 Welcome to the third lecture. I will just make an announcement that the PPTs this presentation files will be available with me. My email address is Dutta DUTTA whoever wants to take off it please write a mail to me I will send it which is permission give the pdf version of course I will give the pdf version. So welcome and I am thankful to you for your generosity of spending the evening valuable evenings with me in this room only two more days of suffering not much longer. So today as I mentioned that the subject is really very vast and I am trying to present only the variations of it because if I want to start discussing the calculation procedure not only that some of you will not be interested in that there is no time for many other things which I would like to discuss will not be possible. So therefore I have advised that the books are there I have been told that already a full set of the 11 volumes of the series has been purchased and it is in the new arrival and I have also given a copy separately. So I think those of you who are interested in the details of calculation so you can see that. So today we will start our discussion on siddhanti gastronomy and after Vedanga jatis I mentioned this that there was a long dark period characterized by the absence of any major and important development or text on the subject and as it happens during this period the outside disturbance started coming rise of Buddhism where astronomy is not or astrology is not preferred so astronomy didn't or it lost its primary impetus and all these things were there that is in generally you will find that even after the I think 14th or 15th century BC there is not much known about it it is a dark period. So but one thing has found that even in the Mahabharata time which is around 15 1600 BC approximately the concept of 12 grasses emerged though of course separate names were not given but the planets were all known their motions were all analyzed qualitatively that means you know whenever they are having a retrograde motion it is found that you know mongrel is in bakri and so on. During this period another thing happened which I will take up in the last lecture which is very interesting astrology is not scientifically very important at least personally to me but I think in the past astrological references sometimes become very useful. One such thing is exaltation of Mars exaltation means when a particular planet is very bright the stars don't change their brightness but the planets do depending on the distance from the earth. Now Mars or mongrel when it is in its perihelion position it is nearest to sun and when earth is in perihelion position it is farthest from the sun when these two positions are side by side the distance between earth and Mars is the minimum and the brightness of that planet is very very large at all three to four times more than what is normally we find and that's why the astrologers called mongrel uccha or exaltation of Mars. Now the importance of these is that if and they also say that mongrel uccha against this nakshatra that nakshatras are our reference point moment they say that you know that that was a situation where if you draw a line from earth to Mars it will go to that that particular nakshatra and mongrel or Mars is in perihelion position and earth is in apahelion position. So you can calculate when it happened so one scientist who is no more professor Rana he was in Ayukha some so he also wrote some books he has done lot of research on that and said that such astrological differences are found which are around 11 or 1200 dc. So during that period astrology etc in a fragmented form we get and we can use them for the chronological ordering of events then. So this 60 year Jupiter or Mercury's Venus time period. Do you know Venus, Jupiter? No this is Jupiter but we said about Venus yesterday. Time period of Venus you mentioned. Oh that was here yesterday. So this is purely from the geocentric point of view. Of course. When it comes back in the same constellation. Exactly, exactly. Now these periods are all sidereal periods. In case of planets they are generally sidereal periods that means against a particular star. And as you as I mentioned that Vedanga period the motion of planets were qualitatively studied and the Jupiter's period was approximately 12 years. So they also developed a Juga system with a 5 years Juga system with a 60 year Jupiter cycle. That was also devised but they are not very relevant and not neither. It does not have much impact. At that time Jaina astronomy flourished. There are lots of texts you know the names are somewhat difficult to pronounce like Shurya Pragyaapati, Mejyotisha Parandaka, then Chandra Pragyaapati, Jammudipra Pragyaapati, like that. And Jaina cosmology etc. they all developed you know those of you who have interest you can go through that. But normally it is not considered very important from the point of view of astronomy. And at the same time as I mentioned that with the rise of Buddhism the astrology lost its importance and so the main impetus for doing astronomy also was gone. So in very fragmented form things were going almost for 1000 years. In the study of comets motion as I mentioned yesterday was there and many comets were found to be periodic in nature and the periods were found out and many astronomers names were associated with those comets and like say for example some of the comets had period which one astronomer could identify or analyse during his lifetime and so they were named after those astronomers. So this requires definitely very accurate observation and prolonged observation. So the observation of many European scholars that Indian ancient Indians were not having the capability to observe etc is absolutely not tenable. And as I mentioned that North India was being disturbed very much so astronomy stopped because astronomy requires peaceful environment where a person can observe day after day the positions etc accurately year after year. So this kind of situation did not but at the same time what happened with the coming of Alexander and later his other persons like Seleucus and other Greeks like Megastinies, Ariane. So exchange of ideas started taking place also. So many ideas of Hellenistic astronomy we find in Indian astronomy but they have it has been found that it was not a copy because the things were only very basic similarity but otherwise in details they are very different which we will discuss in a separate section of discussion about the originality of Indian astronomy. That will be the last lecture Antipity using astronomy we will find out the dates when these kinds of things were there and we will also discuss the points about the originality which parts are original why it is considered original and so that will be later. And now I think what first thing we notice in the Siddhantic astronomy was matured in the 4th century, 5th century AD and the first major famous astronomer in the Siddhantic period was Arya Bhatta 1. There are two Arya Bhattas you know so to distinguish that one is called the earlier one who is more famous is Arya Bhatta 1. Much later there was another Arya Bhatta 2. So we find the first occurrence of weekdays and the names of the zodiacal signs. News for surprisingly the names of the weekdays and names of the zodiacal signs were very similar to that of those found in Hellenistic astronomy. In the Vedic era as I mentioned yesterday that there was a Sharaha kind of