I think Bhattikothara Banke if you see that if you look towards east you see the stars, planets everything goes you know and at from latitude 23 degree north it will appear to be like this. So and this line these lines are actually the various meridian lines these are the longitudes or meridians and the other lines are the latitude lines and this is the ecliptic as you can see this line is ecliptic and the cricket sound is actually the software cricket because it is night time and say for example if I give the time as 21st March 2015 for example you know it is the vernal equinox period. So what will be the location of the sun? Sun will be at the intersection of the ecliptic and the celestial equator. Celestial equator is this line I think which is starting directly here and goes this is the celestial equator and this line is the ecliptic this is sun. So computers can do many things I can rotate the solar system in the opposite direction. So you can see now I think sun is going to set in the west. So this is the sun you can see it is on the ecliptic directly on the ecliptic and most of the planets we will find will be around these two. Now let us go back to nature. So this is approximately a time you will find I can adjust the time and you will get the idea say I want to go to the vernal equinox day so that means it will be March 21st. So you see that then sun will be at the junction point as you know already. So junction point and this is the ecliptic and you will see that sun will rise exactly on the east that is very important because it is an equinoctical day isn't it 21st March because it is on the celestial equator and of course on the ecliptic. So you will find and this is the ecliptic and you will find when it meets this position east you will find sun is there. So and this is I think Saturn all the planets you will find Jupiter you will find they are very near to this ecliptic because they are all in one plane in which they revolve around the sun. So you will see that sun will rise at exactly on the east. Similarly you will find that when on the winter solstice day sun will be on the southern most end and again on the summer solstice day it will be on the northern most end because the location of the sun is already on the ecliptic and wherever ecliptic is meeting the horizon the sun will rise there. So I think that particular junction point I was mistaken I think some of you should have told me that you are wrong sun is not going to rise there, sun is going to rise there now. So that junction point was when in the Dakshinayan period you could see that it was the ecliptic was coming from north to south and I did I gave as 21st March so it is the vernal equinoctial point. Now you will find the vernal equinoctial point and sun will rise there. Can you see the sun is rising. So this is the equinoctial day. If you give your summer solstice day you will find it will rise exactly on the sun will be extreme end that means it will be the extreme left hand side hills that means extreme north and sun is there. So this is the extreme point of the ecliptic. Now if you this is you are observing the whole thing from an attitude of 23 degrees north. You can change that also and then you can see that if you are on the equator how it will look. So if you make 0 latitude. Now you see that celestial equator is straight going like that blue line and this is the ecliptic and it is symmetrical. Now you are getting the whole thing is rotating as if it is from going in the vertical direction because you are on the equator and this way you can see many things as I will show you. Now this is the present situation. So there is nothing unusual about it. You can see that all the planets are on the ecliptic or very near the ecliptic sun is always there. You have seen also that how the equinoctial point or the solstice point can be seen here. Now suppose you want to see the northern direction that means if you see towards the pole formal definition of is there was actually very recent in Presidency College a project was given to the students and one student came to me that the sun rises in the east an article on that. So I found that you know it is very interesting. See speaking east direction is where the celestial equator meets your horizon that is the exact point east but sun does not rise there that is the problem. So now you see if I am at the our latitude we should correct because you are at Kanpur otherwise sitting at equator you cannot see the north pole so easily. So if you see the northern direction you will see the whole sky is rotating about one point where we have a very nice star we call it Polaris is not it and but if I go to say 6000 years before how it will look you will find because these are important I will come to the discussion of the pre Siddhantic astronomy some of these things you will find will come there and that is why it is better that you see how it was actually suppose if I now give the date as minus 4000 something that means BC oh that is you find that there is nothing like a north pole here is not it or north pole star pole star because that point which is actually imaginary point where the axis of rotation of earth meets the celestial dome there is no star. So you will see when I come to the description of the pre Vedic or other yes early Vedic description it matches this when you come to approximately at a later time then you find there is a pole star is not it that is Subang and at that time all the civilizations they use this particular star as the indicator of the north and the directions even the major pyramids of the Egypt or the orientation of the major structures in Harappan and Mahanjodaro those settlements they were matching this. Now when you again go to a later period can you identify where is our actual pole star at that time where is polar is this is polar is this is the pole star actually the Kochab and also this line joining Egyptians they use that as the north and the direction at when it is just vertical that of course is a different lecture I do not want to go into that it will take time. But now let us see what happens when we go to a later period say 1500 BC Mahabharata time say again you find that truly speaking there is no pole star and when you again come to a much later period then gradually we are getting polar is nearer but still not as a pole star but when you come to more recent time or then you again get the pole star not exactly but more or less and if you come to current time it 19th century 28 is very much near the. So you can see these are the things which you will find I will show very soon when I discuss but I hope now you have some better idea than yesterday that exactly what positional astronomy indicates what is the ecliptic the suns rising point at different times of the year and so on. Now of course again I will I am not showing here the intersection point of the celestial equator and the ecliptic two very important points the vernal equinoctial point that also shifts it can be easily seen you know but where the vernal equinox is there today 3000 years back it was a different point that is why Indian scientist or rather astronomers they use the nirayana system to avoid confusion by suitably choosing a particular time or year as the zero precision year. But that means which year the vernal equinox was at the point at the beginning point of the sign areas but the western system is always using the vernal