On request, here is my review of PVR Narasimha Rao’s Article on the Topical / Sidereal Zodiacs and Pushya Paksha Ayanamsha.
It seems to me that the article mainly intends to publish his thoughts about the correct sidereal ayanāṁśā. But he begins with a section entitled “Tropical vs. Sidereal Zodiacs.”
His Statements on the Tropical Zodiac
I am happy that he at least acknowledges the existence of a valid tropical zodiac. However he considers it to only be related to seasons. For example he says, “The entry of Sun into tropical Aries is always aligned with spring equinox.” and “Tropical zodiac is tied to seasons.”
This is problematic. “Spring” is relative to northern and southern hemispheres. When the Sun enters tropical Aries, it is the Spring Equinox only in the northern hemisphere, but the Autumn Equinox in the southern hemisphere. Thus Aries is not tied to spring.
Then what is it tied to? It is tied to the Sun’s passing over the equator and moving into the northern hemisphere. The zodiac is defined this way, not by seasons. As we can see clearly in the astronomical sections of Purāṇas, such as this statement of Śrīmad Bhāgavatam [5.21.2-6]:
Outer space is measured by relation of heaven and earth. The Sun is the king of all the planets, in the center of everything, keeping everything together. It moves to the north, crosses the equator, and moves to the south. When it goes north of the equator days get longer. When it crosses the equator days and nights are equal. When it goes south of the equator days get shorter. On this basis the Sun moves through the twelve divisions called Capricorn and so forth.
The Sun is at Aries and Libra when the days and nights are equal. Passing through Taurus, etc. the days become longer and then decrease until again equal with the night. Passing through Scorpio, etc. the night becomes longer and then decrease to again become equal with the days.
Sūrya Siddhānta gives the same definition of the zodiac [14.7-10]:
It is well-known that the circle of signs is split by two diameters. One is the line from equinox to equinox. The other is the line from solstice to solstice. Between each solstice and equinox are two other markers. Each solstice /equinox and the two following markers represent the three strides of Vishnu.
The Sun has entered Capricorn when it begins moving north for six months. It has entered Cancer when it begins moving south for six months. Seasons last for two signs each, beginning from Capricorn with the frozen season. The twelve signs named Aries, etc. are the months which altogether comprise the year.
As you see, the definition of tropical zodiac is not primarily about seasons, but about the sun’s relationship to the earth, measured by its apparent distance north or south of the equator. In fact the very word “tropical” means “turning” and refers to how the sun turns back and forth, north and south over the equator.
Statements on the Sidereal Zodiac
He then says, “zodiacal signs are supposed to be aligned to nakshatras.”
He does not say why.
He says, “For example, the sign of Aries should contain Aswini nakshatra, Bharani nakshatra and a part of Krittika nakshatra.”
I infer that he may feel this way because many statements in Purāṇas and astrological texts describe Āśvinī as being in Aries, etc. just as he has done. However there are the previously cited definitions of the zodiac which are said in the same texts. We have to understand two conflicting statements in a way that resolves their conflict. Vyāsa himself instructs us to do this, in his statement [brahmā-sūtra 4] tat tu samanvayāt.
It is not difficult to accomplish this here, by taking the statements of the nakṣatra relationships to the rāśīs as observations of the phenomenon extant at the time the authors made those statements. In fact, this will be the only way we will be able to make sense of the oldest surviving Jyotiṣa documents (fragments of Ṛg and Atharva, and the Jyotiṣa Vedāṅga) which state that Kṛttikā (not Aśvinī!) is the first nakṣatra.
The widely accepted traditional and scholastic dating of these oldest documents does in fact agree that much of their content was written approximately 5,000 years ago, when the northerly equinox (i.e. start of Aries and beginning of the zodiac) was in Kṛttikā.
Mr. Rao also says, “If we use the tropical zodiac, signs will slowly shift with time and point to different nakshatras in different eras. This is totally inconsistent with the teachings of rishis.”