thing that means a week of 6 days. And the emergence of 7-day week system happened during the transition between Vedanga and Siddhantic astronomy. It is believed that the Chaldeans they started the 7-day week system. What happened you know you can easily guess why 7-day because 7 planets are there. Sun, Moon, Mercury, Venus, Mars, Jupiter, Saturn. So each planet was associated with a god and the 7 days which we had system based on the 7 planets and 7 gods. I will tell you how it happened and they linked each planet with a planet god and the system was like this. In their system they found that every day was divided into 24 hours. The every hour was ruled by one planet god in series and the planets were placed in order in the ancient idea about the distance from the earth. So you can see this is earth nearest is Moon, next is Mercury, next Venus, then is Sun, then Mars, Jupiter and Saturn. That was the perceived distance from earth in the ancient astronomy. Now I think every if you start here say for example the first hour is ruled by Saturn. So that particular day out of the 24 hours. So Venus should be closer to the earth. No no ancient astronomy was like this. It is not the heliocentric model you know this geocentric model and that was their perceived way of vignetting. So Venus is closer to the earth than Mercury is the first. Yeah but I think the Moon, then Mercury, then Venus that was the way they were doing in those days. I think so unless I make some mistake and see that. But I think basic idea is like this that whichever planet god rules the first hour the day is named after that. So you can see if you start your day with Saturn ruling the first hour okay, then next is 2 is another planet. So you have to complete 2, 3, 4 up to this and up to 24 hours. Next day's first hour is ruled by Sun. So if you will see that this is ruled by Saturn, then Jupiter, then Mars, then Sun, then Venus, Mercury, then Moon, then you go to next will be again Saturn, again Jupiter and so on, again Saturn, Jupiter and so on, again Saturn, Jupiter, Mars and the day is completed here. Next day's first hour is ruled by Sun. So the day will become Sunday okay. So then you see again you go 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23. The day is over 24 hours. So where the next day is which planet rules? This Moon. Moon is so Monday. So that is the scheme by which we get the names of the days on your week. Is it clear? And even in Indian system we are following the same sand, Saturday is a sunny bar, Sunday is a rainy bar, Monday is so bar, so moon you know. Next day you will find if you do after 24 hours or 24 shots, then next day the first hour is going to be ruled by Mars. So it will be Manga Tuesday. So this system it is felt that it was developed by Chaldeans and the Chaldeans their thing was or the text were translated into Greek. I think the person who did it is Berosas in the 6th century BCE he translated these astronomical text into Greek and the system got adopted in Greek astronomy. So when the Greeks came to India with that this exchange of ideas, this 7-week system came and the Siddhantic astronomers started following it. Who were? Chaldeans were like you know in the ancient civilization have many like Babylonians, Chaldeans, all those people. You have to see that Middle East and the Near East border in Europe to Egypt. It will be somewhere near I think Syria. The Central Asia. No this is not Central Asia, definitely not. Syria is not in Central Asia. Now I think as I mentioned that why we call it Siddhantic text because Siddhanta means final decision and each astronomer when he wrote something he thought that is the final final decision or final astronomical text. So they used to give the name Siddhanta. Everyone used to call Siddhanta after his name as you will see very soon. Another feature you will find that the 12 Zodiacal signs those names also were originally given by the Greek people following the Chaldean calendar and that also got transmitted to Indian Siddhantic astronomy. We started following Rashi's. At the same time people started following Nakshatra. So it was a mixture of solar because Rashi means sun takes that position and then 12 times you divide the ecliptic. So each part is one Rashi. Sun takes and spends their time every month solar. So this mixture but we were also using Tithis, Nakshatra etc. So it continued to be a mixture. Even I think you will find later I will come to that not now. So you see the Babylonian first divided the ecliptic into 12 divisions and they gave the names of the Rashi as bull, ram and all kinds of things got beyond that got transmitted and that also kept to India. So that is the general belief that the weakness scheme was first started by Chaldeans and the Rashi and 12 Zodiacal signs their names were given by the Babylonians and all those things came to India via the Greek. Now there is an interesting point you have to mention here. One basic tenet of Siddhantic period astronomy was to avoid you know what they did you know to avoid the occurrence of fractional numbers they considered a period when all the planets will make integer number of revolutions. That means it is a kind of LCM connection and so therefore the Juga system which they developed is a much much longer period than what Juga system they developed in astronomers in the Vedic period. So you will find and it was a unique method which will involve very long periods Juga's, Mahajuga's, Kalpas, Banu's etc. So therefore this was a mathematical requirement you know the LCM thing. Sometimes therefore I personally believe by mistakenly we think that really our history goes back like that that millions of years in the past the Mahajuga Kalpas. I am not so sure that if that really happened or on the other hand it was a mathematical requirement by the astronomers to avoid fractional numbers. You will see more details we will count to that. Now is this point clear? This is a very confusing thing in our history that when you say Mahajuga they think actually our history also goes to Mahajuga but it may not be so. It could be a mathematical requirement. Now this Siddhanta taste it takes you know they are quite massive things and they describe many things the system of the universe, the calculation and other kinds of things like determination of eclipse all these things were there and this Siddhantas also used to be so big that many times the authors of the Siddhantas created a smaller version what we call these days Medici kind of thing you know which will be quickly used for calculating things they used to be called as Karanas. They are nothing but simple text which will be used only for calculating your or preparing the Panchang or the calendar. So these Karana texts were prepared primarily to give readymade algorithms and used more convenient contemporary dates of the evoc. It means I will come to that when I discuss what is epoch and what is era. So the post Vedanga Jyothi astronomy in India it can be divided into periods as indicated in the table. The first period we call early Siddhantic period which started around 100 BC which is not very clearly known and continued up to 4th century AD. Then Siddhanta period when we first find Arya Bhattavaan can be put in this range 400 AD to 1100 AD late Siddhantic period and medieval period 1100 AD to 1800 AD and after 1800 AD is called the modern period when telescopic astronomy was there. So this is the way it is divided