Subject: Re: [HM] Indian astronomy and mathematics
From: Kim Plofker (Kim_Plofker@Brown.edu)
Date: Thu Feb 03 2000 - 23:44:24 EST
> "As a side note, I wonder if Aryabhata's [476-550AD] astronomy
> text Siddhanta (not Aryabhatitya) which deals with a heliocentric
> model of the solar system, the notion of earth rotation, the
> causes of solar/lunar eclipses and the notion of elliptical
> planetary orbits were ever translated to Arabic/Persian."
The _Aryabhata-siddhanta_ (also generally known as his Ardharatrika
or midnight system, owing to its using a midnight epoch as opposed
to the sunrise epoch of the _Aryabhatiya_) is discussed in K. S. Shukla's
and K. V. Sarma's edition of the _Aryabhatiya_ (New Delhi 1976). This
work is lost in Sanskrit, although a condensed version in the form of
an astronomical handbook, the _Khandakhadyaka_ composed by Brahmagupta
in the seventh century, survives in Sanskrit and was also translated
into Arabic (as was the _Aryabhatiya_ itself). I know of no Islamic
version of the _Aryabhata-siddhanta_, although there is an Arabic
translation of a Sanskrit work called _Mahasiddhanta_ which I believe is
known to be the work of the *second* Aryabhata, who lived in the tenth
century (this can get confusing!).
As for the content of Aryabhata (I)'s lost work, we know from the
seventh-century _Mahabhaskariya_ of Bhaskara (I), as Shukla and
Sarma point out, that it used somewhat different parameters from the
_Aryabhatiya's_ for the distances and mean motions of the planets.
Neither Shukla and Sarma nor Bhaskara (nor any other author that I
know of) claims that the basic cosmology of the _Ardharatrika_ =
_Aryabhatasiddhanta_ was different from that of the _Aryabhatiya_,
and I'd be interested in seeing specific citations that support that
assertion. The concept of a rotating earth is quite clearly put
forward in verse 1, 6 of the _Aryabhatiya_ (although the statement was
"corrected" by more conservative later authors), but there is no mention
of a heliocentric system: the sun is given an orbital circumference
and a mean orbital motion, just like the rest of the planets (and
unlike the Earth). The "causes of solar and lunar eclipses", namely,
the fact that they were caused by the interposition of the lunar disk
and the earth's shadow respectively, were perfectly well understood by
Aryabhata's time. The "notion of elliptical planetary orbits" is no
more evident in the _Aryabhatiya_ than is the notion of a heliocentric
system: the planets' orbits are treated in longitude computations as
circles, and so are the epicycles and eccentrics used to account for
their longitudinal anomalies. (The use of iterative techniques to
modify the orbital radius in these calculations *does* generate a
non-circular orbital path, and these techniques should be investigated
further; but there is no explicit mention of elliptical orbits.)
I am finding it difficult to keep up with the self-imposed task of sifting
out fact from fancy in these posts on various aspects of Indian astronomy,
especially when their assertions are unsupported by verifiable references
to specific Sanskrit (or other Indic) texts. I'm therefore going to
drop out of these threads altogether, but I'd like to urge the list to
keep in mind a few basic historiographical precepts: i) While there is
indeed a great deal that remains unknown or unverified about all aspects
of Indian astronomy---and while the "standard view" of them will certainly
be changed in many ways by future discoveries---much is known, and much
has been published. ii) Much of the material disseminated in such an open
forum as the WWWeb, in any field, is notoriously untrustworthy.
iii) Earth-shattering and truly revolutionary discoveries in any field
are rare: the truth of such claims often works out to be about inversely
proportional to their impressiveness and their frequency.
With best wishes,
Kim Plofker
Department of History of Mathematics
Brown University
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