History of Science in South Asia
A journal for the history of all forms of scientific thought and action, ancient and modern, in all regions of South Asia
Review of: S. Balachandra Rao, Indian Astronomy:
Concepts and Procedures (Bengaluru: M. P. Birla
Institute of Management, 2014)
Toke Lindegaard Knudsen
MLA style citation form: Toke Lindegaard Knudsen (2016), “Review of: S. Balachandra Rao, Indian Astronomy:
Concepts and Procedures (Bengaluru: M. P. Birla Institute of Management, 2014),” History of Science in South
Asia 4 (2016): r7–r9. doi: 10.18732/H2BC74
Online version available at: http://hssa-journal.org
HISTORY OF SCIENCE IN SOUTH ASIA
A journal for the history of all forms of scientific thought and action, ancient and modern, in all
regions of South Asia, published online at http://hssa-journal.org
ISSN 2369-775X
Editorial Board:
• Dominik Wujastyk, University of Alberta, Edmonton, Canada
• Kim Plofker, Union College, Schenectady, United States
• Dhruv Raina, Jawaharlal Nehru University, New Delhi, India
• Sreeramula Rajeswara Sarma, formerly Aligarh Muslim University, Düsseldorf, Germany
• Fabrizio Speziale, Université Sorbonne Nouvelle – CNRS, Paris, France
• Michio Yano, Kyoto Sangyo University, Kyoto, Japan
Principal Contact:
Dominik Wujastyk, Editor, University of Alberta
Email: ⟨wujastyk@ualberta.ca⟩
Mailing Address:
History of Science in South Asia,
Department of History and Classics,
2–81 HM Tory Building,
University of Alberta,
Edmonton, AB, T6G 2H4
Canada
This journal provides immediate open access to its content on the principle that making research
freely available to the public supports a greater global exchange of knowledge.
Copyrights of all the articles rest with the respective authors and published under the provisions
of Creative Commons Attribution-ShareAlike 4.0 License.
The electronic versions were generated from sources marked up in LATEX in a computer running
gnu/linux operating system. pdf was typeset using XƎTEX from TEXLive. The base font used for
Latin script and oldstyle numerals was TEX Gyre Pagella developed by gust, the Polish TEX Users
Group.
r7
S. Balachandra Rao, Indian Astronomy: Concepts and Procedures (Bengaluru: M. P.
Birla Institute of Management, 2014) (New Delhi: Yoda Press, 2015), pp. xiv, 328.
| 450.
I
n addition to being the year in which Dr. S. Balachandra Rao’s book Indian Astronomy: Concepts and Procedures was published, the year 2014 was marked by
the 900th birth-anniversary of one of the most renowned astronomers of Indian
history, namely, Bhāskara II (born 1114 ce). It is appropriate that Dr. Balachandra
Rao’s book, a wonderful contribution to the study of astronomy in India, should
appear in a year in which there was a heightened focus on Indian astronomy.
As indicated by its title, the present book deals with the concepts and procedures of Indian astronomy. More specifically, it deals with the concepts and
procedures of the classical schools of Indian astronomy, which arose around the
middle of the first millennia ce. A brief introduction to the earlier history of astronomy in India, namely, astronomy in the Vedic texts and the Vedāṅgajyotiṣa
(an ancient Sanskrit text dealing with the determining the correct time for performing various sacrifices), is given (pp. 1–5), but the remainder of the book deals
with classical Indian astronomy.
The topics covered in the book are by and large those found in a siddhānta; that
is, the topics found in a comprehensive treatise of one of the classical schools of
Indian astronomy, covering not only the formulae needed for making astronomical calculations but also expounding the theory and the underlying model of
the scientific system. The topics include the celestial sphere and its great circles,
coordinate systems, time, mean and true positions of the luminaries and planets, lunar and solar eclipses, and conjunctions of heavenly bodies. The book also
covers, significantly, the Indian calendar (pañcāṅga) and astronomical tables in
the Indian astronomical tradition.
It is important to note that the book is not an academic study of Indian astronomy. While Dr. Balachandra Rao’s erudition is evident to readers of his book,
the book is intended for students and general readers. Its purpose is to generate an awareness of Indian astronomy and proficiency in the computational
procedures developed by the tradition over many centuries (p. iv). By this I do
not mean to imply that the book is not useful for scholars studying the history of
astronomy in India. On the contrary, such scholars will benefit from one of the
significant contributions of the book, namely, the carefully worked-out examples
found throughout it.