and this map shows ancient India and the places where the most important astronomers of Siddhantic period were born or worked because it is not known sometimes whether the fellow was born there or he worked there and along with the approximate year of their birth or work. So you can see this is not very clear this is the Himalaya which is old name was Himabanta that is the old Sanskrit name of Himalaya and this Himabanta the great people started saying it as Hemodos and Hemodos again got distorted into Hemodos. Even today if you go to Italy you will see a station where you have to get down to go to Visuvias and that is called Ercolano actually it is Herculaneum so it has changed to Ercolano it always happens. So it is Hemodos, Hemodos or Himabanta in Himalaya. This is Tanduparni. Tanduparni was the old Sanskrit name of Lanka that the Greek used to call it Taprobene. So like that. So here important places where we have the most distinguished astronomers of Siddhantic period one is you can recognize this part Pataliputra or Kusumapura actually Pataliputra is a kind of flower you know and that is why quite often many astronomers or many philosophers used to call Pataliputra also by the name Kusumapura and it is known that Arya Bhatta worked at Kusumapura which is Pataliputra because Pataliputra is a kind of flower after which the name was given. Maybe Pataliputra had a lot of flower gardens somewhat different from Pataliputra. Then we have the place here with Jain actually with Jain for a long time was our like Drenivich had the Meridian Zero. Then in Gujarat where Brahmavukta worked and born also very famous person. And this is I can do it from here. Sripati was there and Barahamir worked with Jain you all know he was one of the Navaratnas. Sripati was somewhere in Bidarha area then Bhaskara too was there in Telangana what we call today or southern part of they call it Maratha water region and of course finally Kerala. What happened more and more disturbances came here and the most of the academic pursuits gradually shifted towards the south and ultimately accommodated here. So the all the next stage Siddhamthi very famous astronomers Nirkantha and others you know they were all from Kerala. So this is that will give this is actually ancient India this map has been drawn which is contemporary at 300 BC but they were of course not 300 BC but much later. But the names which have been given they belong to 300 BC. So these are the very important astronomers of different periods. Early Siddhanta period we have Srisenna, Mayashura, Latadeva and I think these are the people who were before Aryavarta and they did some work during the transition period. Then also it is told that Romaka Siddhanta is there maybe and then there is Koushira Siddhanta is there. So they are all during the transition period. Then Aryavarta one 46, 476 AD he was in Patna Pihar, Barami was the next 505 at Ujjain, Bhastara at 600 AD in Gujarat, Brahmagupta of 598 AD in Rajasthan, Lalla and Malwa. Then Malwa means Malabh which is near I think what will be Malabh or Indore and those places you can call Malabh. But Bateshwar 88 AD in Gujarat, Manjula was a very important one, Prakashapatam south, Aryavarta 2 958 AD Bhaskara 2 1114 AD and in the late Siddhanta period we have Sripati in Madhya Pradesh, Parameshwara in Kerala and Neelakantha somewhere very famous one in also Kerala. And medieval period Siddhanti gastronomy was done mixed with Jiji gastronomy, Maharaja Swaizhan Sijaisen and the last Siddhanti gastronomy was for Orissa, Samanta Chandrasekha. And you can see their texts, the Basishta Siddhanta, Pita Maha Siddhanta, Romaka Siddhanta, Surya Siddhanta and Aryavarta started with Arya Bhattiam or Arya Siddhanta. And Varahami is a found, he studied all I think at that time there were 26 Siddhantas he found and found most of them were inaccurate or not much use. Actually what was happening, Vedanga Jatis after that all those texts were inaccurate, we have seen the way we calculate very approximate and they are not of much use, so therefore they are not used and they are completely forgotten. Only Vedanga Jatis remained because of that name Vedanga, it was treated as a part of religious texts otherwise you know perhaps it would have survived also. And Arya Bhattiam, then what he found only five of those Siddhantas were of use and he wrote a text called Pancha Siddhantika, Varahami. Varahami's main occupation was of course astrology, you know. So his work in astronomy was primarily compilation, not much fundamental work. Then of course Varahami, then Bhastra, then Brahma, this Brahma Bhutta is considered to be one of the best and his Siddhanto was Brahma Siddhanto or Brahma Sutta Siddhanto, both are same and he had a Karanam which was also very popular that is Khanda Khandaka. They are all translated into Arabic language and that started the Zee Jastramami there. And so on will not go. The last Siddhanto, you have Siddhanta Darpana that is written by Samanta Chandrasekhar, that is the last and that is used even today in calpricians were so accurate. The Puri temple, Jagannam temple, all things are done according to Samanta Chandrasekhar's calculations. Now how texts were arranged in Siddhanti? The material was presented in four chapters generally in Siddhantas. The chapters in Sanskrit are called Adhikaras and first used to be Madhuma Adhikara. So this used to give the method of calculation and data etc for mean positions. You know in all astronomical texts whether in India or in Greece the finding position is the main important objective of positional astronomy. You know that. Finding out the position of sun or moon or a planet. In Vedanga Jatisha only sun and moons position calculations were there. Planet calculation was not there in Vedanga Jatisha. But they were in Siddhanta. Siddhanta, the position of the planets, five planets and sun and moon all were included. Now the technique generally used to be like this. First you find out the mean position. How mean position is found out? You take the average speed of rotation and you find out at a particular time where it is going to be. That is the mean position, not the real thing. Then you make corrections on that to get the exact true position they used to call. I will come to that. So Madhuma Adhikara's main purpose was to calculate the mean position of a planet or sun or moon and the detail the procedure for obtaining the true position of the and Pasta Adhikara was the detailed procedure by applying the corrections which they call samskaras to get the real true correct position of the heavenly bodies. And I will come to that. There are primarily two types of corrections. One is Mandha corrections and the Siddhara correction. Mandha correction was for sun and moon and it took care of the non-uniform speed of the heavenly bodies because you know being on elliptic orbit and the distance from the sun being different and according to Kepler's first law, second law, they will definitely have different speeds. So therefore they do not move with a constant speed or mean speed. So therefore you need to correct it. So that was for sun and moon. The Siddhara correction was important for planets. Of course for planets Mandha correction was also there but you have to also do Siddhara correction that used to take care of because you see real system is heliocentric but we are observing sitting on the earth as a geocentric system. So that needed some samskaras and they