Vedic Cosmography And Astronomy
Richard L. Thompson
INTRODUCTION
1: THE ASTRONOMICAL SIDDHÄNTAS
A. The Solar System According to the Sürya–siddhänta
B. The Opinion of Western Scholars
C. The Vedic Calendar and Astrology
D. The Starting Date of Kali–yuga
E. The Distances and Sizes of the Planets
F. The Size of the Universe
2: VEDIC PHYSICS
THE NATURE OF SPACE, TIME, AND MATTER
A. Extending Our Physical World View
B. The Position of Kåñëa
C. Mystic Siddhis
D. The Activities of Demigods, Yogés, and Åñis
E. REGIONS OF THIS EARTH
NOT PERCEIVABLE BY OUR SENSES
3: VEDIC COSMOGRAPHY
A. Bhü-maëòala, or Middle Earth
B. The Earth of Our Experience
C. Planets as Globes in Space
D. The Orbit of the Sun
4: THE VERTICAL DIMENSION
A. The Terminology of
Three and Fourteen Worlds
B. The Seven Planets
C. Higher-dimensional Travel
in the Vertical Direction
D. The Environs of the Earth
E. Eclipses
F. The Precession of the Equinoxes
5: THE EMPIRICAL CASE
FOR THE VEDIC WORLD SYSTEM
A. Unidentified Flying Objects
B. The Link with Traditional Lore
C. The Events at Fatima
6: MODERN ASTROPHYSICS
AND THE VEDIC PERSPECTIVE
A. The Principle of Relativity and Planetary Motion
B. Gravitation
C. Space Travel
D. The Universal Globe and Beyond
E. The Nature of Stars
7: RED SHIFTS AND
THE EXPANDING UNIVERSE
A. Hubble’s Expanding Universe Model
B. Anomalous Red Shifts:
The Observations of Halton Arp
C. Hubble’s Constant and Tired Light
D. Quasars
E. Quantized Red Shifts
8: QUESTIONS AND ANSWERS
Appendix 1:
VAÀÇÉDHARA ON BHÜ-MANDALA
AND THE EARTH GLOBE
Appendix 2:
THE ROLE OF GREEK INFLUENCE IN INDIAN ASTRONOMY
A. PINGREE’S THEORY REGARDING ÄRYABHAÖA
B. THE MAIN ARGUMENT FOR PINGREE’S THEORY
C. A PRELIMINARY CRITIQUE OF PINGREE’S ARGUMENT
D. THE THEORY OF OBSERVATION
E. INDIAN TRIGONOMETRY:
A SPECULATIVE RECONSTRUCTION
F. ANOTHER SPECULATIVE RECONSTRUCTION
BIBLIOGRAPHY
Richard L. Thompson
Dedicated to
His Divine Grace
A. C. Bhaktivedanta Swami Prabhupäda
oà ajïäna-timirändhasya jïänäïjana-çaläkayä
cakñur unmélitaà yena tasmai çré-gurave namaù
The cover: An astronomical instrument seen in Benares, India, in
1772 by an Englishman named Robert Barker. Said to be about two hundred years
old at the time, the structure included two quadrants that were used to measure
the position of the sun.
INTRODUCTION
“Now our Ph.D.’s must collaborate and study the Fifth Canto to
make a model for building the Vedic Planetarium. My final decision is that the
universe is just like a tree, with root upwards. Just as a tree has branches
and leaves, so the universe is also composed of planets which are fixed up in
the tree like the leaves, flowers, fruits, etc.…So now all you Ph.D.’s must
carefully study the details of the Fifth Canto and make a working model of the
universe. If we can explain the passing seasons, eclipses, phases of the moon,
passing of day and night, etc., then it will be very powerful propaganda”
(letter from Çréla Prabhupäda to Svarüpa Dämodara däsa, April 27, 1976).
In the year A.D. 1068 a group of workmen labored to erect an
earthen mound about sixty feet high in the Anglo-Saxon village of Cambridge,
northeast of London. On top of this mound they built a stone tower that
dominated the small collection of thatched houses huddled alongside the river
Cam. This tower served as a fortress to protect and consolidate this part of
the kingdom, which William the Conqueror had won just two years before.
At this time the Western, or European, civilization, which is so
important in the world today, was just beginning to emerge from the debris of
previous cultures and societies. Science as we know it today was unheard of,
and the Christian Church was in the process of solidifying its position in the
previously pagan territories of northern Europe. The writings of the ancient
Greeks and other early civilizations were largely lost, and would not be
reintroduced into Europe from Arab sources for some three hundred years.
Universities already existed in southern European countries; in Britain some two
hundred years would pass before the founding of Oxford and then Cambridge.
In A.D. 1000, about sixty years before the erection of the stone
tower on the Cam, an Arab scholar named Alberuni completed a book on India
(AL). Alberuni lived in the kingdom of Ghaznia, in the court of one King
Mahmud—a Muslim king who specialized in raiding the northwestern territories of
India, such as Sind and the Punjab. Alberuni was a well-known scholar of his
time who read Plato in the original Greek and who had also studied Sanskrit. He
was apparently employed by King Mahmud to study the Hindus, in much the same
way that the United States government now employs scholars to study the
Russians and the Communist Chinese.
