foreign [Music] details of the various components of Indian astronomy what we would do is to quickly glance on the kind of astronomical contributions that various Indians have made in the last let's say a thousand thousand five hundred years I think it is very useful to understand what kind of work they have done we will go over it because that gives us a little sense of the continuity of tradition that has been very characteristic of astronomy and the developments that has happened in this country so we will first look at a table of important works and understand how each of these Works have contributed to the astronomical principles and the development of astronomy both in India and world over this table has contributions of ancient Indians between 600 CE and 1200 CE which means 6th Century to you know 12th century that you are talking about uh one of the earlier work is Surya siddhanta as you see here dates are not known there are different people who have come with different kinds of dates several versions of it is also available but an ancient version is summarized in varahami hiras wrote what is collected five siddhantas of course there's a modern version which is very popular even now among traditional Scholars and calendar makers and so on I think the first major work is you know there are five siddhantas you know that he has put together and it presents an updated summary of five ancient siddhantas as I told you uh but our entry into a more formal and mathematical approach to astronomy we are entirely in that of aryabhatta his seminal work and called aryabatium which he was born in 476 CE near patiliputra and Bihar he had really put the foundations we have a section on mathematics then foundations of trigonometry sine function he has made some important contributions in sine function which was better than what was used earlier by the Western and the Roman mechanisms and so on I create algorithms for positions of Sun Moon planets etcetera Etc leaves us and so on bhaskara one which explained mathematical and astronomy in detail of what aryabhatia is and he develops his own Arya button system in his own texts and so on seventh actually we also have brahmasputa siddhanta and Kanda kadyaka by Brahma Gupta which proposed a detailed system of calculations pertaining to sun moon and planets many algorithms for astronomy path breaking results in mathematics like Varga prakriti quadratic indeterminate equations all these were actually the real developments for astronomy to formally flourish even more who lived in the 8th to 9th century CE developed a textbook which expounded with new algorithms on the Arya button system in the 10th Century which provided expressions for second correction to the longitude of moon derivative of sine function Etc etcetera sripati came with siddhanta shekhara 11th century C which is an important text quoted by later astronomers because it had some important ideas paskaracharya 2 his famous siddhanta shiromani and then vasana bashya and karnakala all good works which brought standard calculations and algorithms for Indian astronomy ah ratified certain mistakes and then ready-made tables and arithmetic simplifications all these happened during this time but if you look at the time period from 1200 to 1800 CE substantive improvements happened over the earlier ones of notable contribution is this Kerala School of mathematics which had a series of people starting with madhava of sangama grama they contributed between 14th century and 19th century mathematical analysis derivation of infinite series for pi sine and cosine functions ah all those which were developed much before what it was in Europe ah traditional planetary Theory brought some interesting observations and planetary Theory and so on ah Innovations in astronomical computations spherical trigonometry all those were and improved theory for eclipses so a whole lot of people you have madhava you have parameshwara who brought dragonita and Deepika and so on the Deepika nilakantaji as I told as this Tantra sangraha and aryabhatia bashya he made very important corrections to planetary models and so on which is very useful even for modern day things then you have pissaroti and so on all these were there Ganesha devganyan wrote a very interesting text called grahal agawa which is used for preparing almanacs even now he has a very good system and then Kamala karad wrote in 1616 he was born some elaborate work on astronomy Chandra shekhar Samantha who was born in 1835 wrote a siddhanta darpana and important modifications in planetary parameters reform the traditional calendar of Orissa in a big way ah of course then we have Raja savai Jai Singh who created this yantra Raja rachana and so on the Jantar mantas that he built in several parts of India some of most of them are last you have one in Delhi and Jaipur which is still sort of functional in some ways and so on so these are some of the major observations and contributions of Indian astronomers so what we see in in these two tables is there is a continuous Improvement of earlier ideas more mathematical formal models of astronomy and all these actually added to that but the most important thing is aryabhatia which is the magnum opus in Indian astronomy because until aryabhatta 499 CE we had vedant vedanga jyotisha we have some you know astronomical calculations in The Vedic texts and so on they are not fully mathematical they are approximate but it is this aryabhatia which brought mathematical angle to it they are far more sophisticated and elaborate he provides procedures to calculate the planetary positions and eclipses the times of sunrise and sunset duration of the