are called Siddhara samskaras. They are for the five planets not for sun and moon. There was another third chapter that is Triprasna Jhikara. This took up the three aspects of direction, place, time, finding out latitudes of places, times of sunrise, sunset and the changes of position of sunrise etc. That was the objective of Triprasna Jhikara. And last was Chandra and Shrija, Grona Jhikara. That presented the method for determining lunar and solar eclipse. Many mathematical aspects were also taken up. Actually mathematics also developed during this period because it involved calculation etc. Particularly trigonometry they developed during this period. Now there are four schools of Siddhanti customary. You know it happens. So the Greeks used to call it epicycles. Did they have some word like epicycles? Yes, I will say that. Not only that, as I will show you later, Indian epicycles were somewhat different. Greek epicycles were fixed size. Indian epicycles the size used to vary and that was more accurate description because even epicycle is actually fantasy. It was not a reality. So Indian epicycle system was more advanced. It took care of further approximation by giving the variation in the epicycle. It was not like the Greek epicycle. So actually, as I mentioned, when I discuss the originality of Indian astronomy, all these points will come that how much was taken directly and how much actually got developed indigenous. So the four schools or paksa they call were Brahma paksa, Arya paksa, Ardharathrika paksa and Soura paksa. And all the four schools retained the traditional concept of Mahajuga but adopted units of time and epochs differently as you will see. In Vedanga Jyotish you have seen that we had a five-year Juga system primarily to achieve integer number of lunar months and solar years in a Juga that we have discussed yesterday. In Siddhantic astronomy a Juga meant a much longer period of time with an aim to express the revolutions of planets avoiding fractional numbers. So you see that was the Juga system and epoch in Siddhantic astronomy. Now you can see that in the Brahma paksa and Surya paksa followed one set of data and your Arya paksa, Ardharathrika paksa started another set of data. So Kritha Juga was 17,28,000 years. Kritha Juga was 12,96,000 years. Dwaapara Juga was 8,64,000 years. Kali Juga is supposed to be 4,32,000 years. So in total one Mahajuga had 43,20,000 years. In Arya paksa and Ardharathrika paksa system was they divided all Jugas equally and they were of 10,80,000 years. In total again one Mahajuga was 43,20,000 years. Then 71 Mahajugas made one Manantra or a Manu and that was obviously multiplied by 71 and you get such a big number. I do not want to read it. In other system school they had 72 Mahajugas made one Manantra or one Manu and 14 Manus make one Kalpa. So you can see in this school one Kalpa is so many years which is considered Dronbhaj one day and 1008 Mahajugas. Now here you find that in fact got ultimately same number you will find but they added some Sandhapiriya. One Juga, Mahajuga to another Mahajuga they used to add one intercalary Juga or they used to call it Sandhapiriya even in period. So maybe Kominth and Dask. Isn't it something like that from one revolution you are going to a revolutionary period and it is never an abrupt change there will be always a Kominth and Dask or Prak Bipla Vraktavadhuli in Bengali or Sanskrit where lot of killing etc goes on. So you see that is the way they got a huge number one Kalpa is this much in this school and here it was this one Kalpa is this much somewhat different. Sandhapiriya concept is absent here and one Kalpa is 1008 Mahajugas. Here there is a Sandhapiriya each being equal to a Krita Juga between two successive manantharas as the time required for each creation thus one Kalpa is equal to 1000 Mahajugas in this case. So this is the kind of thing but point is to I am not so sure I will leave it to you to judge that whether these are really our history goes like that or it is a mathematical requirement to avoid or taking a large period so that you express all the all the numbers in integer forms like LCM. So I personally believe it was a mathematical requirement not that but I think since everything you have to do if you put everything in purely mathematical form people don't like it. So you give it a kind of reality by giving these things that Brahma is there is one day is one Kalpa etc. Interestingly this four billion years is interesting because we now you know 15 billion years is the age of the present time. And that is the danger immediately people will say we all know about Big Bang and so on. So that creates some I think such coincidence it is not but I think it you have seen perhaps you know I feel it is primarily mathematical requirement to express the revolutions in integer numbers. Just like a five-year Juga a simple case where the solar revolution and lunar revolutions all both were integer numbers. What was it 71, 72, 14? They followed different they are all calculations that's what I am saying that you know they found they calculated that way ultimately their objective was to find out the position of a planet on a particular day and time that's all nothing else. So the use of Mahajuga system the number or number of revolutions in one Mahajuga say the sun revolves so many times stars revolve so many times. Now stars revolve revolution is nothing but revolution of the earth isn't it? Earth rotation is the stars rotation. So then seven days this much the moon seven days will be little less because you have seen one seven take takes little bit more time as I told when you are here seeing the sunrise coming back to the same position next sunrise you don't find you have to do little bit more because sun has gone little bit high because of the orbital motion. So that's why seven day numbers are little less than the rotation of the earth. The moon rotates so many times Mars, Jupiter, Saturn, then civil months, lunar months and t3s. So in one Mahajuga these are the numbers they used to take. The comparison of the numbers in different systems you know I think Bhaskara and modern Surya Siddhanta and Arya Bhattawan. So the data very little bit very much but the system was like different. So you can see this is same by all the astronomers. This also appears to be same in case of Mars it is different. Mercury also when you go to planets the sun and moon they are same and Jupiter again you find that they are little different. Here again Venus you find they are different. So these are the three major systems where they follow these are the numbers. Numbers are nothing but the revolutions you know everything was on that. Now I will explain it in terms which is called epoch and it is very important. Now when you calculate the position how you do? You start with a known position on a certain date and then I say that on such and such date. Now such and such date means you have to count the number of days to the desired position date. So where you start? So the starting date for your all calculations is called the epoch. So the Indian astronomy the commonly used eras, eras means like Christian era, Shaka era they are called eras and epoch is the starting date. So the panchangas were primarily created with these eras were commonly used one is Kali, Arya Bhatt used Kali era that means when the Kali Juga started then Vikram Shaka is there is another one, Shalihana Shaka is another era and