equinoctial point so it shifts okay now I think let us start our today's topic I will come back to this software again later I will need it some for some very interesting things later as I told that pre siddhantic astronomy again can be divided into three main periods one is pre Vedic period pre Rig Vedic period actually in a sense second will be the Vedic period and last will be Vedanga period Vedanga Puranic and all those periods the pre Vedic period also many people you can call it as a prehistoric type that means it is it is a prehistoric and almost in the border of proto history. So the tentative time frames which have been told by many scholars who did research in the recent teams not the 19th century research the pre Vedic period is before 4500 BC Rig Vedic period is this then Atharva Vedic period is this Jeju Vedic period is this and Upanishad as etc this the Puranic literature also comes here. Now of course it has been done of course it violates the theory of Max Muller's Ariane invasion and now many indications are coming that the Rig Vedic period and the Harappan period they are contemporaneous you know and so I think this may look a bit strange but that is what you will see why Rig Veda has been dated like that we will come to that the descriptions in Rig Veda itself will lead to this date. Now the prehistoric period I told something yesterday that the earliest settlements or township we have discovered in the subcontinent is at Mehregar which has been dated by archaeologists as 6500 BC and that was considered to be one of the largest settlement in antiquity. No settlement so old has been found anywhere else so far. The existence of ancient civilization on the banks of river Indus was discovered in 1920s you all know that and was given the name Indus Valley civilization very obviously I was subsequently in the later period particularly starting from 1950s you know what happened that there in the Rajasthan there are many legions that you know there is to be many towns many cities etc but it is all desert now. Hearing all these things that the one he requested Pandit Jehala Nehru immediately after independence of India to grant some fun to the archaeological survey so that they can really find out whether there is any truth behind these legions and rumors. So the first director general of archaeological survey of India that Indian director general after independence was Amal Ananda Ghosh. So he was granted a project by Pandit Nehru first prime minister of 10,000 rupees he was given a big jeep and some assistance one of them was Devala Mitra also quite well known and they then investigated and found out lots of settlements under the sand. Subsequent of course many Harappan settlements Harappan settlement I mean settlement under of that civilization has been discovered very large number their number now the settlements belonging to Harappan civilization more than 3700 and a majority of them are actually on a dried bed of river which now many or most of the scientists are identifying with the lost river Saraswati. I am quite sure Prof. Michel Danino gave a lecture here is not it? So you might have listened to his book is also wonderful. But the research on Saraswati started in the 19th century itself and lots of scholars both from Europe and in India they researched on that and Michel Danino's book is one of the excellent one I will say. So many are nowadays calling that Vedic Saraswati or rather the civilization as Sindhu Saraswati civilization and like that. So this is quickly I am quite sure Danino also showed you that this is actually now the region which was covered by Harappan civilization. It is almost the whole area is like a major part of western Europe it is pretty large. This Harappa and Mohenja that over the initial discoveries but then Mehrgarh is here then this is Garneri Bala then Kali Bangan is a major site. Dhola Vira is here then I think Lothal is somewhere here. So many sites have been found one of the site here Kunal here is side here. Now they are finding settlements which have been dated by carbon dating to more than 5000 BC you know and very interesting thing I think Danino's book says that you know the later Harappan period all the sites were shifting to the east because of the onset of the arid climate you know rainfall change. There is a major change in climate and the whole area was becoming a result you know. Anyhow so the obvious astronomical phenomena in those days Harappan civilization was a very developed civilization most of the Harappan cities are much better than Kanpur city I can tell you that. The cycle the change of day and night is something quite obvious even an aboriginal will realize that. Periodic changes of the shape of the moon also attracted their attention which is also pretty obvious. Link of the ocean tide with moon phase was also familiar to the people who were living near the coastal regions. The rotation of the celestial sphere about one star or near about one star was also noticed that is they found that it is rotating about one point which is not moving much. Then the motion of the moon and the sun along the ecliptic was noticed later that they are shifting their position in the background of the fixed star and then link of the seasons with the positions of the sun that also they found out after long observation and they also align some important structures based on astronomical directions and so on. Now as I just showed you that about 3000 BC we had a pole star like Thuban I just showed you and but subsequently again it shifted and there was no pole star till about 1500 or 1600 or 1700 AD really speaking again we had another pole star. So this thing was also noticed by the people that there is a star which could be used for making the northern direction. Now I think the earliest evidence of some astronomical observation is found at a place called Hanamsagar I told you yesterday in Andhra Pradesh or now Telangana. So what they have found the stones have been kept large stone at the gap of about 120 meter and so therefore there are all the in total 50 stones and each stone was I think 10 stones 120 mean each stone about 12 meters so and in a square shaped. So from this point there is something some marking etc. Now you see this is the west direction this is the east and this direction was considered to be the sunrise on the summer solstice day. It is pretty obvious if you see that this is equal to 1 and this is half isn't it. So this angle is theta tan theta is equal to 0.5. So how much is theta about 26 degrees I think something like that. So and at that latitude when you are in on equator the extreme distance of the sun in summer solstice is 23.5 degrees but as you move towards north the extreme point shift towards north and here it will be around 25 26 degrees. So really speaking the sun will appear to rise along this direction in summer solstice day. Similarly on the winter solstice day sun will appear to rise on this side of the horizon. Similarly here the moon's extreme positions you know moon varies little bit this way that way. So they also had some stone and they thought that these are the indicators of extreme positions of the moon which is of course less correct but these were quite reasonably correct and few other this is not like home stone has not that publicized. So you may not have heard about it but this is a very early observatory you may say in the prehistoric time. Then