day ah relation between the shadow of the sun and the time these are very rudimentary and very important Concepts in astronomy many other quantities of astronomical interest all these were part of the siddhanta tradition which aryabhatta started obviously aryabhatta was the pioneering figure in the tradition of the full-fledged mathematical astronomy in India which I call it as the siddhantik tradition he was the first Arya Bhatia was the first extant discovered and available text on mathematical astronomy in India as I mentioned already is far more convenient than the Greek card for astronomical competitions it's much more sophisticated and convenient so let me quickly take you through this brief contents of Arya Bhatia aryabhatia has divided into four sections ah the first section is called gitika pada it is just as 13 verses ah which has the lateral numeral notation for numbers as I told you there is Aria bhattan scheme of representation of numbers the concepts of kalpa and Maha Yuga Revolution number of planets etcetera all those are described then you have the ganita pada which he introduces in 33 verses important mathematical Concepts square square root Cube cube root area of a triangle trapezium you see all those you know kutaka procedure for solving linear indeterminate equations cubes of the firstian natural numbers all those are there important mathematical Concepts which are required then you have kalak kriya pada which has 25 verses which is all about Reckoning of time calendrical Concepts planetary models explicit procedures for calculation of planetary position these are all very important building blocks of astronomy as we all know then you have the last section which is called golapada which has 50 verses which basically addresses the problems of spherical astronomy as seen at different latitudes diurnal problems associated with the motion of sun moon and planets on the celestial sphere brightness and darkness of Planet so many issues are discussed here so what is astonishing to see is that as early as 499 CE or the fifth century so much of work mathematical foundations Concepts and astronomy has been laid out by Arya bhattani's Arya Bhatia and one of the thing is the planetary revolution in a Maha Yuga according to aryabhatia Yamaha yoga is taken to be composed of four sub-yugas namely krita yoga and Kali Yuga and all of them of equal duration namely 10 lakhs 80 000 years this is a little different from The Vedic Concept in which the four yugas have varying durations but aryabhatia takes it as four equal you know 10 like 80 000 years the beginning of the current kaliga is on February 18 3102 BCE which was a Friday the aryabhatia established that and in Maha Yuga all the planets and the auxiliary quantities associated with them make integral numbers of revolutions this is what aryaba also establish issues in his work and so on so here is a table and the table as you see has planetary Revolutions in a Maha yoga as computed by Arya Bhatia so you have three columns here the First Column is number of revolutions second is the sidereal period and third is the modern value and I'm just showing this table just to tell you how the calculations of Arya Bhatia are so accurate and close to the modern day value as you can see from all these numbers that you see in the table I mean that speaks volumes about the amount of formal analysis that Arya bhatta was able to bring into action when you know studying all these planets and astronomical events and so on another notable contribution is planetary model what really is happening is the Indian model is geocentric ah what geocentric means is all planets revolve around the sun and the sun revolves around the earth I mean it's only a relative thing but you know that's how an observer sees it from the position on the earth so Arya Bata this is very similar to the Taiko brahe model which was proposed in 1580ce which is much later compared to the Indian model and aryabhatta was first proposed corrections to the model there were some errors there were some approximations with respect to Mars and Jupiter there was a Mars and I think Mercury there were some issues and so on so the corrections are called Manda samskara and Manta samskara is to obtain heliocentric longitudes of all plants idea is ah take Sun as the center and obtain all the you know longitudes of planets with respect to the sun which is called Manda samskara and then you have what is called shigra samskara so shigra samskara which is convert the heliocentric longitudes of planets to geocentric longitudes because Indian models are geocentric longitude is a rough graphical description of nilakanta Somaya G planetary model what happens is all the planets say Jupiter Saturn Mars Mercury everything is assumed to be revolving around the sun and the sun itself is assumed to revolve around the earth right so that is what it is as I told you this has been the Indian model but nilakanta somayaji made some important Corrections so that certain errors with respect to Mercury and Venus were actually addressed efficiently and that's been the contribution of nilakanta somiyaj so we will stop here just to give you a little sense of how the Indian astronomical thought has continuously moved on more and more formal understanding building on the earlier Works mathematical foundations correspondingly being developed and how Arya Bhatia has been a very important turning point and contribution for development of autonomy in this country I think with this we will move on to look at very specifics of certain elements of Indian calendar rail system and astronomical principles in the following videos [Music] thank you