Alberuni’s access to source material in Sanskrit was limited. He
had access to the body of Indian astronomical literature called jyotiña çästra,
and he also had access to a number of Puräëas, such as the Matsya Puräëa and
the Väyu Puräëa. He mentions the Çrémad-Bhägavatam, or Bhägavata Puräëa, but
apparently he never saw a copy of it.
In this body of literature, Alberuni was mainly interested in
information relating to the Indian view of the universe and the observable
material events taking place within it. Indeed, the most striking feature of
Alberuni’s book is that nearly half of it is concerned with Indian astronomy
and cosmology.
One important division of the jyotiña çästra consists of works on
mathematical astronomy known as astronomical siddhäntas. These include works of
historical Indian astronomers, such as Äryabhaöa, Brahmagupta, and Viraha
Mihira, some of whom were nearly Alberuni’s contemporaries. They also include
ancient Sanskrit texts, such as the Sürya-siddhänta, that were said to have
been originally disseminated by demigods and great åñis. These works treat the
earth as a small globe floating in space and surrounded by the planets, which
orbit around it. They are mainly concerned with the question of how to
calculate the positions of the planets in the sky at any desired time. They
contain elaborate rules for performing these calculations, as well as much
numerical data concerning the distances, sizes, and rates of motion of the
planets. However, they say very little about the nature of the planets, their
origin, and the causes of their motion.
The calculations described in the astronomical siddhäntas were
well understood by Alberuni, and it seems that at that time there was
considerable interest in Indian astronomy in the centers of Muslim
civilization. He was also familiar with the Greek astronomical tradition,
epitomized by Ptolemy. However, Alberuni found the cosmology presented in the
Puräëas very hard to understand. His account of Puräëic cosmology closely
follows the Fifth Canto of the Çrémad-Bhägavatam, and the Puräëas in general.
When dealing with this material, Alberuni frequently expressed exasperation and
complete incomprehension, much as many people do today, and he naturally took
this as an opportunity to criticize Hindu dharma and assert the superiority of
his own Muslim tradition.
In this book we will discuss the cosmology presented in the Fifth
Canto of the Çrémad-Bhägavatam and try to clarify its relationship with other
prominent systems of cosmology, both ancient and modern. We have begun with
this historical account to show that bewilderment with the cosmology of the
Bhägavatam is not a new phenomenon caused by the rise of modern science. The
same bewilderment also affected Alberuni, even though in his society the earth
was regarded as being fixed in the center of the universe.
Many Indian astronomers of earlier centuries were also unable to
understand Vedic cosmology, and they were led to openly reject parts of it,
even though their own religious and social tradition was based on the Puräëas.
For example, Bhäskaräcärya, the 11th-century author of the siddhäntic text
Siddhänta-çiromaëi, could not reconcile the relatively small diameter of the
earth, which he deduced from simple measurements, with the immense magnitude
attributed to the earth by the Pauränikas, the followers of the Puräëas (SSB1,
pp. 114–15). Likewise, the 15th-century south Indian astronomer Parameçvara
stated that the Puräëic account of the seven dvépas and oceans is something
“given only for religious meditation,” and that the 84,000-yojana height of
Mount Meru described in the Puräëas is “not acceptable to the astronomers” (GP,
pp. 85, 87).
Vaiñëavas of past centuries also discussed the relationship
between the Fifth Canto of Çrémad-Bhägavatam and the jyotiña çästras. An
example of this is found in the Bhägavatam commentary of Vaàçédhara, a Vaiñëava
who lived in the 17th century A.D. In this commentary, Vaàçédhara discusses the
apparent conflict between the small size of the earth, as described in the
jyotiña çästras, and the large size of Bhü-maëòala, as described in the Fifth
Canto. His analysis of this apparent conflict is discussed in Appendix 1.
There are evidently serious disagreements between the cosmological
system of the Puräëas and the world models that human observers tend to arrive
at using their reasoning powers and their ordinary senses. The cause of these
difficulties is not simply the rise of modern Western science. They have
existed in India since a time antedating the rise of modern Western culture,
and to some they may seem to be based on an inherent contradiction within the
Vedic tradition itself.
The long-standing perplexity that has attended the subject of
Vedic cosmology indicates that these disagreements are very deep and difficult
to resolve. However, the thesis of this book is that the disagreements are not
irreconcilable. The apparent contradictions can be resolved by developing a
proper understanding of the nature of space, time, and matter, as described in
the Çrémad-Bhägavatam, and a corresponding understanding of the Vedic approach
to describing and thinking about reality.
In Chapter 1 we begin our account of Vedic astronomy by discussing
the astronomical siddhäntas. We give evidence indicating that these works form
an integral part of the original Vedic tradition. To accept these works and
reject Puräëic cosmology, as some Indian astronomers have done, is to start
down the path of modern scientific materialism, which ultimately leads to the
total rejection of the Vedic literature. But to reject the astronomical
siddhäntas as anti-Vedic means to lose the Vedic tradition of rigorous
mathematical astronomy. This plays into the hands of the modern Western
scholars who wish to reject the Vedas and Puräëas as mythological, and who
interpret the astronomical siddhäntas as products of Greek scientific genius
that were borrowed and falsely dressed in Hindu garb by dishonest brähmaëas.
