Anand Hudli anandhudli at hotmail.com
Fri Mar 26 07:13:07 CDT 2010

```On Tue, Mar 23 2010 Jaldhar Vyas wrote:
>grAhyamiti shrI venkaTeshvara dIkShita sundareshvara shrauti prabhatInAM
>...
>In the matter of calculations for Jyotish, tithis etc. should be
>calculated based on the geocentric[2] method whereas eclipses etc. should
>be calculated according to the heliocentric[3] method.
॥ श्रीरामचन्द्रपरब्रह्मणे नमः ॥
What the scholars are discussing here are not geocentric vs heliocentric calculations but
geocentric vs topocentric calculations of positions of the heavenly bodies, particularly the
sun and moon which are required for determination of tithi, etc. BhUpR^iShTha means
surface of the earth or topocentric based view. BhUmadhya means geocentric view.

In simple terms, calculation of geocentric position of a heavenly body involves treating
the observer as stationed at the center of the earth, considering the earth as a
spherical object. This is, of course, an approximation to the true position of the observer
which is somewhere on the surface of the earth. The position of the heavenly body
as viewed by an imaginary observer at the center of the earth is given by the
geocentric coordinates. The position of the same heavenly body as viewed by an
observer from the surface of the earth (ie. for a given a latitude and height
above sea level) is given by the topocentric coordinates. The difference between the
two positions is caused by what is called geocentric parallax.

The sun and planets are sufficiently far away from the earth, so the geocentric
parallax in those cases does not cause a significant difference between geocentric
and topocentric positions, at least for purposes that we are concerned with here.
However, in the case of the moon, the geocentric parallax can be significant, because
the moon is not as far away from us as the sun and planets. The closer a heavenly
body is to the earth, the more the geocentric parallax. The situation is similar to the
angle of elevation measured by two observers, one on the ground and another on the
roof of a building. If the two observers are looking at a distant object, say a particular
star in the sky, the two angles of elevation will be nearly identical. However, if they were
to be looking at a flag flying on the top of a nearby building, the angles of elevation
could differ significantly.

Therefore, a parallax  correction is called for, at least for the moon, strictly based on
modern scientific thinking. Things are, however, not that simple while dealing with
matters regarding dharma. This is because dharma is also closely related to tradition,
and what elders in the family have followed. This being the case, to resolve an issue
such as the geocentric parallax, requires a decision by knowers of dharma. This is what
seems to have been reported in your Panchanga.

The topic of sUrya siddhAnta vs AryabhaTIya vs driggaNita vs modern astronomical

methods, which I was discussing in my post, has to do with the branch of astronomy

called celestial mechanics. This branch  explains the motion of celestial objects

using methods of mechanics, a branch of physics.

Ancient texts such as the sUrya siddhAnta use methods that are quite different from

modern methods. Accordingly, the positions of celestial objects one arrives at using

the sUrya siddhAnta and modern methods, could differ significantly. The impact of

this difference shows up in the ending times of tithis, for example. This in turn,

could lead to different dates for the same observance, for example ekAdashI, at the

same place. Thus, you will see one panchAnga based on sUrya siddhAnta mention the

date of an ekAdashI as Feb 24, 2010 and another based on driggaNita mention the

date for the same ekAdashI as Feb 25, 2010.

The topic of ayAnAMsha is a different one. It has to do with the frame of reference for
measuring positons of heavenly bodies. One frame of reference is the moving equinox
frame which is caused by the gyrating motion of the earth's axis about a line perpendicular
to the ecliptic through the center of the earth. Another frame of reference is to use
reference points based on stars. This is called the nirayana system while the first is
called sAyana system. All traditional panchAngas use the nirayana system. The
ayanAMsha is the difference between positions of a heavenly body measured as per
the sAyana system and the nirayana system. The phenomenon of moving equinoxes

is called precession.

To be even more precise, we would have to include the effect of nutation also, which

is the slight wobbling motion that the spinning earth exhibits. Please see the links

http://en.wikipedia.org/wiki/Precession
http://en.wikipedia.org/wiki/Nutation

I would like to make a general comment here. If we look at the history of positional

astronomy and celestial mechanics, there have been many improvements to earlier

results over a period of several centuries. These improvements have resulted in the

increase in precision of positions of heavenly bodies. But the question that needs to

be asked is: do we need all such high precision results for matters relating to the

observance and performance of activities prescribed by the dharma shAstras? Perhaps,

such high precision is required for astronomical purposes, for example by observatories.

But for other, more practical purposes, including dhArmic activities, a reasonable

degree of precision is what is needed. We may not need the highest degree of precision.

The decision on what constitutes this "reasonable degree of precision" has to be made

by current day upholders of dharma, under the leadership of the maThas.

Anand

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