Indian Astronomy Pre Ptolemaic By Govind
the Western scholars, Indian Astronomy is mysterious. Let us see what astro
scholars have said about IA.
Dennis Duke, of Florida State University suggests that Indian Astronomy
predates Greek Astronomy
"The planetary models of ancient Indian mathematical astronomy are
described in several texts.1 These texts invariably give algorithms for
computing mean and true longitudes of the planets, but are completely devoid
of any material that would inform us of the origin of the models. One way to
approach the problem is to compare the predictions of the Indian models with
the predictions from other models that do have, at least in part, a known
historical background. Since the Indian models compute true longitudes by
adding corrections to mean longitudes, the obvious choices for these latter
models are those from the Greco-Roman world. In order to investigate if there
is any connection between Greek and Indian models, we should therefore focus
on the oldest Indian texts that contain fully described, and therefore
securely computable, models. We shall see that the mathematical basis of the
Indian models is the equant model found in the Almagest, and furthermore, that
analysis of the level of development of Indian astronomy contemporary to their
planetary schemes strongly suggests, but does not rigorously prove, that the
planetary bisected equant model is pre-Ptolemaic" says he.
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The earliest Indian Planetary Models are two sets from the writer Aryabhata,
both dating from 6th Century AD.
1) The Sunrise System , after the Epoch, which is taken from the sunrise of
18th Feb 3102 (Arya Paksha ).
It appears first in Aryabhatiya
2) The Midnight System, after the Epoch, which is taken from the midnight of
17/18 FEB 3102 ( Ardha
Ratri Paksha ). It
appears first in Latadeva's
The Local Meridien is taken as Lanka, Longitude 76 degrees, Latitude 0
equations have been given for superior planets ( Mars, Jupiter and Saturn )
and inferior planets ( Mercury and Venus ) in Astronomia Indica.
In the case of Mercury, an inferior planet in the diagram above, the center of
the Sheegra Epicycle is located on the straight line running through the Sun
and the observer, on the geographical parallel of the observer.
The above diagram is by courtesy of Jean-Pierre Lacroix and Robert Baywater,www.ancientcartography.net
The Sheegra Phalam, x, in the equation 1/2 Tan ( A -x ), where A is the
Elongation or Sheegra Kendra, obtained is deducted from the Sun's longitude,
to get the geocentric longitudes of Mercury and Venus.
the diagram above, the geocentric distance, EQ called X here , the distance of
the planet from the Earth is calculated by the equation
X^2 = EQ^2(EP+PL)^2 + QL^2
or = EN^2 + QN^2
In a trignometric correction, called Sheegra
equation is given by Bhaskara.
E = Earth
P = Planet in its Orbit
Q = Planet on the Epicycle
QL = Sin
PL = Cos
We have said that Sheegra
Kriya reduces the
heliocentric postions to the geocentric.
According to this oscillating Epicyclic Model of Bhaskara, EP = R ( Called Thrijya ),
PQ is theSheegra Phala, QL is the Bhujaphala and
PL is Kotiphala.
The Hindu algorithms for the computation of mean and true celestial longitudes
seems to be totally different from the Western, from the methods adopted by
Kepler, Laplace and Co. Hence the Hindu Planetary Model is original and not
influenced by Greco Roman sources, as some Western scholars believe.
diagram is by courtesy of Jean-Pierre Lacroix and Robert Baywater,www.ancientcartography.net
We have the Double Epicyclic Model - that of Manda Epicycle and Sheegra
Epicycles - in Indian Astronomy, which explain the Zodiacal and Solar
anomalies. One Epicycle explains the Zodiacal Anomaly and the other the Solar
( Zodiacal Anomaly - That all planets move slower at Aphelion and faster at
Solar Anomaly - The astronomical phenomenon of Retrogression. Backward Motion.
When a planet changes its course from perihelion to aphelion, it retrogrades
in order to gain the Sun's celestial gravity )
Dennis Duke, of Florida State University, says " We have only to conclude
that Ptolemy did not invent the equant. " If Ptolemy did not invent the
equant, as Westerners widely believe, then who did ?
"The bisected Indian equant model is pre-Ptolemaic' says he. Other Greek
books, prior to Ptoemy, may have influenced Indian Astronomy,says he. Then
what are those books, prior to the Almagest, which had influenced the Indian
system? The answer is "unknown sources".
Remarks Duke " Indeed, since the very earliest investigation of the
Indian models by Western scholars it has been presumed that the models are
somehow related to a double epicycle system, with one epicycle accounting for
the zodiacal anomaly, and the other accounting for the solar anomaly
(retrograde motion) This perception was no doubt reinforced by the tendency of
some Indian texts to associate the manda and sighra corrections with an even
older Indian tradition of some sort of forceful cords of air tugging at the
planet and causing it to move along a concentric deferent . Since our goal in
this paper is to investigate the nature of any connection with ancient Greek
planetary models, it is only important to accept that the models appear in
Indian texts that clearly pre-date any possible Islamic influences, which
could, at least in principle, have introduced astronomical elements that
Islamic astronomers might have derived from Greek sources. ( "The Equant
in India: the Mathematical Basis of Ancient Indian Planetary Models" By
Dennis Duke, Florida State University ).