(In Appendix 2 we address some of the arguments of these scholars and show that
they are seriously flawed.)
Our thesis is that the astronomical siddhäntas and the Puräëic
cosmology can be understood as mutually compatible accounts of one multifaceted
material reality. Modern Western science is based on the idea that nature can
be fully described by a single, rational world-model. However, the
Çrémad-Bhägavatam points out that no person of this world is capable of fully
describing the material universe “even in a lifetime as long as that of Brahmä”
(SB 5.16.4). Thus the Vedic approach to the description of nature is based on
the strategy of presenting many mutually compatible aspects of one humanly
indescribable complete whole.
The old story of the blind men and the elephant epitomizes this
approach. Each blind man observed a genuine aspect of the elephant, and a
seeing man could understand how all of these aspects fit together to form a
coherent whole. Even a blind man, after carefully studying the reports coming
from the seeing man and his fellow blind men, could begin to understand the
nature of the whole elephant, although he could not directly sense it without obtaining
a cure for his blindness. We suggest that in our attempts to understand the
material universe, we are comparable to a blind man feeling a particular part
of the elephant.
According to this analogy, the astronomical siddhäntas present the
cosmos as it appears to similar blind men of this earth, and literatures such
as the Bhägavatam present the world view of beings with higher powers of
vision. These include demigods, åñis, and ultimately the Supreme Lord, who
alone can see the entire universe. These higher beings can directly see both
the aspects of the universe presented in the Bhägavatam and the aspects
presented in the astronomical siddhäntas. To these higher beings it is apparent
how all of these aspects fit together consistently in a complete whole, even
though we can begin to understand this only with great effort.
We note that with the development of modern physics, scientists
have at least temporarily been forced to abandon the goal of formulating one
complete mathematical model of the atom. According to the standard
interpretation of the quantum theory introduced by Niels Bohr, atomic phenomena
must be understood from at least two complementary perspectives rather than as
a single, intelligible whole. These perspectives—the wave picture and the
particle picture—seem to contradict each other, and yet they are both valid
descriptions of nature. They are facets of a coherent theory of the atom, but
they cannot be combined within the framework of classical physics. To unite
them and show their compatibility, one must go to a higher-dimensional level of
mathematical abstraction, which is very difficult to comprehend.
In developing an understanding of Vedic cosmology as a
multifaceted description of reality, it will be necessary to free ourselves
from the rigid framework of Cartesian and Euclidian three-dimensional geometry,
which forms the basis of the modern scientific world view. We will attempt to
do this in Chapter 2, where we will discuss space, physical laws, and processes
of sense perception, as presented in the Çrémad-Bhägavatam. In Chapters 3 and 4
we will give an account of Puräëic cosmology and show how the ideas developed
in Chapter 2 can be applied to resolve apparent contradictions within the Vedic
tradition and between the Vedic cosmology and the world of our ordinary sensory
experience. Here a key idea is that the universe as described in Vedic
literature is higher-dimensional: it cannot be fully represented within
three-dimensional space.
In our discussion of Vedic cosmology we will be forced to
interpret the texts of the Çrémad-Bhägavatam and other Vedic literature. This
is inevitable, since even a literal interpretation is based on underlying
assumptions made by the reader—assumptions that may differ from those of the
author of the text, and that the reader may hold without being consciously
aware of them. In making such interpretations we will try to adhere to the
following rule given by Çréla Prabhupäda: “The original purpose of the text
must be maintained. No obscure meaning should be screwed out of it, yet it
should be presented in an interesting manner for the understanding of the
audience. This is called realization” (SB 1.4.1p). We also note that Çréla
Prabhupäda advocated in SB 5.16.10p that we should accept the cosmological
statements in the Çrémad-Bhägavatam as authoritative and simply try to
appreciate them. We will therefore adopt the working assumption that even
though these statements may seem very hard to comprehend, they nonetheless do
present an understandable and realistic description of the universe.
In Chapter 5 we address the question of whether or not there is
any empirical evidence supporting the higher-dimensional picture of the
universe that we derive from the Çrémad-Bhägavatam. It turns out that there is
voluminous evidence along these lines, although practically none of it is
accepted by the scientific community.
In Chapter 6 we return to Vedic cosmology and discuss a number of
controversial topics, including gravitation, the moon flight, the scale of
cosmic distances, and the nature of stars. In Chapter 7 we survey the modern
scientific evidence regarding the theory of the expanding universe. Here we not
only find that this theory is flawed, but we also find evidence indicating that
Newton’s laws of motion fail on the galactic level. Finally, in Chapter 8 we
present brief answers to a number of common questions.