I think as I mentioned that one of the interesting thing it is found that is in Kashmir valley the name of the place I just want to tell the rock art at called Burjahan in Kashmir shows a figure with two sons a hunter killing a deer a dog. The two sons almost side by side have been interpreted as the sun and a supernova because otherwise it is impossible supernova is the only thing which can be visible even being here sun and examining the David Green's online supernova catalogue it is found that is supernova occur near the ecliptic so that it can be seen near the sun around 5000 BC. So it is about 7000 years old some observation which was recorded by because it must have been very unusual thing. So even if you today you find tomorrow morning that there is another sun near the sun you are going to put it on your diary or your computer or laptop everywhere you will say that you will put it in your Facebook I am quite sure of that. So I think this is one of the earliest thing and the date also matches that around 7000 years back there was a supernova very near the ecliptic so that it could be seen very near the sun because sun moves along the ecliptic. So at some day it will be very near the supernova because it is visible for couple of weeks you know not this not this that this drawing is not that I have not put that you know it as I mentioned that is a rock art from Kashmir this is actually a seal from Harappan settlement. Now many have interpreted this as the 7 this is because two major persons work on this is Ascoparpola and Asfak. So I think according to a Parpola who is a Scandinavian scholar very well known scholar he identified these as seven sages at the bottom of the seal with the seven stars of Saptersimandl which is a very prominent consideration most of us who are not aware of the others but Saptersimandl, Cassiopeia and Orion we all understand we know that. But of course Asfak thinks that these seven are the seven stars of the constellation or other asterism Krithika I will show you Krithika later and Krithika was a very important star because you will see another I will show with the software long back during the Vedic period Krithika used to rise exactly in the east and it was mentioned how the sages noticed all these things is that the sages were not like IIT students or faculty members they used to get up very early in the morning go near the bank of a river or a tank for all kinds of sacrifices and offerings they used to call it as Brahmamurta and they used to see the heliacal rising of the stars and others heliacal rising means the heavenly bodies which rise just before sun comes up and everything becomes light you cannot see anything after that. So there they saw that this particular asterism used to rise exactly in the east they have mentioned it you will see later when I go to the astronomy part because it was the deity of fire the Krithika and fire was a very important thing even today bear many people bear the title Agnihotri it was a very pious and important occupation to maintain the fire with purity you do not have a matchbox and you just do that it was not possible you know. So this he thinks asfak he thinks that it is the seven stars of asterism Krithika but that is besides the point now as I mentioned yesterday there are some bones and stone pieces with 30 marks of different lengths showing the phases of the moon in a lunar mark that have been also been found. So astronomy was definitely a part of life it has to be because such a advanced civilization it cannot do without the astronomical thing particularly it was an agriculture based civilization as you all know and agriculture means dependence on season and flooding of Nile used to be a very not Nile following of this river Nile or Indus sorry used to be a very important part actually Manjidaro has been ravaged by the flood of Indus many times it has been recorded. Now I think let us go to the astronomy during the Vedic period because pre Vedic period that is Harappan and others we have not been able to read the script so we cannot decipher much. The astronomy during the Vedic period again can be divided into four parts the Vedic period includes Rig Veda which starts at 4500 BC and ends at 2400 BC Jejur Veda is there Atharva Veda has a long period because its particular nature was such it was for a longer period and Upanishads came later. The number of verses in the four Vedas you know these are some common general knowledge Indians should have because you must be very proud being an Indian to have the oldest possible literature in the whole world. Rig Veda is considered by everybody in the world to be the oldest literature we have and the reason why it has survived though many other texts we have lost primarily because it is a religious connotation whenever something is religious you know you protect it. So Rig Veda and the other Vedas have survived primarily because they were considered to be of religious significance. Rig Veda has 10,522 verses Jejur Veda 1984 verses Sam Veda 1875 and Atharva Veda 5977 in total the four Vedas contains 20358 verses. Now the important thing what I think I will mention here that these Vedic literature there are many astronomical references and other kinds of descriptions which help us to date them and I will show you. Now the primary heavenly bodies which are known in Rig Vedic period which we mentioned we find the sun, the moon, planet Jupiter and planet Venus and in Rig Vedic Sanskrit planet Venus was called Vena meaning daughter of the sun and whether it is the same Vena which has become Venus in Hellenistic astronomy we do not know but it is a very interesting coincidence. The moon's daily positions were recorded and 27 groups of stars as I mentioned yesterday which were called Nakshatras were identified and thus the Nakshatra based astronomy in ancient India became developed. Now the study of the astronomical references in Rig Veda indicates that the sages were aware of a few astronomical facts that also you should mention here. There is one sun earlier there was a confusion because sun is rising every day is it the same sun because there are many civilizations where it was considered there is not one sun, sun is going down getting clean etc and it is coming up next day but Rig Veda it is that basic period it was known to the sages that there was only sun and it is also mentioned that it supplies all energy and light to us. The moon's luminosity was because of the reflected sunlight is also there. Oceanic tides were caused by the moon of course it is not very difficult because with the moon's phase you see the tidal phenomena say they also notice that earth is round and freely floating in space was also another knowledge the Vedic sages knew and it is also mentioned that sun neither rises nor sets. Now before I go further what will be important to say that what are the kinds of Rig Vedic references in astronomical references in Rig Veda and how you use those for dating. So I think let us go to that. So you see that day and month which is described in Veda one civil day or called Savana day was from one sunrise to the next sunrise and I mentioned in the last class that it is slightly longer than a true period of revolution of the earth because if you take a fixed star in the sky use this board quickly this is earth and this is sun. So it is rotating and say this is the point where you are so if sun remains fixed when you find one sunrise