Ayanamsa -Zero Ayanamsa Year (Views of Chandrahari as per the book ‘Hindu Zodiac’) Introduction This article is an effort to compile the mathematical concepts of Chandrahari, related to Zero ayanamsa year as presented in his book ‘Hindu Zodiac’. I have tried my level best to keep the continuity of the mathematical concepts and thought process involved. The following are some of the constants used in the derivation. Y = 365.258756 days (Solar year of Suryasidhantha) Ys = 365.256450 days (Modern sidereal year - AD.500) Y| = 365.24219 days (Modern tropical year) // It changes always [The tropical year-length undergoes constant change. What is the formula to find Tropical year length?] Words used Zodiac = The fixed stellar background. The substratum over which the Calendar phenomena occurs. The fixed reference against which movements are validated. Calendar phenomena = Many movements such as movement of equinoxes, moon phases, movements of Sun and Planets etc. All this helps to assess time (calandaram), and that is why the word Calendar. (People used to mix-up the above two. Zodiac and Calendar phenomena are entirely different things) Meshadi/Aswinyadi = Starting point of Aris/Starting point of the stellar division Aswathi (Both of them coincide) Ahargana = Number of days counted from Kali-yugadi. Moola = The fiducial star located at 2400 (λ-Scorpi) Ayanamsa = Distance from Vernal-equinox to Meshadi Kaliyugadi = Beginning of Kaliyuga. (K0 = 17/18 February 3102 BC) Precession = Movement of Vernal-equinox Sexagesimal system = The division of a circle in to multiples of 60. Tropical (Sayana) months = Madhu, Madhva,... etc. Sidereal (Nirayana) months = Chaitra, Visakha,... etc Basic concepts In his book ‘Rasichakram’ itself Hari has given sufficient evidence for the following two concepts. Therefore in the book ‘Hindu Zodiac’, he jumps to the next issue to be solved, i.e. Fixing of the Zero ayanamsa year, in which anomalies pops up. The Basic concepts are 1) Moola is the fiducial star used for zodiac division, and stellar division. The starting point of Aris is 1200 away from the fiducial star Moola. 2) The position of vernal equinox at the beginning of Kali-yuga = 460 40| [This means that we can calculate the Ayanamsa of any year by taking the point 1200 away from Moola star (λ-Scorpi) as the starting point of Aris (Meshadi/Aswinyadi). So the question “What is the ayanamsa to be used?” is already answered] If these basic concepts are taken for granted, the remaining question to be answered is “Which is the Zero ayanamsa year?”. Let us try to answer this question. The 3 Entities While considering the rhythm of Equinox and sun, considered by the saints and inherent in Yuga system 3 entities comes in to consideration. They are 1) Kali-year beginning - The technical term used to refer to this is Chaitradi. That is the year begins in Chaitra-sukla-prethipada (It means that not only Sun but Moon also should be there in Meshadi) 2) Meshadi (starting point of Aris) 3) Vernal Equinox Only a year in which all these 3 entities coincided can be taken as the Zero-Ayanamsa year.

Concepts inherent in Suryasidhantha The mean-equinox since the beginning of Kaliyuga as per Suryasidhantha can be expressed as, Ahargana (Nth equinox) = NY+60 - N (Y-Y|) = 60+NY| ............................................(1) Where Y| is the modern tropical year = 365.242371 days (in AD.500) Mean tropical-sun (Nth Kali year) = 3600 -600 + N (Y-Y|) = 3000 + N (Y-Y|)...........(2) Hari says that, both these equations can be shown to be true by computation. At the expiry of 3623 Kali years (1323332.5 days), N (N-Yt) = 60 days and hence the mean-sun of Kali year 3623 (elapsed) coincided with the vernal equinox of K3623 or AD.522. Taking the ayanamsa of K0 to be 460 40| for the sidereal zodiac implicit in Suryasidhantha: Sidereal mean-sun = 3460 40| (Y| / 360) + N (Y-Y|) = 347d 21gh + N (Y - Ys)............(3) Where Y|/360 converts 460 40| into days. Coincidence of the sidereal and tropical zodiac requires to be equal at some year after Kali yugadi. Therefore equating (2) and (3), we get 300+N (Y-Y|) = 347d 21gh + N ..................................................................................(4) i.e. N = 47d 21gh / (Ys - Y|) = 3339 ............................................................................