Subject: Re: [HM] Indian astronomy and mathematics
From: Kim Plofker (Kim_Plofker@Brown.edu)
Date: Mon Feb 07 2000 - 22:21:12 EST
I can only implore listmembers to stop writing interesting posts so
I can achieve the necessary willpower to ignore them. :-)
> Let me start by quoting H. Thurston, Early Astronomy, Springer-Verlag,
> New York, 1994:
>
> "Not only did Aryabhata believe that the earth rotates, but there
> are glimmerings in his system (and other similar Indian systems)
> of a possible underlying theory in which the earth (and the planets)
> orbits the sun, rather than the sun orbiting the earth. The
> significant evidence comes from the inner planets: the period of
> the sighrocca is the time taken by the planet to orbit the sun."
>
> Mind you, H Thurston's work was published in 1994 and is more recent
> than the work of Shukla et al [1976].
"More recent" is not always the same as "better informed"; I like
Thurston's book (a general survey of premodern astronomy in world
cultures) very much and find much useful information in it, but
Shukla and Sarma know more about Indian astronomy than Thurston does.
Nonetheless, the point about a sun-dependent (_not_ necessarily
implying a sun-centered) system is an interesting one: see below.
> A paragraph from "Mac tutor's" write-up on Aryabhata reads as follows:
>
> "Aryabhata gives the radius of the planetary orbits in terms of the
> radius of the Earth/Sun orbit as essentially their periods of rotation
> around the Sun. He believes that the Moon and planets shine by
> reflected sunlight, incredibly he believes that the orbits of the
> planets are ellipses. He correctly explains the causes of eclipses of
> the Sun and the Moon."
We've already gone through these points and discussed which of them
are supported by textual sources from what's known of Aryabhata's work
and which are not. A reference to MacTutor that provides no verifiable
citations of primary textual sources will not further the discussion much,
I'm afraid.
> Aryabhata's surviving work Aryabhatiya does not explicitly mention
> heliocentric model but assumes a heliocentric model because the planetary
> periods in Aryabhatiya are with respect to the Sun.
>
> The sighrocca maps the motion of the inferior planet around the sun to
> an imaginary point moving around the earth with the same angular velocity
> as the angular velocity of the planet around the sun; it's direction from
> the earth is always parallel to the line joining the sun and the inferior
> planet. For the superior planets, the sighrocca coincides with the mean
> place of the sun. The mandocca, in the case of the moon , is the apogee
> where the angular motion is the slowest and in the case of the other
> planets it is the aphelion point of the orbit. The mandocca point serves
> to slow down the motion from the apogee to perigree and speed up the motion
> from the perigree to the apogee. (It is a representation of the non-uniform
> motion of the planet.)
True. What this indicates is that the position of the planet was
computationally linked to that of the sun; it reflects an awareness of
the periodic relations of planetary and solar motion (and it's difficult
to do positional astronomy in this solar system without such an
awareness). What I object to is the overenthusiastic inference that
this somehow constitutes a heliocentric theory (even "glimmerings of
a possible underlying" heliocentric theory seems a little strong to me).
The Sanskrit texts we see quite definitely assign to all seven planets,
including the sun, orbital periods and orbital distances with respect to
the earth. If we assume that the existence of the sighra-correction
implies a truly heliocentric cosmology, we will have to assume that
almost all ancient astronomy had a heliocentric system too: for example,
Babylonian astronomy was based on synodic planetary periods, which also
computationally link the position of the planet to that of the sun. My
point is that such a sun-dependence in ancient models of planetary motion
does not have to imply a physical conception of the solar system that was
actually sun-centered.
Recall, after all, that Brahmagupta and many later authors,
who all used the sighra-correction as a matter of course, strongly
rejected Aryabhata's notion that the earth might even rotate; this
was considered impossible for many of the same intuitive physical
reasons that European anti-Copernicans put forth. I don't feel that
we're justified in inferring that these siddhanta authors accepted the
hypothesis of the earth's hurling through space, when a simpler
interpretation (i.e., sun-dependent models need not be literally
sun-centered) will cover the facts.
> The word "Siddhanta" in Sanskrit literally means "theory/Philosophy" and
> is the common way of denoting a theoretical work e.g. Surya Siddhanta,
> Brahmasphuta Siddhanta, Siddhanta Shiromani etc. I would expect Aryabhata
> to have expounded on the theory of the astronomy in detail in _Aryabhatiya_
> Sidhanta - sidhanta being the more theoretical work. And that's why I am
> looking for it.
The _Aryabhatiya_ is also classified by many authors as a siddhanta,
in fact. As for looking for the lost _Aryasiddhanta_, all I can do
is wish you luck!
[...]
> I think, the people on this forum are mature, capable and open-minded enough
> to make up their own mind and need not be "told "as to what to trust and what
> not to trust.
True.
With best wishes,
Kim Plofker
Department of History of Mathematics
Brown University
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