to another sunrise it is exactly your period of rotation but by that time sun has moved here. So you have to rotate some little bit extra to get the next sunrise isn't it very obviously that is why these two periods are somewhat different the sidereal rotation period of the earth and the sunrise to sunrise a civil day they are not the same time it is very clear from this. This is called the Savana day one full moon to next full moon was a lunar month and again I told you that it is slightly more than the period in which moon makes a rotation around the earth that means going from this one set of fixed stars in the sky coming back to the same set of fixed stars that period is less than one full moon to another full moon that also I explained is it necessary to explain it again. So therefore the lunar month full moon to full moon and in Rig Veda time the moon used to be called Masa. So a full moon that is a Purna Masa meaning a compression of a month because the full moon to next full moon and that is why we get the word Purnima, Purnimasa and ultimately the Masa also became the word for the month. So this Purnimanta system that one Purnimata to next Purnimata this is the Purnimata system for lunar month was changed in the subsequent period from Amanta system that means one new moon to next new moon. One lunar month was divided into 30 units that is called tithis that is also typically Indian system and full moon and new moon played very important roles you know in everything. So what they did now full moon is actually an instant of time isn't it? Full moon indicates a position of the moon exactly opposite to sun but it is an instantaneous phenomena full moon cannot be a whole night thing. So to indicate that point what they did they treated the Purnima and new moon that means the Amavasya as two days. So the full moon day is to call Raka and day before that is to be called Anumati and the junction between the two was the real full moon. Similarly new moon was again to two days the day before used to call Senibali and the next day used to call Kuhu and Senibali and Kuhu junction point was the real Amavasya. So they are very particular about these two things and that was the Vedic system of identifying the moment of real full moon and real new moon. Now five year Juga system is a very interesting thing. So therefore you know for if you are an astronomer of that type yeah please I will come to that only now no no no that they did not know no no no they they thought that all those things are really moving if somebody is taking more time somebody is taking less time it is its business the real kinematics they did not know. So I think you will find now I will come to that as you are saying that this created a problem for Indian astronomers and it became a far more complicated thing than the other system. Now in ancient Indian astronomers notice that the sun takes a little more than 365 civil days to complete one cycle along the ecliptic. So I think they approximately will find in Vedanga Jatish it is considered as 366 days but they knew it is more than 365 days but less than 366 days. They also noticed that the seasonal changes were linked with the sun's position they noticed that. So a purely lunar system which constituted of 354 days that is 29 and half day is a lunar month and multiplied by 12 is 354 days civil days. So since the lunar day is 30 days you know and that is a month but actually it is 29 and half days solar day. So total number of civil days in 30 or 12 lunar month is only 354 days. So therefore it does not match just now as Varma is saying that the total period of the moon and total period of the sun they are not commensurate they do not match and that makes the difficulty. So you know in the Islamic calendar they depend completely on the lunar system no question of bringing sun very pure system only thing what happened that things keep on rotating. So you get throughout the year you will find that Maharam is in summer or sometime it is in spring sometime it is in the autumn time. In the Hellenistic astronomy or the western or European system it is purely dependent on sun. So their calendar is purely solar again no problem. In India we made the system very complicated because our dependence on sun was there because of the season and dependence on moon was there because of all our performance sacrifices all kinds of festival everything dependent on lunar calendar even today everything is done based on lunar calendar t3 etc. So therefore they had to develop a lunar solar system combining the two. The earliest thing what they did remember these were all happening 5000 years back. So the shortfall of 11 to 12 days how do you manage the actually it is 366 but you are with the moon you are getting 354. So what they did that they consider a 5 year Juga system. In 5 year Juga what will happen how many extra days you will get in the solar system 60 and in so what they did that they added two extra intercalary months in a 5 year Juga period. So they developed firstly Juga system meant a 5 year 5 solar year period where you have 32 lunar months and that is how they managed you know matching the two. This in this period both the systems had some integral number of rotations and you could manage and this 12 extra days were taken care of by the 5 year Juga 60 extra days they introduced after 2 and half years of your Juga they will put one extra month. Even now in Indian calendar to match the lunar and solar system we put intercalary month and they are called Malmas you might have heard about it. So you know it has special significance you do not do things in that month and at the end of the 5 year Juga system they will add another 30 days month. So that way whole thing matches and for that purpose the name of each year in a 5 year Juga they gave the 5 year first year of the Juga system was Sambhatsara next was Paribhatsar, next Idhavatsar, then Anubhatsar and Idhbatsar. These were the 5 years in a 5 year Juga system. Then again the cycle will repeat that was the system in the Vedic period they did you know and a Lunisolar calendar was devised to adjust this mismatch as Prof. Burma is saying that how they manage this is the way because they needed both the solar system or solar calendar they also need the lunar thing. Next is also they are also they define Ionals. The sun moving from south to north is called the Uttarayana. You have seen that the ecliptic that intersection point of the ecliptic with the horizon it moves shifts like that is not it. So when it is going in this way it is Uttarayana when sun is there and when the intersection point moves in this direction and sun is there then that is the Dakshinaayana. And in the original time they used to call as Devayana which is from south to north from winter to summer and that or Uttarayana and the other used to be called Pithyaayana or Dakshinaayana. There is another version of course that they say that from Vernal equinox to Atam equinox was called as Uttarayana or Pithyaayana and next was called. And they notice that sun comes from say south to north. Near the end it stops that is why it is called solstice in English or Greek also. So they found it is about 21 days it looks almost immovable. So the 11th day of that stationary period they treated as the solstice day whether it is winter solstice or summer solstice and they used to call these as Vishubhanta days. The route to the exact south, south