HK kan bare konkludere noget ud fra oplevelsen af Solen og den potte er ude.
Men den te er åbenbart for stærk for HK.
For mange tusind år siden beskrev den vediske tekst - Surya Siddhanta
- at afstanden fra solen til jorden er hvad der i km. svarer til
omkring 193 millioner km. I moderne tid har astronomer beregnet en
afstand til solen på omkring 150 millioner km. I Surya-siddhanta
beskrives også alle planeterne i vores solssytem - deres omløbsbaner,
deres diameter, deres afstand til jorden osv., og de svarer med med
stor nøjagtighed til, hvad man er kommet frem til i moderne stronomi.
(Surya betyder solen og siddhanta betyder konklusion)
Som sædvanligt brillierer den vediske version.
The Astronomical Siddhantas
Af Dr. Richard Thompson
Since the cosmology of the astronomical siddhantas in the Vedas 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 Vaishnava tradition. In a number
of purports in the Caitanya-caritamåta, Srila Prabhupada refers to two
of the principal works of this school of astronomy, the
Surya-siddhanta and the Siddhanta-Siromani. The most important of
these references is the following:
These calculations are given in the authentic astronomy book known as
the Surya-siddhanta. This book was compiled by the great professor of
astronomy and mathematics Bimal Prasad Datta, later known as
Bhaktisiddhanta Sarasvati Gosvami, who was our merciful spiritual
master. He was honored with the title Siddhanta Sarasvati for writing
the Surya-siddhanta, and the title Gosvami Maharaja was added when he
accepted sannyasa, the renounced order of life [Cc adi 3.8p].
Here the Surya-siddhanta is clearly endorsed as an authentic
astronomical treatise, and it is associated with Srila Bhaktisiddhanta
Sarasvati Thakura. The Surya-siddhanta is an ancient Sanskrit work
that, according to the text itself, was spoken by a messenger from the
sun-god, Surya, to the famous asura Maya Danava at the end of the last
Satya-yuga. It was translated into Bengali by Srila Bhaktisiddhanta
Sarasvati, who was expert in Vedic astronomy and astrology.
Some insight into Srila Bhaktisiddhanta'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 Srila Bhaktisiddhanta 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 Surya-siddhanta, Srila Bhaktisiddhanta
Sarasvati published the following works in his two magazines: (a)
Bengali translation and explanation of Bhaskaracarya's Siddhanta-
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-Siddhanta according
to western calculation, (e) Whole of Arya-Siddhanta by AryabhaTa, (f)
Paramadishwara's Bhatta Dipika-Tika, Dinakaumudi, Chamatkara-
Chintamoni, and Jyotish-Tatwa-Samhita [BS1, p. 26].
This list includes a translation of the Siddhanta-Siromani, by the
11th-century astronomer Bhaskaracarya, and the Arya-siddhanta, by the
6th-century astronomer AryabhaTa. BhaTTotpala 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.
Srila Bhaktisiddhanta Sarasvati also published the Bhaktibhavana
Païjika and the Sri Navadvipa Païjika (BS2, pp. 56, 180). A païjika is
an almanac that includes dates for religious festivals and special
days such as EkadaSi. These dates are traditionally calculated using
the rules given in the jyotisha Sastras. During the time of his active
preaching as head of the Gaudiya Math,
Srila Bhaktisiddhanta stopped publishing works dealing specifically
with astronomy and astrology. However, as we will note later on, Srila
Bhaktisiddhanta cites both the Surya-siddhanta and the Siddhanta-
Siromani several times in his Anubhashya commentary on the Caitanya-
caritamrita. It is clear that in recent centuries the Surya-siddhanta
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 Bhagavatam 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 Vaishnavas have traditionally made use of the astronomical
siddhantas and that both Srila Prabhupada and Srila Bhaktisiddhanta
Sarasvati Thakura have referred to them. At the same time, we have
pointed out that the authors of the astronomical siddhantas, such as
Bhaskaracarya, have been unable to accept some of the cosmological
statements in the Puranas. How could Vaishnava acaryas accept works
which criticize the Puranas?
