Subject: Re: [HM] Indian astronomy and mathematics
From: Chris Linton (C.M.Linton@lboro.ac.uk)
Date: Fri Feb 18 2000 - 12:06:46 EST
I would like to comment on two remarks made recently in this thread.
1. Don Cook wrote
<<
Denish refers to the Ptolemic system. There is no Ptolemic system!
Each planet has its own system incompatible with the other planets.
>>
Ptolemy's geometrical theories for the planets are certainly not
incompatible, but it is fair to say that they are treated
independently in the _Almagest_. However, Ptolemy later wrote the
_Planetary Hypotheses_ in which he combined all his geometrical
theories together to produce a physical model of the universe. To do
this he used the Aristotelian principle of the impossibility of a
vacuum and argued (roughly) as follows.
Each of his geometrical models produced a ratio for the maximum to
minimum distance from the earth for the heavenly body being
described. He already had values for the earth-sun and earth-moon
distances (in earth radii, e.r.) from observation (wildly inaccurate
of course). From these given values he could pack in the other
planetary mechanisms as tightly as possible so as to avoid any empty
space. Starting from the moon (min distance 33 e.r, max distance 64
e.r.) he worked outwards arriving at a maximum distance to Venus of
1079 e.r. Ptolemy's value for the minimum distance to the sun was
1160 e.r. and so he was forced to leave a small gap. Continuing out
from the sun he arrived at a maximum distance to Saturn of 19,865
e.r. and then put the fixed stars at 20,000 e.r.
This system is based on physical principles that we recognize today
as being incorrect, but it nevertheless represents a fully-fledged,
wholly integrated, physical description of the universe. Ptolemy's
ideas were developed by Arabic scholars and his physical and
mathematical descriptions became more and more intertwined as time
passed. Al-Farghani (Alfraganus) (c800-870) repeated Ptolemy's
calculations and managed to conveniently remove the philosophically
objectionably gap between Venus and the sun. Al-Farghani's textbook
on Ptolemaic astronomy (in its original Arabic and then in Latin
translation) was the primary medium by which knowledge of Ptolemy's
work spread until the 16th century. The _Sphere_ of Johannes de
Sacrobosco (13th century) and the _New Theories of the Planets_ by
Peurbach (15th century) were both extremely influential and both
described the Ptolemaic system of the world as originally set out in
the _Planetary Hypotheses_.
Thus while the _Almagest_ can be read nowadays without reference to a
physical system, this was not how it was read by astronomers before
Copernicus.
2. Dinesh Maheshwari wrote
<<
BTW, my understanding is that the Copernicus' system had less epicycles
than employed in Ptolemic system(80 circles), but a recent post suggests
otherwise; can someone please clarify.
>>
It's hard to count the actual numbers of circles used in each system,
because the answer depends on whether one counts all implied circular
motions, or the actual number of spheres required to implement the
system physically.
In Ptolemy's _Planetary Hypotheses_, the author claims that he has
used 34 spheres and Copernicus concluded his _Commentariolus_
(written about 1507) with the remark "Altogether, therefore,
thirty-four circles suffice to explain the entire structure of the
universe and the entire ballet of the planets." Subsequently,
however, the examination of more observational data led Copernicus to
realize that the theory presented in the _Commentariolus_ was
insufficient to accurately predict the positions of the heavenly
bodies over long periods and he had to discard many of the
geometrical constructions and replace them with more complicated
devices.
Chris Linton
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* Chris Linton * Tel: 01509-223482 *
* Department of Mathematical Sciences * Fax: 01509-223969 *
* Loughborough University * E-mail: *
* Leicestershire LE11 3TU * C.M.Linton@lboro.ac.uk *
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