of the direction was considered as Pithyaayana or direction towards Jamaloka. People go after their death they go towards south and you will find that such pass. You see in Rig Veda it says pass by a secure path beyond the two spotted four-eyed dogs the progeny of Swarama and join the wise Pithris who rejoice fully with Jama. So Jams the Kshindua is known in our tradition. So suddenly direction they had to also find out and they have given a method for that. That method says you know that the two red-eyed dogs as I was mentioning if you add these two stars they will indicate an exactly southerly direction and these two stars are called alpha canis minoris and alpha canis majoris like this. Say 4200 BC the star I will show you the actual thing also. This is alpha canis minoris and alpha canis majoris which is Sirius Lukdak. If you join these two it is almost exactly towards south. South pole is not visible from the northern hemisphere you know from this latitude but these two stars if you join you know they will indicate exactly southerly direction as mentioned in Rig Veda. Now if you do that 2008 this is the alpha canis minoris and this is alpha canis majoris if you join it does not indicate towards south. So if you we go back to our this thing this is this and let us see now the time we will put at which we will give 4200 BC we have reached computer is a wonderful thing. So now you see that if you give the rotation you will find the alpha canis majoris and minoris they will be pointing exactly to the south. So let us see whether we do it or get it or not you have to identify the two stars. Moment you see Orion you can see that you are nearing that and its longitude. Melodian lines are not very nicely visible here after projection. So this is you are looking towards the south pole this is the ecliptic I think we are approaching that you have to identify this is Orion is not it Orion constellation and once you because those two stars are near Orion I think this is alpha canis majoris just a moment I have to stop the universe yeah you see this is alpha canis minoris and this is alpha canis majoris area you join the two it goes exactly to the south and that was mentioned in Rig Veda but then it is possible only such an old time and today the situation is very different now of course somebody may say that it was all a hoax I do not know they do not say names because in those days they they said that four eye dogs two spotted four eye dogs because they are also they are that is why Jamraja is associated with a dog you know and the problem is the coincidence that here also in Hellenistic astronomy it is being called as dog canis means you know dog so how come that this connection you know there that is also very interesting. So 2008 if you go you will find that situation is very different now here this is alpha canis minoris and this is alpha canis majoris if you add the two I think it does not indicate towards south at all so this is also a very important clue that how old the observation is when it was recorded now if you say that people did it deviously by back calculating I think that kind of logic does not hold because nobody will do that but this is something which is there I think let us see the what next we get in Rig Vedic texts or Vedic texts now we come to months and seasons when that means whole solar tropical year was divided into seasons in the Rig Veda initially only three seasons were mentioned in a later texts of Rig Veda there are three seasons were with five seasons were mentioned towards the end all the six seasons were mentioned and in Prisiddhantic astronomy the names of the six seasons were Vasanta, Grishma, Varsha, Sarad, Hemanta and Sisira these were the names in the most early texts of Rig Veda Vasanta word was not there it was called Madhu and the two months of the Vasanta Ritu are Madhu and Madhava Grishma means Shukra and Suchi, Varsha is Navas and Navasya, Sarad is Isha and Urja, Hemanta is Sahas and Sahasya, Sisira is Tapas and Tapasya these are the names of the months and these are the six seasons mentioned in Vedic texts you know in Rig Veda again there are very important reference to Madhu Veda they call it Madhu Veda is a subject knowledge by which you can identify when the onset of spring and they said that when heliocaly the Ashini nakshatra will come up that triangular after two months of the winter solstice day you will realize that onset of spring that means it is one month before the vernal equinox and it is found that around 4000 BC it used to happen that after two months of winter solstice triangle will rise in the eastern sky heliocaly I will not go into showing the software it is taking time. So time units in this time Vedic texts where the sunrise to sunset was found to be divided into 2, 3, 4, 5 and 15 parts when it was two divisions one is called Purvanna other is Aparanna in three divisions the day was called Purvanna, Madhanna and Aparanna and four divisions each period was called a Prahara and the names of that is why we have Astra Prahara you know that means 24 hours. The parts were Purvanna, Madhanna, Aparanna and Sayanna. In five divisions the names were Prata, Sanghava, Madhanna, Aparanna and Sayanna. In 15 divisions again each part was called a Muhurta and there are 30 Muhurtas in a civil day each Muhurta was subdivided into 15 Prati Muhurta with their individual names. So when you specify a time come to the class you know on such and such tithi on this Muhurta and this Prati Muhurta you know that was the kind of thing your time table would have been like that. So a one Muhurta is 48 minutes and one Prati Muhurta is 30 minutes and 12 seconds. Planets, comets and meteor in the later Vedic and Puranic era names of all the five planets are found. Initially as I mentioned on the Sun, Moon and Jupiter and Venus later Mars, Mercury and Saturn were also known. In the early Rig Vedic text there are no mention of any pole star. You see this is very interesting in the earliest Rig Veda no mention of any Dhruvanak Sattva that means it was beyond before 4000 BC then there was no pole star. Then I think the Dhruvanak Sattva is found as a Thuban it took place of the celestial north place then again for sometime Dhruvanak Sattva was there in the Vedic text. Again in the subsequent text you know it disappears from astronomical literature and only it comes as a reference to a previous Dhruvanak Sattva. So you see that you know it was not there then it was there and then again it vanished. So it very nearly nicely matches these days with the kinds of planetarium software you can really match all those things nicely. The Dhruvanak was not at the celestial pole before 3000 BC or 3500 BC and again it lost its premier position after 1500 BC. In the Jajur Vedic era it is always mentioned that Krithika rises in the exact east meaning it was at the equinoctial point because equinoctial all the nakshatras must be on ecliptic is not it? And to rise something exactly on the east it must be also on the celestial equator. So for a nakshatra to rise exactly on the east it means what? It has to be on the ecliptic and also on the celestial equator that means the vernal equinoctial point or one of the equinoctial point but if it is equinoctial point it will go beyond 15,000 BC that is not a very logical time. So within the logical period you know it is found that it was in the vernal equinoctial point and exactly in this way you will