Kolam which was followed by Kerala. Of course when the Islamic innovation came then I think his era also became another era which was used by astronomers. Now for each era there is zero point or starting point as I mentioned that is Kali epoch. Now Arya Bhatt once started the Kali era counting the midnight of 17th, 18th February 3,102 BC as the epoch and so yeah 30202. Yeah actually these dates are actually currently our dates but they didn't have the BC kind of thing before yeah it was 3,102 and it says that I will come to that Arya Bhatt wrote Arya Bhatt was born when I think it was 26 I will come to that when I come to Arya Bhatt. So Arya Bhatt started took this as the epoch that means all his calculations he started at that point and you will see that when you calculate the technique of doing it I will explain next so you need to be clear that why they needed a starting date or epoch. No because he thought that it is the beginning of Kali and mistakenly many people used to think that all the planets were in one line they had one meridian but it was not correct but that is many people suspect that that was their impression maybe they are not exactly in one line but very near so they thought that that is a nice time to start because if all the planets are in one line and if you take as the starting point it gives you some obvious advantages. The epoch of Vikramasaka is 58 BC and Shalibahan era epoch was 78 AD and epoch for Kullam era is 824 AD similarly Bengalis they also use one era and I think that is something that is 593 AD is the Bengalis era that is starting point. Now this is the point that you have to do few things one is determination of tithi there a particular day what is the tithi and what is the nakshatra that means where is the moon nakshatra all the nakshatra are there so that particular day nakshatra means where which nakshatra the moon is there and tithi is what tithi means what is the phase of the moon now phase of the moon depends on the longitudinal difference of moon with the sun isn't it when it is zero that means they are together that is a new moon day then tithi is one or zero so then as you go when it goes opposite 180 degrees then it is the punima as you know so phase of the moon and tithi they are linked and nakshatra means the position of the moon in the eclectic so this is a major task in siddhantic astronomy and the rudiments are like this now tithi is referred to the phase of the moon as I mentioned just now and so it refers refers to its longitudinal distance from the sun if sun is at 10 degree then if the moon is at 30 degree then the difference of longitude between moon and sun is 10 and how to then use it for finding tithi i will give it so indians always use nirayana longitude system as i mentioned that means they had a fixed starting point from point meshadi starting point of rasi rs the zero point in indian nirayana system is the starting point of rs meshadi and there are 12 signs each spanning 30 degrees 12 into 30 is 360 degrees so if you divide the eclectic into 12 divisions each division will be 30 degrees that is each rasi the longitude in indian system is mentioned this way it will be n 6s the small s indicates sign and each sign is 30 degrees so therefore ns means n into 30 degrees then x degrees so you have to add that so ns x degree means 30 n plus x degrees y minutes z seconds and the sun moves by approximately 1 degree every day because 365 days it takes 360 degrees so approximately 1 degree and the moon moves every day by 13 degrees 20 minutes you can easily find out and thus moves longitude increases relative to sun every day at the rate of 12 degrees and 20 minutes here today if it is a new moon so tomorrow the moon will be 12 degrees 20 minutes ahead of sun and so on and now what is a tithi it is the longitudinal difference with the sun if the longitudinal difference is 0 then tithi is 1 prathipa or or new next day it will be prathipa and so on so how to find out that very simple what is moon's longitude subtract sun's longitude and divide by 12 so that you give you the and so therefore you will find that and the whatever is the question that you take and add one suppose if you find the difference is 12 that means what is the question one so longitudinal difference is one tithi and so current tithi will be another one you have to add so it will be dithya so on so this is the tithi calculation was done like this difference of the two longitudes divide by 12 and take the quotient and add one nakshatra of a particular instant is the particular asterism occupied by the nirayana moon as I mentioned so as each nakshatra occupies 13 degrees 12 minutes along the eclipty because there are 27 of them and 360 degree if you divide by 27 you get 13 degrees 20 minutes so how do you find out nakshatra starting from zero point so what is the nirayana longitude of the moon in degrees find out and divide by 13.33 which is 13 degrees 12 minutes take the quotient and add one so that gives you the current nakshatra starting from the beginning nakshatra of the moon very simple calculation and that is the way the nakshatra of that particular instant is calculated which specifies the position of the moon in the eclipty. Now I think the main thing another very important task as I mentioned was the determination of the mean position of the sun moon and planet that is the job of muddhamadhikala first you have to even in a greek astronomy always yes 13 degrees 12 minutes or 13 degrees 20 minutes because 13 degrees 12 minutes should be 13.2 I think it is 20 minutes 20 minutes I think 20 minutes I think last time 13 degrees 20 minutes yeah 20 minutes yeah I don't know why I here thank you for correcting it now you see that how to find out the mean position that now becomes our next task so there took a very straightforward approach Indian astronomers what they did from a starting point which you assume which you call as the epoch find out how many rotations or revolutions it has gone through you know the mean rotation speed per day of any heavenly body see if I say 2 degrees per day or 30 seconds per day so that so if you can find out the number of days from the epoch to a particular day I say on such and such date it means starting from the epoch how many days have elapsed that you have to find out and you have to multiply it by the mean motion so you get the mean position very straightforward the problem came because in Indian astronomy the mixture of solar and lunar thing you know that created most of the complications otherwise you know it is a straightforward thing if you know the number of days to the particular day you are interested in from the epoch and you need the position at the epoch then you just find out the number of days and how much movement is possible in so many days divide by 36 degrees because that will give you the so many full cycles and take the residue so it has advanced that much is it clear so I think that's what they did but the only problem were there because the mixture of the because you know observationally they used to depend on tithi and that kept the lunar day tithi and the year was solar and number of civil days are there and mean motions were known as per civil day so what you have to do you have to calculate first number of civil days that is called ahar gana ah is a day and ahar gana means count count of day how many day count that is called ahar gana and that is the first thing you have to do so at