(5) That means, the sidereal and tropical longitudes of sun coincided at the expiry of Kali 3339. AD.238 This is the year in which sidereal and tropical longitudes of sun coincided. This is the importance of the year AD.238 (K3339). It is the zero ayanamsa year, derived by a computation across 3339 years from the epoch of Kaliyugadi. But the Ahargana of 3339 Kali (elapsed) = [3339 x 365.258756 = 1219598.986284] ≈ 1219599 days do not correspond to the mean equinox, as 3339 (Y-Y|) = 55d 17gh only from Aswinyadi. i.e., The sun reaches the zero point after 60d - 55d 17gh = 4 days 43 ghaties, corresponding to the Ahargana for the mean equinox of AD.238 (23rd March, Friday) that marked the coincidence of sidereal and tropical zodiacs. i.e. The Ayanamsa is roughly 46| more than that of Lahri Ayanamsa (Chitrapaksha ayanamsa). [It means that of the 3 entities considered 2 and 3 coincides, but not the one mentioned as 1. Why? There is some miner error. Any one may stop here and say - “why bother? The calculations matches well for the year...an error of some days only...may be caused by the calculation mistake of ancient saints”. But Hari does not stop here. He searches for the root cause of that error.] But why is it so? Why this exact coincidence of the 3 entities [1) Kali-year beginning (Chaitradi) 2) Meshadi (starting point of Aris) 3) Vernal Equinox] does not occur? We should find out how and why this error crept into their calculations. A similar problem can be observed if we look at the years AD.499/AD.522. AD.499/AD.522 [It is the period of Aryabhata, the author of new Suryasidhantha. Some say that he compiled the work in AD.499, and some say that it was in AD.522. Some are of the opinion that these numbers have nothing to do with the year of birth or year of Aryabhateeya compilation, but that it is the zero ayanamsa year] The expiry of Kali year 3623 (Ahargana = 365.25875 x 3623 = 1323332.451) coincided with the respective equinox of AD.522. [It can be proved by considering the equation (2). Mean tropical-sun of AD.522 (K3623) = 3600 - 600+ N (Y - Y|) where N=3623 = 3000 + 3623 (365.258756 - 365.24219) = 3000 + 60.018618 = 3600.018618 ≈ 3600 i.e. In AD.522 vernal equinox and Kali-year beginning coincided] i.e. Of the above said 3 entities 1 and 3 coincided. As such this epoch could have represented coincidence of sidereal and tropical zodiacs (If the 3rd entity also coincides). But it does not happen. We already know that for AD.238 (K3339) the precession accounts to 460 40|. Therefore in view of the 30 58| precession between K3339 (AD.238) and K3623 (AD.522) the total precession amounts to 500 38|. To put it mathematically -

Total precession on AD.238 (K3339) = 460 40|. Precession for 284 years (AD.522 - AD.522) = 30 58|. Total precession on AD.522 (K3623) = 460 40| + 30 58| = 500 38| As no such coincidence of points occur in AD.499, that year, even though represents the whole number K3600 is not that relevant. [Then why the year AD.499 is given this article? It is only due to some historical reason. According to popular belief it was K3600 (AD.499) rather than K3623 (AD.522) that represented the epoch of Aryabhata and led to the genesis of the solar year 365.25875 days. But Kerala tradition as well as modern astronomical computation supports K3623(AD.522). The year AD.499 has another importance. The almost zero longitude of Ravathi (Zeta Piscium) got incorporated in the Sidhantic tradition after the advent of Brahmagupta in the 7th century AD. According to CRC report, the expiry of K3600 (AD.499) very nearly coincided with vernal equinox of that year. These are all just historical importance of the year AD.499] AD.285 What is the importance of this year? If we stick to the basic prepositions such as, 1) Moola is the base of Rasi and Nakshathra division. 2) Kaliyugadi position of vernal equinox = 460 40|. Does any coincidence of earlier mentions 3 entities occur at that time? No. According to CRC, the only thing of importance is that in AD.285 vernal equinox was opposite Chithra star. [There is another point to be considered which will be revealed later] AD.231 Even though the treatises like Aryabhateeya (Kalakriyapada-verse 11) declares Chaitra-suklaprethipada (Chaitradi) as the beginning of the year and the greater divisions of time such as Yuga, Kalpa etc., neither of the Sidhantic epochs, say of Suryasidhantha or Aryabhateeya satisfied this stipulation. It must be remembered here that even Vedanga-Jyotisa had a computational epoch beginning from Sukla-pratipada that coincided with the winter solstice. Obviously when the year beginning had a shift to the vernal equinox it must have taken place at a coincidence of the vernal equinox with the