We suggest that the astronomical siddhantas have a different status
than transcendental literature such as the Srimad-Bhagavatam. 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 Siddhanta-
Siromani, were composed in recent centuries and make use of empirical
observations. Others, such as the Surya-siddhanta, are attributed to
demigods but were transmitted to us by persons who are not spiritually
perfect. Thus the Surya-siddhanta was recorded by Maya Danava. Srila
Prabhupada has said that Maya Danava "is always materially happy
because he is favored by Lord Siva, but he cannot achieve spiritual
happiness at any time" (SB 5.24cs).
The astronomical siddhantas constitute a practical division of Vedic
science, and they have been used as such by Vaishnavas 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 Puranas, 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 Surya-
siddhanta. Otherwise they could not have produced comparable results.
In presently available Vedic literature, such computational methods
are presented only in the astronomical siddhantas and other jyotisha
Sastras. The Itihasas and Puranas (including the Bhagavatam) do not
contain rules for astronomical calculations, and the Vedas contain
only the Vedaìga-jyotisha, which is a jyotisha Sastra but is very
brief and rudimentary (VJ).
The following is a brief summary of the topics covered by the
Surya-siddhanta: (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 Vyatipata), (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 Surya-siddhanta's basic model of the planets and their
motion in space.
The Solar System According to the Surya-siddhanta The Surya-siddhanta
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 Rahu, but it makes no mention of Uranus,
Neptune, and Pluto. The main function of the Surya-siddhanta 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 Surya-siddhanta'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 Surya-siddhanta 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 Surya-siddhanta 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 Surya-siddhanta 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 Surya-siddhanta. 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 Surya-siddhanta,
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 [Surya-siddhanta]
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 Surya-siddhanta
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
Rahu -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 Rahu. 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 Rahu. Rahu is
not recognized by modern Western astronomers, but its position in
space, as described in the Surya-siddhanta, 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 Surya-siddhanta, the planet Rahu 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 Rahu. (These times have minus signs because
Rahu orbits in a direction opposite to that of all the other planets.)
TABLE 4
Heliocentric Distances of Planets, According to the Surya-siddhanta
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 Surya-siddhanta 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.
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 Srimad-Bhagavatam and in the other Puranas, the
Mahabharata, and the Ramayana. The astronomical siddhantas seem to
have much more in common with Western astronomy than they do with
Puranic 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 siddhantas was
imported into India from Greek sources in the early centuries of the
Christian era. Since the siddhantas 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 Puranas represents an earlier, indigenous phase in
the development of Hindu thought, which is entirely mythological and
unscientific.
This, of course, is not the traditional Vaishnava viewpoint. The
traditional viewpoint is indicated by our observations regarding the
astronomical studies of Srila Bhaktisiddhanta Sarasvati Thakura, who
founded a school for "teaching Hindu Astronomy nicely calculated
independently of Greek and other European astronomical findings and
calculations."
The Bhagavatam commentary of the Vaishnava scholar VamSidhara also
sheds light on the traditional understanding of the jyotisha Sastras.
His commentary appears in the book of Bhagavatam commentaries Srila
Prabhupada used when writing his purports. In appendix 1 we discuss in
detail VamSidhara's commentary on SB 5.20.38. Here we note that
VamSidhara declares the jyotisha Sastra to be the "eye of the Vedas,"
in accord with verse 1.4 of the Narada-samhita, which says, "The
excellent science of astronomy comprising siddhanta, samhita, and hora
as its three branches is the clear eye of the Vedas" (BJS, xxvi).
Vaishnava tradition indicates that the jyotisha Sastra is indigenous
to Vedic culture, and this is supported by the fact that the
astronomical siddhantas 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 Bhagavatam 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 Surya-siddhanta 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 brahmanas and yogis 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 Yayati was the ancestor of the Greeks, and SB
2.4.18p says that the Greeks were once classified among the kshatriya
kings of Bharata 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.