the the starting at the epoch the number of civil days till the desired date was found out and multiplying the mean speed of a body per day with this number gives the total angular distance divide by 360 so you then subtract the full cycles and take the residue and add to the starting latitude to get the present mean position and total number of civil days as I mentioned is called ahar gana the count of days so how do you find out ahar gana I show that but before this I think this is a table which gives the position of the various rashes and the other hand this table gives the position of the various nakshatras so mesha is from 0 degree to 30 degree then brishabha is 30 degree to 60 mithuna from 60 to 90 and so on and 27 nakshatras they are like ashrini nakshatra you start with that in indian system that is the nirayana longitude that is 0 degree to 13 degree 20 minutes vharani ashrini vharani krtti karohini in a moment you start saying that people will immediately say it is astrology because you know I have found out whenever you utter these words people think it is astrology because astrologers always show your moon is in this nakshatra etc they do it in a manner that this gets associated but they have nothing to do with astrology they are nothing but the markers in the eclipse and the position of each nirayana longitude of each nakshatra is given here so this is the way you calculate the mean position so if lambda prime be the longitude and the epoch your starting day of a particular day in the body then the present mean longitude is given as follows so you divide the mean speed by ahadana number of days divide by 360 take the residue remove the integer number because they represent only full cycles and then add the original longitude that gives the current longitude very straightforward classified exercise isn't it so now I think when n is the mean speed and object and a is the ahadana now since sums and moons motions are mixed up that is little bit problematic and I think what they did was like this suppose this is the epoch at A and number of moony solar years elapsed you know that then number of lunar months elapsed because Indian astronomy months used to be always lunar months not solar months because it is very easy to see a lunar month one full moon to next full moon or one new moon to next new moon so it was so therefore the number of moony solar years then you add is that number of lunar months and then number of tichi because they always worked on lunar month and tichi not solar day as we do in modern system now of course they are different units how do you make the argument so number convert these number of moony solar years into number of lunar months so that way you get the total number of lunar months by converting this moony solar years into lunar months that can be done that is not multiplying then this number of lunar month and lunar month only so you can directly add so the same unit and this is the number of tichi now what they used to do this total number of lunar months they used to convert into tichi just by multiplying by 30 so therefore you get up to this total number of tichi and add this number of tichi so it is the same unit now so total number of tichi you get and then you know how much how many single days will be there that you can get by dividing this by the that number which relates now tichi this civil day that is there you can easily find out so therefore the basically the principle is you will see on such and such year on such and such month and such and such tichi what is the position and to do that you first convert this into lunar month lunar months are already there you add then again you convert all this lunar month into tichi and tichi you get everything in tichi then convert everything into civil days and this total number of civil days is called ahaka if you had the system to to work with only civil days and solar system solar astronomy all these complications should not happen easily but we always depend on the lunar month and then solar year that is how quite the whole thing conversions is it clear that is the basic scheme now actual calculations you do that is different but the basic scheme or philosophy and then the whole thing was this to find out the mean position okay so the mean motion of different objects in the heaven in siddhantic astronomy what various ah people ah astronomy was did like say per day motion of sun was this much by in surya siddhanta it was this much in modern value is this much so you can see that how with naked eye astronomy so amazing accuracy they could achieve you believe moon of course is much faster 13 degree 10 minutes 34.87759 seconds it is 13 degrees 10 minutes 34.5202 second and modern value is 34.9 so you can see that eye of time is much nearer to modern value which is accurate value so these are the then they also had the the perigee motion venus perigee motion mass jupiter satan the in case of mercury and venus since they are inner planets so inner planets will never go around completely isn't it so they work with the perigee motion it is little complicated but I think you can recognize that fact so they are not planets which go around the earth continuously they don't you have seen it is always near the sun going this way that way now manda and sigra corrections or samskaras I mentioned after the mean positions are determined the above corrections are applied to get the true position actual position in the cases of sun and mean moon only manda correction was there because in that case the change over from heliocentric to geocentric did not create any problem but the other planets which are going around the sun and you are observing from moon which earth which is also going around the earth you needed the corrections and that's why the sigra corrections or sigra samskaras were necessary for planets you needed both manda and sigra in case of sun and moon you needed only so here things become more complicated and I don't think that we need to go to disconverting the system from this those who are interested the whole detail thing how it is done the theory behind it you will find in the book it's finally kinematics little involved not much but those who are interested can always find that out but the basic idea is this that these corrections are to find out the true position since they are not really moving with constant speed varying speed so correction is needed for that another is change over from the reference frame from earth to sun that also you need some corrections now I think I think you will find in the book that you know while doing these corrections they have to have the epicyclists or cyclists so so there all these things you know another correction was necessary it was that which was relatively minor which was called bujantara correction for the planets and that bujantara correction they did because of the eccentricity of the orbit of the earth another correction was needed and that is called bujantara correction which was minor or small but still they did it in the next numbers and your lagna is one thing which you have heard and you should know just for the sake of knowledge but it has no scientific significance lagna is the time when for the nakshatra when the moon rises you know it is used mostly in astrology it has no astronomical significance now I think let us go to some of the important astronomers which is very important we must discuss that the first one obviously