find it happened around 3000 to 2300 BC using the software. I am leaving this thing with the computer and Amit will have it any student want it you can give it to them. So in a much later Vedic text it is found that the winter solstice was at the beginning of Maghanakshatra implying 1700 BC. This is the way the researchers now they have the chronology of the Vedic and Puranic texts they have done and this is also very fascinating to note that a three family possessed a special knowledge to predict solar eclipse. Actually it is also mentioned in Rig Veda that they also saw one annular solar eclipse on the summer solstice day and professor P.C. Sengruthar he was a professor of Indian astronomy in Calcutta University. So he did lot of research and found I am sorry that this happened I will discuss this later when I discuss at the anti-pity of this I will not spend time now because I have quite a lot things to discuss. So astronomy during Vedanga period now the earliest text in Indian astronomy which is available today is called Vedanga Jatis. You can find that book anyone who is interested you can find and it is found in two recensions one is called Rig Jatis another is Jojur Jatis. Now how it has remained why it has not been lost is because it was considered as a part of Veda that is why it is called Vedanga and the people have kept it memorizing because it is a part of a religious that is how a scientific text has survived the onslaught of time. So in Rig Jatis it has 36 verses and Jojur Jatis has 43 out of his 30 are common with the Rig Jatis. So in total there are 49 verses and from 19th century the Europeans sorry they have they had lot of difficulty because these are nothing but mathematical algorithms. You can easily get Vedanga Jatis and you can see but ultimately a lot of effort you know they could gradually decipher all of them they found these are nothing but algorithms on the basis of which all the meanings have been discovered and it has been understood. Because of insufficient accuracy Vedanga Jatis also very rough model it was stopped being used long back but it was memorized because as a part of Vedanga or Vedanga that is why it has survived and this is it has been now dated that means again from the astronomical references that it was written around 1400 BC and the location where it was it was also done because you can find out from the time of the relative day long the period of the daylight and period of the night on the winter solstice day and summer solstice day it is described and from that they found it is 34 degrees 50 minutes north which matches with the Punjab region where the Vedas were really composed it is not in central Asia or someplace many people tell you. So this is the way the match the basic framework you know the 5 year Juga system you can see so lunar cycle is on this side and solar cycle on this side and you can see the first intercalary month they have added here and the second intercalary month they have added and so the total number of civil days they have matched number of civil days in a solar cycle of 5 Juga system is how much it is that 1830 and similarly on the lunar cycle also you will find that it is 1830 so that is the way they matched the two lunar cycle and solar cycle and as you see that this is how they tried to solve but of course it is not accurate because again those timings are not exact you know there are fractional things so it changed and the it was a crude solution but it survived their purpose 3,500 years ago and during Vedanga Jatish period Purnimant system was already replaced by the Amanthamarth system the sun's motion that was two major calculations are given in Vedanga Jatish one is the sun's motion other is the moon's motion you have to calculate both the relative position of the sun and moon in one year sun traverses a 27 nakshatras if you consider the if you do not take the precision of the equinox precision of the equinox makes the tropical year and sidereal year slightly different because by the time sun comes back to approximately same position the axis of the earth has rotated slightly maybe a fraction of a degree a fraction of a minute actually so therefore just before that the winter if you start from winter solstice the next winter solstice will be slightly before that because earth's axis has rotated slightly in the western direction so that the small difference is there but I think it is quite obvious they really did not notice that they treated the tropical year that when sun comes from one vernal equinoctial point the next vernal equinoctial point because it was easier for them to identify an equinoctial point than solstice points obviously so this and during the whole ecliptic because that was their only reference line ecliptic along with the moon sun all the planets move 360 degree of ecliptic it took 27 nakshatras and again one year where how many lunar months 30 lunar months so 30 lunar day sorry 12 months and 30 lunar day or tithi in every lunar month so 30 into 12 plus 12 why this plus 12 tithis come because there are extra days the when you take lunar month which is 29 and half days civil days so again it does not match so they had to add this 12 so total number of tithis in a civil year solar year is 372 tithis so the sun traverses one nakshatra in so many tithis divided by 27 so therefore this 124 by 9 tithi and one nakshatra they divided again this is a spatial division they divided into Bhamsa 124 Bhamsa and that is one nakshatra span and one nakshatra is approximately 13.3 degrees so in one tithi the sun travel through nine Bhamsa that is the angular displacement of sun in one tithi one nakshatra is 370 degrees by 27 so 13.33 of the ecliptic so one Bhamsa is 13.33 degrees by 124.1075 degree of the ecliptic that was the spatial division yeah that was temporarily they did but there is a lot of confusion it was used 28 only for a very short period then it was dropped again because nothing was very accurate they were all the time trying to manage with integer numbers but it does not work you know they are so so therefore sometime it is there sometime it is not there so the 27 nakshatras in Vedang of Jyoti which are mentioned I will not read 27 names are there you are all familiar all the panjikas like say Ashini, Rohini, Poonar Vasu then and the modern names are also have given the original nakshatra and the modern names like Ashini is R.E.S this Rohini this Rohini is Tauri and Poonar Vasu is something here Moga is Leonis, Hastai is Kri, Visakha is Libra and so on. Now I come to the 12 months in a year how they manage to name them identify them as I mentioned in the last class itself that they gave the name of the month based on that which nakshatra the moon is having its full moon shape and they found this system they started and we have stuck to the same names though we do not follow the same methodology. So when the full moon is again Visakha nakshatra the name of that month they gave Visakha then when the next full moon takes place it is against the nakshatra jestha so the month name is jestha so that way you get the names Asara, Sravana, Bhadra, Ashini, Karthik, Agrayan, Pous, Magha, Falgun and Chaitra. The 12 names in Indian system it is very scientifically given whereas in the western astronomy the names of the months are not that and the distribution of time you all know that why February has 28 days you do not know. Augustas wanted that Julius and Augustas you