While academic studies present and comment on the formulae given in a
source text, the emphasis is rarely on their practical use. Rather, emphasis is put
on the exact phrasing of the formula, a theoretical discussion of the formula’s
history of science in south asia 4 (2016): r7–r9
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correctness, or a comparison of the formula with similar formulae found elsewhere in the Indian astronomical tradition (or in other traditions, such as Islamic
astronomy).
Dr. Balachandra Rao’s book, on the other hand, does not proceed chronologically in terms of the historical development of the system, nor does he discuss variations of the formulae in the works of different astronomers. Rather, he
presents the formulae clearly and illustrates them with useful examples. Considering the complexity of many of the formulae and methods, simply having
access to a correct formulation of particular formula is not sufficient for understanding how it is to be used practically. It takes some practice and experience
to become familiar with the system and how the formulae work within it.
The book uses two texts as representatives of Indian astronomy as found in
siddhānta treatises, namely, the modern Sūryasiddhānta, generally dated to the 9th
or 10th century ce, and the Grahalāghava of Gaṇeśa Daivajña, composed in the
early 16th century (p. 14). There are, of course, numerous other excellent texts
that could have been used, but the two chosen are good choices. While there
are differences between the various texts, if one is able to master the computational system of one text, working with the system of another will not prove too
difficult.
To give an example, formulae from Indian astronomy often rely on the socalled “day-group” (Skt. ahargaṇa), the number of civil days elapsed since a given
epoch is used, where the epoch is a specified time used for astronomical computations. However, given a date in our current calendar, it is not straightforward to compute the number of days elapsed since a given epoch from Indian
astronomy (the epoch could be the beginning of the kaliyuga, a time period from
Indian mythology which began more than 5,000 years ago, or a given historical
date used by an astronomer in a text).
Chapter 8 in the book, which covers the ahargaṇa, contains many practical
examples. Two such examples (p. 62–63) provide practical examples of how to
compute the ahargaṇa of a given date (April 12, 1991 and December 24, 2010,
respectively) when the epoch is the beginning of the kaliyuga. Other examples
demonstrate how to find the modern date corresponding to a date in the Indian
calendar via the ahargaṇa (pp. 67–68).
Other examples of useful worked-out procedures include how to practically
compute true positions for the luminaries and planets, described in chapters 10–
11. The Indian model for planetary motion is complex, involving two epicycles
to describe the motion of the five planets known to the Indian astronomers (the
model describes the motion of the sun and moon through one epicycle for each).
The two epicycles are presented as if independent though in reality they are not.
As such, their combination is not obvious and is computationally complicated.
The inclusion of the worked-out examples in this case are extremely useful as
history of science in south asia 4 (2016): r7–r9
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they enable the reader to understand how the model works on a deeper level.
Furthermore, the examples of the computations involved with lunar and
solar eclipses in chapter 13–14 are equally valuable. These computations
involved with a solar eclipse are especially complicated.
Overall, the worked-out examples constitute a significant contribution to the
field. It enables the interested reader to get to know the Indian astronomical
model at a deeper computational level. At the same time, it does the same for
the specialist scholar of Indian astronomy, who can use the book as a reference
work to be consulted on computational aspects.
Beyond computational examples, Dr. Balachandra Rao’s book makes another
important contribution to the study of Indian astronomy in chapter 20, which
focuses on astronomical tables in Indian astronomy. The important topic of astronomical tables in Indian astronomy has only recently received significant attention. As such, the discussion in the book is important. Moreover, in addition
to merely discussing known tables, Dr. Balachandra Rao reports on new material
in the book. More specifically, he managed to procure a manuscript of a text entitled the Grahagaṇita-padakāni from a private collection (p. 288). The manuscript
belongs to a place named Tyāgarti in Karnataka and the tables are based on the
modern Sūryasiddhānta.
The book thereby provides a glimpse into how astronomical computations
were done in practice at a local level. This glimpse provides a wonderful companion to the material covered previously in the book.
It is also important to note that the book has an extremely useful glossary of
technical terms. The glossary has both an “English to Sanskrit” and a “Sanskrit
to English” part. The glossary is especially useful for a student working on an
Indian astronomical text in the original Sanskrit.
Overall, Dr. Balachandra Rao’s book is a real contribution to the field of Indian
astronomy. It is recommended for both interested readers and scholars working
more seriously with the history of Indian astronomy.
Toke Lindegaard Knudsen, Ph.D.
Department of Mathematics, Computer Science, and Statistics,
State University of New York at Oneonta,
Oneonta, U.S.A.
history of science in south asia 4 (2016): r7–r9
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