The material presented in this book constitutes a preliminary
study of Vedic cosmology and astronomy. To properly answer the many questions
that arise, much further research will have to be done. This will include (1)
careful study of cosmological material in a wide variety of Vedic literatures,
(2) study of Vedic geographical material, (3) careful analysis of the theories
of Western scholars about the history of Vedic astronomy, (4) study of ancient
astronomical observations, (5) study of dating and the Vedic calendar, (6)
study of empirical evidence relating to Vedic cosmology, and (7) the careful
analysis of modern cosmology and astronomy. It is our hope that these studies
will culminate in the development of a Vedic planetarium and museum that can
effectively present Kåñëa consciousness in the context of Vedic cosmology.
This, of course, was Çréla Prabhupäda’s plan for the planetarium in the Temple
of Understanding in Çrédhäma Mäyäpura, and similar planetariums can be set up
in cities around the world.
In this book we will use the terms Vedic and Puräëic
interchangeably. Although modern scholars reject this usage, it is justified by
the verse itihäsa-puräëaà ca païcamo veda ucyate in Çrémad-Bhägavatam (1.4.20).
According to this verse, the Puräëas and the histories, such as the
Mahäbhärata, are known as the fifth Veda. References to Sanskrit and Bengali
texts are of three forms: A reference such as SB 5.22.14 means that the
quotation is from the 14th verse of Chapter 22 of the Fifth Canto of
Çrémad-Bhägavatam. A reference such as SB 5.21.6p means the quotation is from
Çréla Prabhupäda’s purport to verse 6 of Chapter 21 of the Fifth Canto. And a reference
such as SB 5.21cs means the quotation is from the Chapter Summary of Chapter 21
of the Fifth Canto. AL or ML after references to the Caitanya-caritämåta
indicate Ädi-lélä or Madhya-lélä. For books not divided into verses and
purports, we cite the code identifying the book, followed by the page number
(see the Bibliography).
VCA1: THE ASTRONOMICAL SIDDHÄNTAS
1
THE ASTRONOMICAL SIDDHÄNTAS
Since the cosmology of the astronomical siddhäntas is quite
similar to traditional Western cosmology, we will begin our discussion of Vedic
astronomy by briefly describing the contents of these works and their status in
the Vaiñëava tradition. In a number of purports in the Caitanya-caritämåta,
Çréla Prabhupäda refers to two of the principal works of this school of
astronomy, the Sürya-siddhänta and the Siddhänta-çiromaëi. The most important
of these references is the following:
These calculations are given in the authentic astronomy book known
as the Sürya-siddhänta. This book was compiled by the great professor of astronomy
and mathematics Bimal Prasäd Datta, later known as Bhaktisiddhänta Sarasvaté
Gosvämé, who was our merciful spiritual master. He was honored with the title
Siddhänta Sarasvaté for writing the Sürya-siddhänta, and the title Gosvämi
Mahäräja was added when he accepted sannyäsa, the renounced order of life [CC
AL 3.8p].
Here the Sürya-siddhänta is clearly endorsed as an authentic
astronomical treatise, and it is associated with Çréla Bhaktisiddhänta
Sarasvaté Öhäkura. The Sürya-siddhänta is an ancient Sanskrit work that,
according to the text itself, was spoken by a messenger from the sun-god,
Sürya, to the famous asura Maya Dänava at the end of the last Satya-yuga. It
was translated into Bengali by Çréla Bhaktisiddhänta Sarasvaté, who was expert
in Vedic astronomy and astrology.
Some insight into Çréla Bhaktisiddhänta’s connection with Vedic
astronomy can be found in the bibliography of his writings. There it is stated,
In 1897 he opened a “Tol” named “Saraswata Chatuspati” in
Manicktola Street for teaching Hindu Astronomy nicely calculated independently
of Greek and other European astronomical findings and calculations.
During this time he used to edit two monthly magazines named
“Jyotirvid” and “Brihaspati” (1896), and he published several authoritative
treatises on Hindu Astronomy.… He was offered a chair in the Calcutta
University by Sir Asutosh Mukherjee, which he refused [BS1, pp. 2–3].
These statements indicate that Çréla Bhaktisiddhänta took
considerable interest in Vedic astronomy and astrology during the latter part
of the nineteenth century, and they suggest that one of his motives for doing
this was to establish that the Vedic astronomical tradition is independent of
Greek and European influence. In addition to his Bengali translation of the
Sürya-siddhänta, Çréla Bhaktisiddhänta Sarasvaté published the following works
in his two magazines:
(a) Bengali translation and explanation of Bhäskaräcärya’s
Siddhänta-Shiromani Goladhyaya with Basanabhasya, (b) Bengali translation of
Ravichandrasayanaspashta, Laghujatak, with annotation of Bhattotpala, (c)
Bengali translation of Laghuparashariya, or Ududaya-Pradip, with Bhairava
Datta’s annotation, (d) Whole of Bhauma-Siddhänta according to western
calculation, (e) Whole of Ärya-Siddhänta by Äryabhaöa, (f) Paramadishwara’s
Bhatta Dipika-Tika, Dinakaumudi, Chamatkara-Chintamoni, and
Jyotish-Tatwa-Samhita [BS1, p. 26].