know they both wanted to have at least 31 days in their month so they consume some extra days there so the place where it had to be taken away was February. So I think this is the system Indian earliest Indian system of identifying the months. So the terminologies in Vedanga jethis solar year the time sun takes to go from one vernal eukinox to the next day is a civil day the duration of sunrise to sunrise lunar month the period from one new moon to the next new moon solar month the solar year is divided into 12 equal parts that is all. It was not of much use they did not use this much. Lunar day or tithi was very important because that was which was visible directly. Lunar month is divided into 30 tithis. Paksha is 15 tithis from new moon to full moon is called Sukhla paksha and the next one is called Krishna paksha and there is another term is Parva it is the angular distance which is traversed by the sun along the ecliptic during a paksha is called the parva. So paksha is a temporal thing parva is a spatial thing that you have to keep in mind. Time measurement and division time measurement was done using a cleft cedra the following units were in use during Vedanga jethis period. 50 pala is one adhaka, 4 adhaka is one drona that is equal to 200 pala equal to 64 kurava, one kurava is 1 by 16 adhaka. Do not ask me questions one drona is 3 kurava is equal to 4 adhaka minus 3 by 16 adhaka is 61 by 16 adhaka is one nadika. Furthermore, there are other units like one muhurtha is two nadika and one nadika is equal to 10 plus 1 by 20 kala. One day is 30 muhurtha as I mentioned earlier that is 60 nadika that is 603 kala some final divisions one kala is 4 pada that is 12, 124 kastha, one prastha is 4 kurava, 4 prastha is one adhaka, one prastha is 12 and a half pala or 4 by 16 nadika. Then using one civil day equal to 24 hours in modern time ancient Indian time units are like this one day is 24 hours, one muhurtha is 48 minutes, one nadika is 24 minutes, one kala is 2.4 minutes, one kastha is 1.1 second and some still very final units of time I mentioned in Vedanga Jatish one that says 10 matra is one kastha that means one matra is 0.11 second. Another very small time unit in ancient text is found as truthy that is 0.0003 second it is not known for what purpose they had this unit. These are the time units they are all mixed up you can see and the moons motion the basic parameter how they did that these are the sun and moons motion they are most important. The number of synodic lunar months in a Juga is 62 and number of lunar cycles in a Juga will be 62 plus 5 extra because of the extra time they had. So in total 67 lunar cycles in a Juga of 5 years. So in a 5 year Juga there are 366 number of days in a year into 5, 1830 civil days or savanadin the moon moves through 27 nakshatras 67 times in a 5 year Juga. So the moon traverses through 27 into 67 or 1809 nakshatras in one Juga. So in one Juga there are 1830 into 603 kalas because each nakshatra spans with 603 kalas. So the moon takes 1830 into 603 divided by 27 into 67 or 610 kalas in one day and 7 kalas one day and 7 kalas to cross a nakshatra. So this is the way they tried to work with the moon's motion. In Mahabharata that is much later period you know they it is found that all the planets are mentioned even their retrograde motions are observed that is called bakri. Mangal is in bakri you know that is mentioned you know and garga was subsequent to Parashara. So Mahabharata is dated between 1500 to 1900 BC Parashara is believed to belong to 1800, 1100 to 1300 BC and garga is little bit later. In Mahabharata there are many reference to 7 planets but no mention of the 7 day week. There is evidence that the motion of the planets like Saturn, Jupiter, Mars, Venus and Mercury are well studied and ample references are made to commits and eclipses. Parashara Samhita is available in fragmented form. Actually you know all Vedas also used to have each Vedas two major parts Samhita and Brahmana. Samhita is to be with the philosophical part, Brahmana is to be the more practical parts. So Parashara Samhita is available in fragmented form and the most interesting thing is that the text is in prose. That is a very unique thing. It is very unusual to get a prose form text in ancient literature. There is no reference to the zodiacal signs and Parashara Samhita states that the cycle of Venus to be 591 days whereas the modern average value is 584 days only 7 days difference. And sidereal motion of Saturn is studied and the period of revolution is mentioned in this 28 years which is also very correct. 100 number system. I am not getting maybe most probably they are not no decimal things. Decimal came much later from the Bhaksali manuscript which is found in mathematics experts must be here. Maybe they used only integers. That is why you will find when I come to even see Dhanthik text you will find that they always use large number of integers which are nothing but the LCMs kind of thing. So what I think it was a very crude system you can realize that 5000 years back the observation was a very crude observation. It served their purpose identifying the seasons etc and taking care of the various sacrifices etc these jaggas these that is to be there it is to satisfy. They are not worried about the setting sending and satellite orbit so that they have to be very accurate that is why it is very peculiar how why they had such a small time in it that is of course much later Vedanga Jatish much 3000 years later. So I think 101 comets are discussed and actually it was found that they also identified some comets came back again and again. And since the period of comets are pretty large their observation periods must have been very large they used to name the comet after that astronomer who used to identify them and also identify their period. So I will finish it here the session 2 and I have kept something to tell you. Now the details of Moon's motion I have not discussed today because it is slightly complicated and involved so I thought that the book is there and those who are interested in getting more direct and hands on to the calculation procedures. Otherwise here just numbers etc you will not like people will start living. So I think that it is better you consult the book there you will find I have given also not the real detail calculation but whatever is understandable to a common man you know you are not really an astronomer not in that train in that. So for knowing the real calculation procedures of panchang etc you have to really do that but these are actually simplified form I have given from Vedanga Jatish whatever I could extract and there are texts from Vedanga Jatish you can read they are nothing but algorithms each verse is an algorithm and tomorrow's class I will discuss something that how Indian astronomers developed a compression technology you are nowadays you do compression technology in computer their compression technology was fantastic and tomorrow you will be amazed to see what they did that is something I want to tell and what happened you know I think what happened is after Vedanga Jatish there is a dark period not any major texts is found whether it was there and lost is also not known. The reason many people suspect that around 600 BC the rise of Buddhism and in Buddhism astrology used to have not at all a very favorable position. So what happened the the Charcha that is the pursuit of astrology was more or