Chaitra-sukla-prethipada. In the absence of such a tradition there was no reason for the Sidhantic astronomers to ascribe a beginning for the year and Yugadi with the Chaitra-sukla-prethipada. It is apparent that the intricacy may be because of the redactions undergone by the Sidhantic treatises around AD.500 in which the original epoch of Sidhantic astronomy might have got obliterated. On examining the luni-solar configuration of the vernal equinoxes around AD.233, the following astronomical data strikes our attention. The vernal equinox of AD.231 precisely satisfied all the aforementioned astronomical factors that would have truly characterized the original Sidhantic epoch and year beginning with Chaitra-sukla-prethipada. Epoch: 21 March 231AD, Monday 15 30 UT (2033 Ujjain LMT), Vernal Equinox coincided with Chaitra-sukla-prethipada. JD [TDT]: 1805510.22908. Moola (λ-Scorpi) precisely had a longitude of 2390 58| ≈ 2400 from the vernal equinox. New moon took place on Monday at 1035UT or Ujjaini LMT for JD [TDT] = 1805510.0238655. Tuesday coinciding with the Sukla-pratipada marked the beginning of Chaitra at Ujjain. The epochs K0 and K3332 corresponded to JD [TDT] of 588466.34939 and 1805510.372718 respectively. In terms of UT the epochs were separated by 1217045 days = 1217045 days = 3332 x 365.2596038 i.e. 3332 anomalistic years. Notice the fact that this year satisfies the above said condition of the coincidence of 3 entities. [Still the reasons for the calculation deviation from AD.231 to AD.238 remain to be identified. We should also find out the anomalies that caused this deviation from AD.231 to AD.238] AD.233 (Considering Moola’s fiducial role) Moola has a fixed longitude of 2400 over the sidereal zodiac. As can be seen in Indian Astronomical Ephemeris the proper motion of Moola can be taken as zero and accordingly Moola had it’s sidereal and tropical longitude equal to 2400 at the vernal equinox of AD.233. (UT: 21 March 233, 03:23; JD [TDT] = 1806240.72368). Ayanamsa as such may be computed either from the vernal equinox of AD.233 or by subtracting 2400 from the modern tropical longitude of λ-Scorpi. On 2nd

July 2000 the tropical longitude of λ-Scorpi is 240 35| 33.76||. Alternatively, if we take the vernal equinox of AD.231 coincident with Chaitra-sukla-prethipada as marking the zero point the ayanamsa will be 240 37|. i.e. The Ayanamsa is roughly 44| more than that of Lahri Ayanamsa (Chitrapaksha ayanamsa). [The Chaitra-sukla-prethipada condition (entity 1) is not satisfied when AD.233 is accepted] AD.231 is better than AD.233 as all the 3 entities coincide. If we consider Moola’s fiducial role as well, Ayanamsa should be roughly 44| more than that of Lahari ayanamsa. Now let us go back to the original question. Why this exact coincidence of the 3 entities does not occur in AD.238 (K3339)? Movement of Nirayana Zero-point It is apparent from equation (2) that the mean tropical sun coincided with vernal equinox of K3623 for the solar year-length of 365.25875 days. As a result of the continued use of this extra-long sidereal year the zero point had a progressive movement towards east by 0.00239 days per year. Could it be the cause of error in calculation? [The precession of equinox is approximately 50|| per year. But there is continuous change in precession speed. According to modern science precession speed of AD.285 is 49.9049 and of AD.2100 is 50.3132. It means that there is a change of 0.0222226|| in 100 years. Could it be cause?] Earlier it was said that - ‘There is another point to be considered which will be revealed later’. It will be discussed here. The eastward progress of the Sidhantic zero point touched the point opposite Chithra (or vernal equinox of AD.285), only towards the end of 19th century i.e., near about AD.1885. The Sidhantic panchangas (ephemeris) of this period (for e.g. Vakya-panchanga that prevailed over South India) therefore had their zero point falling opposite Chithra by accident and consequently the modern astronomical tropical longitude of sun and the corresponding Sidhantic sidereal value had the difference equal to an ayanamsa based on Chithra’s opposite point. At this point I think it won’t be irrelevant to present a statement Hari made in a letter to me. “When you don’t know about the secular variation rate of precession, accept what others say? For ayanamsa how you are concerned about the year AD.231 or AD.238. Do you know that Chithrapaksha is no longer based on AD.285? AD.285 is the value of zero year based on the astronomical