This list includes a translation of the Siddhänta-çiromaëi, by the
11th-century astronomer Bhäskaräcärya, and the Ärya-siddhänta, by the
6th-century astronomer Äryabhaöa. Bhaööotpala was a well-known astronomical
commentator who lived in the 10th century. The other items in this list also
deal with astronomy and astrology, but we do not have more information
regarding them.
Çréla Bhaktisiddhänta Sarasvaté also published the Bhaktibhävana
Païjikä and the Çré Navadvépa Païjikä (BS2, pp. 56,180). A païjikä is an
almanac that includes dates for religious festivals and special days such as
Ekädaçé. These dates are traditionally calculated using the rules given in the
jyotiña çästras.
During the time of his active preaching as head of the Gauòéya
Math, Çréla Bhaktisiddhänta stopped publishing works dealing specifically with
astronomy and astrology. However, as we will note later on, Çréla
Bhaktisiddhänta cites both the Sürya-siddhänta and the Siddhänta-çiromaëi
several times in his Anubhäñya commentary on the Caitanya-caritämåta.
It is clear that in recent centuries the Sürya-siddhänta and
similar works have played an important role in Indian culture. They have been
regularly used for preparing calendars and for performing astrological
calculations. In Section 1.c we cite evidence from the Bhägavatam suggesting
that complex astrological and calendrical calculations were also regularly
performed in Vedic times. We therefore suggest that similar or identical
systems of astronomical calculation must have been known in this period.
Here we should discuss a potential misunderstanding. We have
stated that Vaiñëavas have traditionally made use of the astronomical
siddhäntas and that both Çréla Prabhupäda and Çréla Bhaktisiddhänta Sarasvaté
Öhäkura have referred to them. At the same time, we have pointed out that the
authors of the astronomical siddhäntas, such as Bhäskaräcärya, have been unable
to accept some of the cosmological statements in the Puräëas. How could
Vaiñëava äcäryas accept works which criticize the Puräëas?
We suggest that the astronomical siddhäntas have a different
status than transcendental literature such as the Çrémad-Bhägavatam. They are
authentic in the sense that they belong to a genuine Vedic astronomical
tradition, but they are nonetheless human works that may contain imperfections.
Many of these works, such as the Siddhänta-çiromaëi, were composed in recent
centuries and make use of empirical observations. Others, such as the
Sürya-siddhänta, are attributed to demigods but were transmitted to us by
persons who are not spiritually perfect. Thus the Sürya-siddhänta was recorded
by Maya Dänava. Çréla Prabhupäda has said that Maya Dänava “is always
materially happy because he is favored by Lord Çiva, but he cannot achieve
spiritual happiness at any time” (SB 5.24cs).
The astronomical siddhäntas constitute a practical division of
Vedic science, and they have been used as such by Vaiñëavas throughout history.
The thesis of this book is that these works are surviving remnants of an
earlier astronomical science that was fully compatible with the cosmology of
the Puräëas, and that was disseminated in human society by demigods and great sages.
With the progress of Kali-yuga, this astronomical knowledge was largely lost.
In recent centuries the knowledge that survived was reworked by various Indian
astronomers and brought up to date by means of empirical observations.
Although we do not know anything about the methods of calculation
used before the Kali-yuga, they must have had at least the same scope and order
of sophistication as the methods presented in the Sürya-siddhänta. Otherwise
they could not have produced comparable results. In presently available Vedic
literature, such computational methods are presented only in the astronomical
siddhäntas and other jyotiña çästras. The Itihäsas and Puräëas (including the
Bhägavatam) do not contain rules for astronomical calculations, and the Vedäs
contain only the Vedäìga-jyotiña, which is a jyotiña çästra but is very brief
and rudimentary (VJ).
The following is a brief summary of the topics covered by the
Sürya-siddhänta: (1) computation of the mean and true positions of the planets
in the sky, (2) determination of latitude and longitude and local celestial
coordinates, (3) prediction of full and partial eclipses of the moon and sun,
(4) prediction of conjunctions of planets with stars and other planets, (5)
calculation of the rising and setting times of planets and stars, (6)
calculation of the moon’s phases, (7) calculation of the dates of various
astrologically significant planetary combinations (such as Vyatépäta), (8) a
discussion of cosmography, (9) a discussion of astronomical instruments, and
(10) a discussion of kinds of time. We will first discuss the computation of
mean and true planetary positions, since it introduces the Sürya-siddhänta’s
basic model of the planets and their motion in space.
1.A. The Solar System
According to the Sürya–siddhänta
1.A. The Solar System
According to the Sürya–siddhänta
The Sürya-siddhänta treats the earth as a globe fixed in space,
and it describes the seven traditional planets (the sun, the moon, Mars,
Mercury, Jupiter, Venus, and Saturn) as moving in orbits around the earth. It
also describes the orbit of the planet Rähu, but it makes no mention of Uranus,
Neptune, and Pluto. The main function of the Sürya-siddhänta is to provide
rules allowing us to calculate the positions of these planets at any given
time. Given a particular date, expressed in days, hours, and minutes since the
beginning of Kali-yuga, one can use these rules to compute the direction in the
sky in which each of the seven planets will be found at that time. All of the
other calculations described above are based on these fundamental rules.