is Arya Bhattavaan he was born in 476 AD at Kusumapura today is Patna and consisted of four sections is Arya Bhattavaan the four sections are Gittika, Ganita, Kalakriya and Gola he also started two schools in one in one the civil day used to be from midnight to midnight just like our current international system and that is called Arjharathrika system and the other was one civil day was counted from sunrise to sunrise that is the Oga Yaka system from Uda Surya Yaka so these are both the systems were developed by Arya Bhattavaan and calculations will differ little bit obviously because count of day etc are different and he divides an alphanumeric system which is very interesting where a war or later represented a number I will come little bit of that it is very interesting and it is nothing but a compression technology they will give a slope but it is a mathematical formula or mathematical quantity that way they used to remember now you see amazing thing is that whole book Arya Bhattya which had Gittika, Ganita, Kalakriya, Gola everything description of the universe calculation of the Maddhamadikara mean position calculation of the exact correct position then various tici calculation Kalakriya all those things plus direction eclipse finding all those things total number of horses were only 121 13 were in Gittika 33 were in Ganita 25 in Kalakriya 15 Gola and his Maddhamadikara which I was explaining that means finding out the mean position he used only 10 horses that was can you imagine that whole information mathematical information he compressed into only 10 horses so the alphabetical representation of numbers you know what Arya Bhattya and that system followed like say A was 1, I was 100, U was 10,000 and so on like K, A was 1 like that so this system was improved by Kerala astronomers and it was called Katapaya the system a good example given by Shankaracharya is that this verse in Sanskrit Gopivaya, Madhubrathasmi, Gadhi something you know and this really means value of Pi up to 30 decimal places using that system Katapaya the system those who are interested you can go to Shankaracharya's text and you can see how it happened that actually the value of Pi up to 30 decimal places is represented by this one line of sloka using that alpha numeric system I cannot I am not an expert in that yeah it is a Sanskrit slope Gopivaya, Madhubrathasmi in general by and large they used to also have a meaning that's why you could remember it is not just some alphabets so that is the credit you know how it is possible to create a verse but which he actually also had a lot of mathematical formula contained in that's why Arya Bhattam text is extremely difficult for the subsequent astronomers not very happy at all. Arya Bhattam also found out yeah This is the first one used decimal this is like decimal system you know in this no you see a decimal system was there by that time Arya Bhattam found the value of Pi as 3.1415 4 decimal places and Greeks always use the value of Pi as 22 by 7 for very long time and you know the modern mathematicians are amazed because to find the value of Pi up to 4 decimal places required inscribe a regular polygon with 768 sides in a circle then only you'll be able how it was done you draw a circle and inscribe a regular polygon count the number or the length of the each side add and divide by the radius you get the value of Pi to get the value up to 4 decimal places it was necessary to inscribe a regular polygon with 768 sides is not a very easy task so this is the most accurate value in ancient time as used by Arya Bhattam in the 5th century Arya Bhattam was aware of the fact that the planets appeared luminous because of reflected sunlight and he was the first to announce the daily rotation of the earth and he received of course many abuses and he later you will see that he calculated the rotation period serial rotation of the earth as 23 hours 56 minutes 4.1 second which is very accurate when compared with the modern value 23 hours 56 minutes 4.09 1 second so you imagine their brilliance by naked eye observations you and they didn't have clock etc also so finding out the values quantitatively to this really something amazing unbelievable in my opinion he also was very emphatic that the eclipses were not caused by Rahu but by the moon and the shadow of the earth and he received lots of abuses not only by other astronomers of the later period by even those who followed his schools and like his disciples the luckily we didn't have the system of burning somebody alive perhaps he could have been he could have had the same fate like Jyotana Bruno the way you know his revolution the revolutionary ideas were rejected by the subsequent astronomers for a very long time so Arya Bhattam one in my opinion stands much higher compared to many others they are also brilliant like Barahamir Barahamir used very abusive language about Arya Bhattam one then Brahmagupta Bhaskara they are all brilliant astronomers but nobody can match the merit of Arya Bhattam one in my opinion now another thing is as I mentioned precision of the equinox Ayana Chalama and the zero precision here we discussed little bit you know that earth not only spins about its axis but the axis of spin also slowly precesses because of which our vernal equinoctial point slowly ships towards west in the starry background and in the ancient time it was it is not found and only Bhaskara Charya realized earlier people observed that but they thought that to be a motion of the starry background not of the planets or anything so but only Bhaskara Charya first realized that it is a shifting of the equinoctial intersection point and since the Indian astronomers used the nirayana system and the western system you always start from that vernal equinoctial point but here we start from meshadi so I think this it was necessary to take into calculation of this shift how much it has shifted from meshadi to the current vernal equinoctial point and then the rest so this variation this difference caused by the precision was called Ayana Chalama that is the angular distance of the vernal equinoctial point at present with the meshadi that is the starting point of the sign areas and the first definitive mention was by Vishnuchandra and the 5th century AD of that but a much clearer statement came from Munjal around 932 AD and his estimate of the rate was 59.9 seconds of hour per year whereas the Greek astronomy will be 36 seconds but 59.9 is much nearer the correct value about I think 56 seconds per hour is the actual value so the year when the vernal equinox coincided with meshadi or which is called the zero precision year Indian various astronomers considered the following as the zero precision year like Munjal took 449 Sakha year as the zero precision year modern Surya Siddhanto takes 421 Sakha year as the zero precision year then Karanakuntala, Gujarat Laghava, second Arya Siddhanto and Damodara they all have different Sakha year as the zero precision year in their calculations actually that's why there are so much of errors and variations and later time Begnath Sah was very emphatic that you know some major correction or major work is needed to take care of that. Now when you come to the late Siddhantic period by the time of Bhaskaracharya most of the important developments were done and during the latest Siddhantic and medieval period no major original development took place in Indian astronomical system only in Kerala