Q: New Year

[Luis Arnold Gonzalez-Reimann]

On Thu, 18 Apr 1996, Girish Beeharry wrote:

> Hi,
> 
> There seems to be some confusion about basic spherical trigonometry in an
> astronomical context. As my pedagogical skills are not quite up to the mark, I
> would suggest to interested people to consult these two books:
> 
> 1) General Astronomy by Spencer Jones, Former Astronomer Royal, (3rd Ed, 1951),
> published by Edward Arnold, London. [No ISBN code]  
> (Chapter 3 is related to matters being discussed here.)
> 
> 2) The Astronomical Almanach for the year 1996 [ISBN 0 11 886502 1]
> 
> The Govt. Bookstore, PO Box 276, London, SW8 5DT (World distribution)
> HMSO Bookshops, 49 Holborn, London, WC1V 6HB (for the UK)
> US Govt. Printing Office, Washington DC, 20402, (for the USA)
> 
> (There are sections on the geocentric motions of the Sun, Moon and Planets.)
> 
> These books make use of O-Levelish maths only and they should be accessible to
> a non-mathematical audience.
> 
> One can actually get a good physical sense of the matter by drawing closed 
> great circle lines on a fixed ball. One can then complicate matters by rotating
> the ball about an axis which is at an angle (say 20 to 30 degrees) to a line 
> passing through the centre of the ball and perpendicular to one of the great
> circle lines drawn previously. This is quite entertaining! :-)
> 
> Bye,
> 
> Girish Beharry
> 
> 
I am sure anyone on the list not conversant with spherical astronomy 
would benefit from these books if they were interested in pursuing the 
matter at that level. There are also other good introductions to the subject.
Nevertheless, our discussion about the beginning of the uttarAyaNa (the 
Sun's movement towards the North) does not require of spherical 
astronomy.  If one wishes to understand precession, such texts could be 
useful, as might a visit to the local planetarium. But it must be kept in 
mind that a concept such as uttarAyaNa (as also, for that matter,that of 
solstice "when the Sun stands still") is not derived from an 
understanding of our kind of astronomy, which is fully aware of the fact 
that the earth is round, and that it revolves around the Sun.

The concept of uttarAyaNa is derived from the observation of the apparent 
daily movement of the Sun above the horizon. More precisely, it is based 
on the fact that the Sun does not rise at the same point along the 
horizon each day. At the winter solstice (the shortest day of the year), the 
Sun rises far to the right 
of due East. Each subsequent day it rises more to the left, i.e. to the 
north; first slowly, and then faster as it passes by due East (at the time 
of the spring equinox), and it slows again when it nears the point where 
it rises further to the north of due East, at the time of the summer 
solstice (the longest day of the year).  The Sun then turns, and begins its 
movement towards the South (the right), the dakSiNAyana.
All of this happens regardless of what the position of the solstices and 
the equinoxes is against the backdrop of the stars.  In other words, it 
doesn't matter what rA'si - or should we rather say, in a Vedic context, 
what nakSatra- the solstices might happen to fall on at the time.
These two halves of the year played an important role in Vedic ritual, 
particularly in the gavAm Ayana.

Cheers,

Luis Gonzalez-Reimann
Department of South and Southeast Asian Studies
University of California, Berkeley