The basis for these rules of calculation is a quantitative model
of how the planets move in space. This model is very similar to the modern
Western model of the solar system. In fact, the only major difference between
these two models is that the Sürya-siddhänta’s is geocentric, whereas the model
of the solar system that forms the basis of modern astronomy is heliocentric.
To determine the motion of a planet such as Venus using the modern
heliocentric system, one must consider two motions: the motion of Venus around
the sun and the motion of the earth around the sun. As a crude first
approximation, we can take both of these motions to be circular. We can also
imagine that the earth is stationary and that Venus is revolving around the
sun, which in turn is revolving around the earth. The relative motions of the
earth and Venus are the same, whether we adopt the heliocentric or geocentric
point of view.
In the Sürya-siddhänta the motion of Venus is also described, to a
first approximation, by a combination of two motions, which we can call cycles
1 and 2. The first motion is in a circle around the earth, and the second is in
a circle around a point on the circumference of the first circle. This second
circular motion is called an epicycle.
It so happens that the period of revolution for cycle 1 is one
earth year, and the period for cycle 2 is one Venusian year, or the time
required for Venus to orbit the sun according to the heliocentric model. Also,
the sun is located at the point on the circumference of cycle 1 which serves as
the center of rotation for cycle 2. Thus we can interpret the Sürya-siddhänta
as saying that Venus is revolving around the sun, which in turn is revolving
around the earth (see Figure 1). According to this interpretation, the only
difference between the Sürya-siddhänta model and the modern heliocentric model
is one of relative point of view.
Table 1
Planetary Years, Distances, and Diameters,
According to Modern Western Astronomy
Planet Length of year Mean Distance from Sun Mean Distance from Earth Diameter
Sun — 0. 1.00 865,110
Mercury 87.969 .39 1.00 3,100
Venus 224.701 .72 1.00 7,560
Earth 365.257 1.00 0. 7,928
Mars 686.980 1.52 1.52 4,191
Jupiter 4,332.587 5.20 5.20 86,850
Saturn 10,759.202 9.55 9.55 72,000
Uranus 30,685.206 19.2 19.2 30,000
Neptune 60,189.522 30.1 30.1 28,000
Pluto 90,465.38 39.5 39.5 ?
Years are equal to the number of earth days required for the
planet to revolve once around the sun. Distances are given in astronomical
units (AU), and 1 AU is equal to 92.9 million miles, the mean distance from the
earth to the sun. Diameters are given in miles. (The years are taken from the
standard astronomy text TSA, and the other figures are taken from EA.)
In Tables 1 and 2 we list some modern Western data concerning the
sun, the moon, and the planets, and in Table 3 we list some data on periods of
planetary revolution taken from the Sürya-siddhänta. The periods for cycles 1
and 2 are given in revolutions per divya-yuga. One divya-yuga is 4,320,000
solar years, and a solar year is the time it takes the sun to make one complete
circuit through the sky against the background of stars. This is the same as
the time it takes the earth to complete one orbit of the sun according to the
heliocentric model.
TABLE 2
Data pertaining to the Moon,
According to Modern Western Astronomy
Siderial Period 27.32166 days
Synodic Period 29.53059 days
Nodal Period 27.2122 days
Siderial Period of Nodes -6,792.28 days
Mean Distance from Earth 238,000 miles = .002567 AU
Diameter 2,160 miles
The sidereal period is the time required for the moon to complete
one orbit against the background of stars. The synodic period, or month, is the
time from new moon to new moon. The nodal period is the time required for the
moon to pass from ascending node back to ascending node. The sidereal period of
the nodes is the time for the ascending node to make one revolution with
respect to the background of stars. (This is negative since the motion of the
nodes is retrograde.) (EA)
For Venus and Mercury, cycle 1 corresponds to the revolution of
the earth around the sun, and cycle 2 corresponds to the revolution of the
planet around the sun. The times for cycle 1 should therefore be one revolution
per solar year, and, indeed, they are
listed as 4,320,000 revolutions per divya-yuga.
The times for cycle 2 of Venus and Mercury should equal the modern
heliocentric years of these planets. According to the Sürya-siddhänta, there
are 1,577,917,828 solar days per divya-yuga. (A solar day is the time from
sunrise to sunrise.) The cycle-2 times
can be computed in solar days by dividing this number by the revolutions per
divya-yuga in cycle 2. The cycle-2 times are listed as “SS [Sürya-siddhänta]
Period,” and they are indeed very close to the heliocentric years, which are
listed as “W [Western] Period” in Table 3.
For Mars, Jupiter, and Saturn, cycle 1 corresponds to the
revolution of the planet around the sun, and cycle 2 corresponds to the
revolution of the earth around the sun. Thus we see that cycle 2 for these
planets is one solar year (or 4,320,000 revolutions per divya-yuga). The times
for cycle 1 in solar days can also be computed by dividing the revolutions per
divya-yuga of cycle 1 into 1,577,917,828, and they are listed under “SS
Period.” We can again see that they are very close to the corresponding
heliocentric years.