less gone and you know astronomy's main motivation for EMF was astrology you know otherwise why who cares for the movement of those heavenly bodies. So since the astrology had a very low and subdued or rather almost static position and the kings and others who are mostly following Buddhism they didn't sponsor court astronomers and therefore for a long period there was no not much activity and apart from that many people feel I don't know about Purana etc that means those because in Indian ancient his time is all mixed up whether Puranas are actual description of events or their stories you know it is a very confusing thing but we never had the system of writing history. The reason also is their Megastinist book if you read I have gone through I found many amazing things in Megastinist and Aryan's description of ancient India. I think 4th century AD they came or BC they came I think. So they said you know Megastinist mentions that in India society is very peculiar here they do not create big structure in memory of a human being or a man or a king. They say that Indians say that a person should be remembered by his good deeds not by a big structure that's why you will find that only the Buddhist tuppas started being erected much later but no king like whether it is Ashoka or Chandragutta you won't find a big memorial nothing is there. He also mentioned that society you know who were the most protected part of the society not the teachers but the farmers. The rule was that if anyone injures a farmer or hampers or brings any physical entry to a farmer the sentence was a death sentence. Even during the war the enemies of the opposition will not touch a real farmer. So they are so careful about the food security and today the number of suicides of farmers you know and because of love affairs that is what is being told by some ministers. So I think that shows the maturity of the Indian society even in the before that 5th century 6th century BC and perhaps that is why since the erecting a structure in memory of a king or a big man was not in the philosophy of India ancient India they never recorded also because history means what this king owned this war this king died this king took the throne. This is history we read isn't it? So that kind of history was not done and whatever was written I think we consider them as Puranic texts and their mythology. So it is a very difficult thing that is why ancient India's history is very difficult to extract in a very depend or acceptable way acceptable to particularly the western style historians. So after Mahabharata Mahabharata war is considered to be a landmark thing or a historical event where lots of things got destroyed kingdoms, kings or died and it was also there was a deluge by Dwarka there was a physical and major tectonic uphebals. So because of the major classes wars big fight lot of death and also many physical happenings the things were very disturbed and not much thing we hear only thing we hear about this that Pariksit did that who did Pariksit or Sarka Jagga. So actually whole Mahabharata is told as a story to get rid of the sin because of killing snakes. So if there is a slope in Puran you will find from Pariksit to Nanda Mahapad Nanda you know Nanda Bangsa the last one was Dhanananda who was killed by Chandragukta and there are 10 generations the first one is called Dhanananda. Dhanananda is a very very special person you find his name in history and also in Puran something like the number E you find an equation in one side E and one side a trigonometry. So it is something which connects trigonometry and algebra the only thing is E. So Dhanananda is the only link who is mentioned in Puran Puranic literature Vishnu Puran is there and he is also mentioned in history. So he was 1500 or 1050 that is there is a controversy. So they say that it is in one version it is 1050 years and another version 1500 years. So this has been analyzed very critically by Bankim Chandra in his Krishna Charitya. It is a very fantastic book. It has been translated in Hindi also and you can read it it is excellent book real critical almost I will say almost scientific analysis of the whole thing. So there is a reference that how much time passed from Pariksit after that there was a dark period Pariksit to Dhanananda or Mahapad Nanda was either 1050 or 1500 years and then 10 generations you come to Chandra Gupta's period Alexander that way you can link the historical period with Puranic period or proto-historic period. So but there was a very dark period not much is known about that time and maybe that is why astronomy also suffered a dark period like that. Then again we find extremely glorious period of Indian astronomy we call it Siddhantic period. It is important for me to tell you why the names have come. Siddhant in it has nothing special in connection with astronomy it is very clear. Siddhant means a decision or final thing. So the Siddhanta text were considered as the final text that is why they are called Siddhantas this Siddhanto that Siddhanto and so on. And something which is not a Siddhanto they called is pre Siddhantic like which is not linear we call non-linear you know in a similar way. So Siddhantic astronomy will start in the second actually it started in second century AD but it got maturity in the fourth century and fifth century AD at the time of Arya Bhattava and that I will start tomorrow's session. If you have any short brief question you can spend it. This all analysis was done by a major scholar who published this you know in the 1940s who was a professor of Sanskrit and also Indian astronomy Sengupta. Rigbada is the earliest this is 4500 BC they have done it using the astronomical references. So if towards the end last session there is a part I will discuss on the antiquity of Indian there I will discuss how they have done this I will come to that. Yeah that is what I could find yeah yes oh that will come that is in Siddhantic astronomy that is tomorrow we will start that yeah that is what is mentioned somewhere they found some sloka definitely some sloka verse where it is mentioned earth is round who proved that Rigbada people much before that even I think Greek astronomers even 600 BC they knew earth is round and they also knew it is not cylindrical it is spherical there are actually you know I used to give a course here long back I told you know there I used to give all these things that how they found out the the size of the or relative size of the earth relative size of the they are also I gave all the reasons how they found out I do not know I have not read Rigbada please actually my difficulty I do not have access to the principal sources because I do not know Sanskrit so I have to depend on the translated things observation only yeah normally what happened when you travel north or south you find new stars yeah 2000, 2072 what but which era you are using this because so many eras are there shaka era Islamic calendar they follow Hijra era some era you have to find fix the otherwise you cannot say what what shaka of the is there banga of the is there yeah I will come to to those things tomorrow siddhantik astronomy I will come to the various eras which were there one era the earliest thing which was used by R. F. Attawan was Kali era that 3070 BC kind of thing you know so but subsequent astronomers use different era one is Vikram Sambath and the latest one was some Kerala astronomers they also used