some new concepts evolved and the innovative ideas were proposed by astronomers there. Now actually after the Islamic invasion in the 13th century the northern and western India was somewhat disturbed and again even then there were Nadir Shah, Taimur Blang and their invasions created havoc temporarily again when Mughals came it was stabilized like that it happened. The considerable interaction with the West Asian scholar took place of course in that time so influence there was some positive influence but Indian asthmatics were translated into foreign languages as I mentioned and I will discuss it in much more details in tomorrow when I discuss the medieval period and Pancha Siddhantika was also translated into Chinese by Chu Tan Sita in 718 AD and its name was Chu Chi Li. After this Indian astronomical knowledge made a substantial influence on Chinese astronomy more or less during the same period Brahmagupta's Brahmashputra Siddhant was translated into Arabic and that called Sinhind you know at the time of Khalif al-Masud of Baghdad and the text was known as Aziz al-Sinhind al-Kabid and subsequently Arya Bhatia was also translated into Arabic by Abul Hassan and the text was called Azhar Bhatia and Brahmagupta's Khanda Khaddaqa was also translated Al Biruni you know was a very important person and great scholar of visited India and wrote a lot about Indian science and astronomy he was here for 14 years and he knew he was an exponent in many languages including Sanskrit so he not only translated Indian Sanskrit text into Arabic but also Arabic or Persian text into Sanskrit that also he did and he was a great admirer of Brahmagupta in his opinion he was truly an outstanding astronomer and he translated Brahmashuddhanta and Khanda Khaddaqa and his famous book Kitab Taikik Ma El Hin, oh my god goes quite long better not to attempt so it means verification of what is said about India which is accepted or rejected by reason that is the name of the book so it is something like thesis title in chemistry department comprehensive information on India is also found in his other book Taikik Al Hin and you know nowadays you can read Al Biruni's India there is a good book in English it is available you can read about Al Biruni's whole writing on India it's very interesting as mentioned earlier it is commonly acknowledged that in the post-Haskara too late Siddhantic period there was a gradual decline in Indian mathematics and astronomy however in the southern part of this country which was less affected work continued and actually in Kerala they developed an astronomy which was same as Taikobahe's system that means Taikobahe's system was the earth is stationary sun is going down the earth and all other planets are moving down the sun same kind of because you know you will find if you study little bit kinematically the observation will be same whether it is the real heliocentric system or geocentric system or the Taikobahe's or Kerala system so Kerala astronomy also evolved a system where sun goes down the earth and all other planets go around the sun and I think I am not sure I couldn't find but it is said that there were hints of heliocentricity in many of the works they did and data was very clear because if you see the epicycle sizes which are nothing but the orbital radius their ratios are very similar to the astronomical units that means which we use for telling the radius of the orbit of various planets in the book you will find the whole thing but still the whole thing escaped their mind I think I was being asked by Professor Bhattacharya that how come this happened that they never really because they are so busy with accurate determination of the position the physics behind the whole thing perhaps they were they missed the point. Secondly the reason why the aria-hatta is rotating earth or these things were aristocracies heliocentric system or not because the laws of physics were not ready for people to accept inertia the first law of inertia until and unless you have first you cannot accept a moving earth everybody will say that if it is moving if I drop a stone why not the stone falls far behind so it is only when the concept of inertia first law of inertia by Galileo and Descartes came it was not possible for people to accept the moving earth or a rotating earth so I think I will stop here if you have a few questions I can discuss and tomorrow we will start the medieval period and we will end that and final day will be the story of how interestingly interesting and some of them are very pathetic also you will see they are known as tragedies in astronomy you will see that and some discussion on the originality and antiquity of Indian system so any question in today's okay just a moment which which period you want to go oh no no I think yeah I think it has been suspected that they felt that something like that happened but really it didn't happen that because you are expecting to get all the planets at one point isn't it yeah I don't think it happened that way you said your date was minus yeah minus 3 1 0 7 0 2 3 1 0 2 2 0 2 and February February 17th we have to go to midnight hours 12 0 0 it should be no 17 0 18 0 then you can leave it okay ready location of course you can say 80 degree our longitude is 80 degrees isn't it 80 degrees 80 degrees and 23 degrees for the family approximately the latitude north okay let us see you know it should not change with latitude the meridian of the thing okay so I think but only thing of course then sun also has to be there so we have to see where the sun is February means it will be after the winter solstice so let us wait this softer cricket is really wonderful you know it gives the feeling yes we are in darkness looks one planet we saw green one that's the planet it has been checked they found it is not correct oh this is the Saturn but they are not very different you can see you can see this is Saturn this is I don't know another one not this is Mars Mars and sun very near moon is also very near and Jupiter also is very near so I think there is a point you can see only a few degrees I think Jupiter moon and there is one more one more what is that the blue so that is four I could see the blue is coming up this is Jupiter and blue is something now modern time means it will be some Eulena's Neptune everything can be there and this is sun and this is Mars so you can see there are one two three four five a moon and Saturn so I think there is a point they're very near they're not exactly in one line they're very near so there is some some merit in it though it is not exactly correct they're within few degrees all the planets were together at that time okay other questions okay I have one question yeah so Arya Bhatia gave the name Arya Bhatia himself or somebody else but normally they don't give the name on this after themselves was the book written his name was I don't know his father's name otherwise I could say that actually Bhatta means Arya Bhatta it is still not known that whether he is from south or he actually was he worked in Kusum Pura but since Arya Bhatia's school was very ardently followed in the south not in the north so many think that actually he was from south not much no even people suspect Arya Bhatta also from the south because in south only his whole paksha was followed strictly but he worked in Kusum Pura and Kusum Pura is considered to be in Bhattana but because partly is a flower trumpet flower so if not just thank you