Indian Astronomy- Concepts and Procedures

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It is truly heartening that this book, "INDIAN ASTRONOMY-CONCEPTS AND PROCEDURES" has gone to the second print within a short span of time. Highly appreciative and supportive reviews in acclaimed journals speak for the value of the contents and popularity of the book. Our M.P. Birla Institute of Management(MPBIM), Bengaluru is really proud to bring-out the second print of the book.

It is befitting that in the context of the year 2014 being celebrated as the Ninth Birth Centenary of one of the greatest Indian mathematicians and astronomers, Bhaskaracharya Il (born 1114 C.E.), the present book, "Indian Astronomy Concepts and Procedures" by Dr. S.Balachandra Rao is being brought out by our M.P. Birla Institute of Management (MPBIM).

This book is designed to provide an insight into the contributions of classical Indian astronomers through the ages. The author, Dr S.Balachandra Rao is well-known through his books -- in English and Kannada -as well as workshops in this field.

I congratulate the author for this thoughtful contribution to popularize the scientific contributions of our Indian mathematicians and astronomers of the world stature like Aryabhata (born 476 C.E.), Bhaskara I (c. 629 C.E.), Brahmagupa (c.628 C.E.), Bhaskara II (born 1114 C.E.), Ganesha Daivajna (c. 1520 C.E.) and the remarkable Kerala astronomers (c. 14 to 19th centuries).

MPBIM has always been in the forefront of disseminating the ideals and concepts of our great Indian cultural and scientific heritage by publishing many titles for the purpose besides providing modern management education to our youth.

I have great pleasure in expressing my gratitude to Dr. S.Balachandra Rao for giving this opportunity of publishing this book. I thank Sri Rajaram of Canvas Cretaives and Sri V.Ganesha Aithal for their thoughtful and attractive cover-design and M/s. Aditya Printers for the excellent printing of this book.

I am sure this book will be welcomed by the discerning lovers of the Indian. scientific heritage.

This book "Indian Astronomy - Concepts and Procedures' is designed mainly for the benefit of students and general readers. The purpose of the book is not only to create an awareness about Indian astronomy among the readers, but also to make them fairly proficient in the concepts, technicalities and computational procedures developed by great Indian mathematicians and astronomers over the past two thousand years.

Most of the concepts used in Indian astronomy like sauramana, cândramana, the solar and lunar calendars, tithis, naksatras, sankranti, yugadi, etc., are encountered by every Indian in his day-to-day life. A discerning person would be interested in knowing more about these concepts and many such issues of astronomical interest that form an important part of Indian culture. There is a great dearth of suitable books which systematically explain important and interesting topics of Indian astronomy to our modern students in a simple and intelligible language and style. No doubt, important classical Sanskrit texts like the Suryasiddhanta and Siddhantakiromani are critically edited and even translated into English, Hindi and some other Indian languages. But these texts are generally beyond the grasp of a modern reader.

The current book is an inclusive and more comprehensive sequel to my earlier titles "Indian Astronomy An Introduction" (Universities Press, Hyderabad) and "Ancient Indian Astronomy-Planetary Positions and Eclipses" (BRPC, Delhi).

Organization and Content

The development of astronomy in India from the Vedic times to the recent times - is briefly surveyed in Chapter 1.

The basic concepts of the celestial sphere, zodiac, constellations, equinoxes, etc. are discussed in Chapter 2. The different coordinate systems, viz., celestial longitude and latitude, right ascension and declination, azimuth and altitude, transformation of coordinates, the phenomenon and effects of the precession of the equinoxes constitute Chapter 3. The naksatra system is explained in Chapter 4. Division of time into convenient units like civil day and sidereal day, solar and civil calendars, solar and lunar months, adhikamāsa (intercalary months) and ksayamasa and the six rtus (seasons) are explained in Chapter 5.

The yuga system and the different eras are discussed in Chapter 6. Calendar systems, viz., the Gregorian, Hindu and Muslim solar and lunar systems and the five limbs (paricanga) -tithi, vara, naksatra, yoga and karana-form the subject matter of Chapter 7. The methods of finding ahargana (number of civil days from a chosen epoch) are dealt with in Chapter 8.

The number of revolutions of heavenly bodies in a mahayuga (of 432 x 10 years) computations of mean longitudes of the Sun, the Moon and the five planets (Mars, Mercury, Jupiter, Venus and Saturn) and the delântara correction (due to the difference in terrestrial longitudes) are explained in Chapter 9.

From the mean positions of the Sun and the Moon, their true positions can be obtained by applying the 'equation of the centre" (mandaphala). For this purpose, Indian astronomers have prescribed the peripheries(paridhi) of the manda epicycles of different heavenly bodies. These aspects as well as the true daily motions of the Sun and the Moon, the bhujantara correction, etc. are elaborated in Chapter 10.

In the case of the five planets, in addition to the mandaphala (equation of the centre), one more important equation called sīghra samskara (equation of conjunction") has to be applied. Here again, Indian astronomers have considered the peripheries of fighra epicycles. Chapter 11 deals with these equations for the determination of true longitudes of the planets as well as their true daily motions, retrograde motion (vakra gati) and the bhujantara correction for the so-called taragrahas (star planets),

Topics related to the three important issues (triprasna), viz., direction, place and time (dik, desa and kala) are examined in Chapter 12. These include the determination of the latitude of a place, sunrise and sunset times, rising of the signs of the zodiac and finding the Logna (ascendant) at a given time and place.

The cause of lunar eclipse, the angular diameter of the earth's shadow cone, the ecliptic limits for lunar eclipse and half-durations of a lunar eclipse and of maximum obsuration and the procedures of computation of lunar eclipse form the subject matter of Chapter 13.

Chapter 14 deals with the cause of solar eclipse, the angular distance between the Sun and the Moon at the beginning and end of a solar eclipse, computation of solar eclipse according to the Suryasiddhanta, and Ganesa Daivajta's Graha-laghavam, saros and metonic cycles.

We enjoyed witnessing the exciting phenomenon of Venus transit in 2004 as also in 2012. This interesting phenomenon of transit of the inferior planets, Mercury (Budha) and Venus (Sukra) are explained, with the classical Indian as well as the Improved Siddhäntic procedures in Chapter 15.

Even as in solar eclipse the Moon hides the Sun, partially or totally, the phenomenon of 'occultation' and the Indian computational procedure for the Moon hiding a fixed star or a planet is presented in Chapters 16 and 17 separately for stars and planets. The interesting event of a double occultation of Jupiter and Venus (Guru and Sukra) is worked out in section 17.2 of Chapter 17.

We have developed an 'Improved Siddhantic Procedure(ISP)' - for the computations of eclipses, transits and lunar occultations which yields results reasonably close to the modern ones.