For the sun and moon, cycle 2 is not specified. But if we divide
1,577,917,828 by the numbers of revolutions per divya-yuga for cycle 1 of the
sun and moon, we can calculate the number of solar days in the orbital periods
of these planets. Table 3 shows that these figures agree well with the modern
values, especially in the case of the moon. (Of course, the orbital period of
the sun is simply one solar year.)
TABLE 3
Planetary Periods According to the Sürya-siddhänta
Planet Cycle 1 Cycle 2 SS Period W
Period
Moon 57,753,336 * 27.322 27.32166
Mercury 4,320,000 17,937,000 87.97 87.969
Venus 4,320,000 7,022,376 224.7 224.701
Sun 4,320,000 * 365.26 365.257
Mars 2,296,832 4,320,000 687.0 686.980
Jupiter 364,220 4,320,000 4,332.3 4,332.587
Saturn 146,568 4,320,000 10,765.77 10,759.202
Rähu -232,238 * -6,794.40 -6,792.280
The figures for cycles 1 and 2 are in revolutions per divya-yuga.
The “SS Period” is equal to 1,577,917,828, the number of solar days in a yuga
cycle, divided by one of the two cycle figures (see the text). This should give
the heliocentric period for Mercury, Venus, the earth (under sun) Mars,
Jupiter, and Saturn, and it shold give the geocentric period for the moon and
Rähu. These periods can be compared with the years in Table 1 and the sidereal
periods of the moon and its nodes in Table 2. These quantities have been
reproduced from Tables 1 and 2 in the column labeled “W Period.”
In Table 3 a cycle-1 value is also listed for the planet Rähu.
Rähu is not recognized by modern Western astronomers, but its position in
space, as described in the Sürya-siddhänta, does correspond with a quantity
that is measured by modern astronomers. This is the ascending node of the moon.
From a geocentric perspective, the orbit of the sun defines one
plane passing through the center of the earth, and the orbit of the moon
defines another such plane. These two planes are slightly tilted with respect
to each other, and thus they intersect on a line. The point where the moon
crosses this line going from celestial south to celestial north is called the
ascending node of the moon. According to the Sürya-siddhänta, the planet Rähu
is located in the direction of the moon’s ascending node.
From Table 3 we can see that the modern figure for the time of one
revolution of the moon’s ascending node agrees quite well with the time for one
revolution of Rähu. (These times have minus signs because Rähu orbits in a
direction opposite to that of all the other planets.)
TABLE 4
Heliocentric Distances of Planets, According to the
Sürya-siddhänta
Planet Cycle 1 Cycle 2 SS Distance W
Distance
Mercury 360 133 132 .368 .39
Venus 360 262 260 .725 .72
Mars 360 235 232 1.54 1.52
Jupiter 360 70 72 5.07 5.20
Saturn 360 39 40 9.11 9.55
These are the distances of the planets from the sun. The mean
heliocentric distance of Mercury and Venus in AU should be given by its mean
cycle-2 circumference divided by its cycle-1 circumference. (The cycle-2
circumferences vary between the indicated limits, and we use their average
values.) For the other planets the mean heliocentric distance should be the
reciprocal of this (see the text). These figures are listed as “SS Distance,”
and the corresponding modern Western heliocentric distances are listed under “W
Distance.”
If cycle 1 for Venus corresponds to the motion of the sun around
the earth (or of the earth around the sun), and cycle 2 corresponds to the
motion of Venus around the sun, then we should have the following equation:
circumference of cycle 2
= Venus-to-Sun distance
circumference of cycle 1
Earth-to-Sun distance
Here the ratio of distances equals the ratio of circumferences,
since the circumference of a circle is 2 pi times its radius. The ratio of
distances is equal to the distance from Venus to the sun in astronomical units
(AU), or units of the earth-sun distance. The modern values for the distances
of the planets from the sun are listed in Table 1. In Table 4, the ratios on
the left of our equation are computed for Mercury and Venus, and we can see
that they do agree well with the modern distance figures. For Mars, Jupiter,
and Saturn, cycles 1 and 2 are switched, and thus we are interested in
comparing the heliocentric distances with the reciprocal of the ratio on the
left of the equation. These quantities are listed in the table, and they also
agree well with the modern values. Thus, we can conclude that the
Sürya-siddhänta presents a picture of the relative motions and positions of the
planets Mercury, Venus, Earth, Mars, Jupiter, and Saturn that agrees quite well
with modern astronomy.