knowledge of AD.1956 or so. Till the advent of the new theories, when ever precession was accounted a few years difference for zero value (of year) was normal. AD.238 is the value derived by a computation across 3339 years from the epoch of Kaliyugadi. But there the Chaitradi (Kali-year beginning) does not coincide with zero. Zero coincidence of Chaitradi is in AD.231. These are all intricacies related to ancient Calendar. Unless you read thoroughly about ancient Indian astronomy and its computations, you may not grasp the intricacies. Continue the study; keep the doubts in mind and as you progress in your studies you will understand. Everything cannot be made simple by correspondence.” I truly agree with those statements. An unending search for the truth of astrology, and its true foundations is necessary, for the acceptance of astrology as a science. Chadrahari’s search for correct zero ayanamsa year also continues. We will wait for worthy knowledge that would be revealed by this scholar in his search for truth of astrology. [What ever be the zero ayanamsa year, one should also remember that - “The zero ayanamsa year is not the year in which astrology originated”. Fixed zodiac with Moola as fiducial star, Ayanamsa, Zero ayanamsa year etc are all mathematical concepts and therefore the origin of astrology could be either before or after the zero ayanamsa year such as AD.231. But the stellar divisions are mentioned in Vedas, and as every historian agrees that Vedas are written before BC.1500, we can be sure that the Zodiac was in use far before the zero ayanamsa year. This was possible only because of the fact that Zodiac is a mathematical concept (A fixed reference frame based on which movements could be evaluated). Chandrahari’s idea is that the formation of Sidereal zodiac originated in BC.4137 among the Tantric cults of Pre-Aryan (Pre-Vedic) origin (Sarawathy River Valley Civilization/Sidhu Civilization). This idea of Hari is not discussed here; at it is not relevant for understanding Ayanamsa and Zero-Ayanamsa year].

Is there any empirical testable method to ascertain the accuracy of Hari’s Ayanamsa? In the words of Einstein - “In order to be able to consider a theory a physical theory, it is only necessary that it implies empirically testable assertion in general”. Is the Ayanamsa of Chandrahari such a one? Yes, it is. In the astrological context 1) In Mrithyubhaga research ayanamsa is very important. 2) Sputa (Nirayana planetary longitudes) of all planets, Birth time rectification, Desa systems, Varga Systems etc all depend on the accuracy of Ayanamsa, and is affected by any change in it. 3) But the best possible assertion could be the testing of the hypothesis “Rhythm of the Universe is in tune with the rhythm of breath pattern”. (The equivalence of Microcosm and Macrocosm) Although this Ayanamsa hypothesis has very good mathematical and theoretical foundation, to verify the trustworthiness of this Ayanamsa, we need to concentrate our studies in the above-mentioned 3 areas. [That is why Chandrahari jumped into studies such as 1) Mrithyubhaga Research 2) Microcosm - Macrocosm equivalence concept in Tanthra. 3) Biological - Circadian rhythm etc] Conclusion Hari is calling for the support of every learned astrologer, who is searching for the truth of astrology. Why he needs help? In his own words - “To strikeout a new path in this labyrinth is a difficult task and no single author however resourceful he may be unable to adequately support each and every one of his sentences or arguments by quoting appropriate authorities”. It is said that once you catch the tail of a tiger you cannot leave it!! I would elaborate. It revealed to Chandrahari that there are some fundamental mathematical concepts behind the Nirayana zodiac. (He started studying the subject). Then there came the necessity of refining those mathematical concepts (Again through study of the connected subjects became a necessity). Now comes the stage of giving empirical proof for the trustworthiness of his mathematical theory on Ayanamsa. (The study continues - and he always comes out with some fruitful results!) This man is a true learner. A truth seeker!... Let this man continue his studies... This is the research path by which astrology may get accepted as a science one day. So encourage this person and say - “Go on...thousands are behind you...” Sreenadh Malayinkeezhe Arsha Astrological Research Center Email: sreelid@yahoo.com -0-

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