I do not know why he says this is “inconsistent with the teachings of the ṛṣis.” As far as I understand, it is very consistent with Ṛg, Atharva, etc. as explained just previously.
He admits, “we have no observable phenomena based on which we can conclude that so and so point in the zodiac is the start of sidereal Aries.” and “the precise point where Aries starts is not known!”
This in and of itself is very strong evidence that the start of Aries is not sidereal! On the other hand, there is a very significant event – the equinox – marking the beginning of Aries by the tropical definition. This alone is compelling evidence that Aries is inherently a tropical location.
The rest of Mr. Rao’s paper is dedicated to establishing an accurate sidereal ayanāṁśa which can solve the problem of disagreement amongst siderealists about where the zodiac actually starts.
I am not particularly interested in this issue, because
(a) I do not consider the rasi to be dependent on ayanāṁśa; just the opposite, it is calculation of the nakṣatra which depends on an accurate ayanāṁśa.
(b) The plain old vanilla Lahiri ayanāṁśa has not given me any significant reason to doubt it.
However, I will briefly review a few remaining points that Mr. Rao brings up.
He basis his doubt on Citrapaksha (Lahiri) Ayanāṁśa on the idea that “As per Surya Siddhanta, latitude of the yogatara of Chitra nakshatra is 2° south of the ecliptic plane. However, Spica is 1° south of the ecliptic plane right now.”
I don’t think this 1º of declination should warrant serious doubt that the yogatāra (primary star) of Citra Nakṣatra is Spica.
He sites other astronomical treatises also disagreeing about the location of Citra’s yogatāra – all of which are within 3º. I think this can be expected of observational astronomy during the era in which these texts were written.
He says, “there is no philosophical or esoteric justification for why Chitra nakshatra, whose deity is Tvashta, should be the anchor of the zodiac.”
This is why Kṛttikā (!) is the first nakṣatra in the Vedas: it’s deity is Agni – who is always the first deity in a ceremony and the etymology of whose very name means “going first.”
However if you would like to fabricate a justification, Tvaṣtā is the creative ability itself, without which even Brahmā cannot create.
Mr. Rao says, “Though people speak of ‘fixing’ Spica at 0Li0, we actually can not fix Spica there, for it does not even lie on the ecliptic plane or the zodiacal plane! … A star that lies right on the zodiacal plane is a better candidate for being the ‘anchor’ of the zodiac.”
This is a good theoretical point, but Spica is only one degree away from the ecliptic.
He argues nicely that the best anchor point for the sidereal zodiac is the yogatāra of Puṣya Nakṣatra. Though one flaw he did not address is that the seed value of 106º has to be used for this ayanāṁśa. There is nothing philosophically or geometrically special about 106º.
Citrapakṣa Lahiri Ayanāṁśa uses the 180º value, which is much more compelling by geometry.
He gives the value of Puṣyapakṣa Ayanāmśā at January 1st 2014 as 22° 55 ́ 3.87 ́ ́ – by contrast, the value of Citrapakṣa Ayanāmśā at the same date is 24° 03′ 16″. The difference between the two is only about one degree. By contrast, the problem of treating rāśi as sidereal things introduces a discrepancy of about twenty-four degrees!
Thus, the issue of sidereal rāśi is a much more important issue to sort out than the few degrees up for grabs by various opinions on ayanāṁśa. Posts regarding my studies on this issue can be found here.
Two Statements I Particularly Liked
Mr. Rao wrote:
The argument “I am so successful that my ayanamsa must be correct” holds no water. Bottomline is that many people using contradictory calculations are successful using techniques relying more on intuition and less on precise calculations!
This is a very important point we all must remember when investigating the sidereal / tropical rāśi issue as well.
He also wrote:
Thumb rules people develop in practice may not be reliable. Learning the correct knowledge may sometimes require un-learning wrong knowledge. One needs to be open-minded and intellectually sharp and alert.
I agree wholeheartedly!