1.B. The Opinion of Western Scholars
1.B. The Opinion of Western Scholars
This agreement between Vedic and Western astronomy will seem
surprising to anyone who is familiar with the cosmology described in the Fifth
Canto of the Çrémad-Bhägavatam and in the other Puräëas, the Mahäbhärata, and
the Rämäyaëa. The astronomical siddhäntas seem to have much more in common with
Western astronomy than they do with Puräëic cosmology, and they seem to be even
more closely related with the astronomy of the Alexandrian Greeks. Indeed, in
the opinion of modern Western scholars, the astronomical school of the
siddhäntas was imported into India from Greek sources in the early centuries of
the Christian era. Since the siddhäntas themselves do not acknowledge this,
these scholars claim that Indian astronomers, acting out of chauvinism and
religious sentiment, Hinduized their borrowed Greek knowledge and claimed it as
their own. According to this idea, the cosmology of the Puräëas represents an
earlier, indigenous phase in the development of Hindu thought, which is
entirely mythological and unscientific.
This, of course, is not the traditional Vaiñëava viewpoint. The
traditional viewpoint is indicated by our observations regarding the
astronomical studies of Çréla Bhaktisiddhänta Sarasvaté Öhäkura, who founded a
school for “teaching Hindu Astronomy nicely calculated independently of Greek
and other European astronomical findings and calculations.”
The Bhägavatam commentary of the Vaiñëava scholar Vaàçédhara also
sheds light on the traditional understanding of the jyotiña çästras. His
commentary appears in the book of Bhägavatam commentaries Çréla Prabhupäda used
when writing his purports. In Appendix 1 we discuss in detail Vaàçédhara’s
commentary on SB 5.20.38. Here we note that Vaàçédhara declares the jyotiña
çästra to be the “eye of the Vedas,” in accord with verse 1.4 of the
Närada-saàhitä, which says, “The excellent science of astronomy comprising
siddhänta, saàhitä, and horä as its three branches is the clear eye of the
Vedas” (BJS, xxvi).
Vaiñëava tradition indicates that the jyotiña çästra is indigenous
to Vedic culture, and this is supported by the fact that the astronomical
siddhäntas do not acknowledge foreign source material. The modern scholarly
view that all important aspects of Indian astronomy were transmitted to India
from Greek sources is therefore tantamount to an accusation of fraud. Although
scholars of the present day do not generally declare this openly in their
published writings, they do declare it by implication, and the accusation was
explicitly made by the first British Indologists in the early nineteenth
century.
John Bentley was one of these early Indologists, and it has been
said of his work that “he thoroughly misapprehended the character of the Hindu
astronomical literature, thinking it to be in the main a mass of forgeries
framed for the purpose of deceiving the world respecting the antiquity of the
Hindu people” (HA, p. 3). Yet the modern scholarly opinion that the Bhägavatam
was written after the ninth century A.D. is tantamount to accusing it of being
a similar forgery. In fact, we would suggest that the scholarly assessment of
Vedic astronomy is part of a general effort on the part of Western scholars to
dismiss the Vedic literature as a fraud.
A large book would be needed to properly evaluate all of the
claims made by scholars concerning the origins of Indian astronomy. In Appendix
2 we indicate the nature of many of these claims by analyzing three cases in
detail. Our observation is that scholarly studies of Indian astronomy tend to
be based on imaginary historical reconstructions that fill the void left by an
almost total lack of solid historical evidence.
Here we will simply make a few brief observations indicating an
alternative to the current scholarly view. We suggest that the similarity
between the Sürya-siddhänta and the astronomical system of Ptolemy is not due
to a one-sided transfer of knowledge from Greece and Alexandrian Egypt to
India. Due partly to the great social upheavals following the fall of the Roman
Empire, our knowledge of ancient Greek history is extremely fragmentary.
However, although history books do not generally acknowledge it, evidence does
exist of extensive contact between India and ancient Greece. (For example, see
PA, where it is suggested that Pythagoras was a student of Indian philosophy
and that brähmaëas and yogés were active in the ancient Mediterranean world.)
We therefore propose the following tentative scenario for the
relations between ancient India and ancient Greece: SB 1.12.24p says that the
Vedic king Yayäti was the ancestor of the Greeks, and SB 2.4.18p says that the Greeks were once classified
among the kñatriya kings of Bhärata but later gave up brahminical culture and
became known as mlecchas. We therefore propose that the Greeks and the people
of India once shared a common culture, which included knowledge of astronomy.
Over the course of time, great cultural divergences developed, but many common
cultural features remained as a result of shared ancestry and later
communication. Due to the vicissitudes of the Kali-yuga, astronomical knowledge
may have been lost several times in Greece over the last few thousand years and
later regained through communication with India, discovery of old texts, and
individual creativity. This brings us down to the late Roman period, in which
Greece and India shared similar astronomical systems. The scenario ends with
the fall of Rome, the burning of the famous library at Alexandria, and the
general destruction of records of the ancient past.
According to this scenario, much creative astronomical work was
done by Greek astronomers such as Hipparchus and Ptolemy. However, the origin
of many of their ideas is simply unknown, due to a lack of historical records.
Many of these ideas may have come from indigenous Vedic astronomy, and many may
also have been developed independently in India and the West. Thus we propose
that genuine traditions of astronomy existed both in India and the eastern
Mediterranean, and that charges of wholesale unacknowledged cultural borrowing are
unwarranted.
1.C. The Vedic Calendar and Astrology
1.C. The Vedic Calendar and Astrology