Patam_parallel Declinations_errors In Indian Astronomical Ephemeris

Pātam - A Unique Observational Phenomenon of Indian Astronomy K. Chandra Hari1 Abstract Present paper is an attempt to cast light on a unique astronomical phenomenon about which we have mention even in the earliest texts of Indian astronomy. Pātams, Vaidhrtam and Vyatīpāta are unique for the fact that the siddhāntic treatises gave them importance as eclipses and devoted separate chapters for accurate computation of the same where as in modern astronomy we find no mention of the phenomenon. In the light of computations, the Pancasiddhāntikā verses III.20 and 22 have been given a correct interpretation and the three varieties of the phenomenon Vaidhrtam, Vyatīpātam and Sārpamastakam have been specifically identified and explained. Varied interpretations of the above verses are shown to be untenable using computation. Phenomenon was of more astrological significance than observational and hence the phenomenon has become obscure in the era of modern astronomy. Modern softwares do not provide for the computation of these Pātams and precise computation of sparśa, madhya and moksa is missing even in Indian ephmerises both local and the Rāstrīya Pancāňga. It is understandable that the cumbresome computations may be the cause of the obscurity of precise treatment of the Pātams which are essential for the observances as prescribed in scriptures in comparable manner to eclipses. Lead by Rāstrīya Pancāňga to give precise computational details of this phenomenon shall enable the Pancāňga makers to do more justice to the classical prescriptions on the topic and also uniformity and scientific practice in Jyotirganitam. Appendices provide illustration of the mean computations that form the basis of the Vaidhrtam and Vyatīpātam as being dealth with in the Rāstrīya Pancāňga and also of the precise computations possible as given in the Malayalam Pancāňga Jyotiścakram. Key Words Pātam, Vaidhrtam, Vyatīpātam, Pancasiddhāntikā, Declination, Yogasphuta, Krāntisāmyam, Rāstrīya Pancāňga

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Institute of Reservoir Studies, ONGC, Ahmedabad-5. [email protected] 1

1. Introduction When we look back into the history of astronomy from modern times to the 1500 years of the Siddhantas, we meet with a unique astronomical phenomenon viz., Pātam, almost unheard of in modern times when eclipses and occultations have come under increased attention. Pātam is of two kinds Vyatīpātam and Vaidhrtam and most classical texts have a separate chapter on Pātādhikāram. In modern times this phenomenon has not been given much observational significance and is absent in modern astronomical treatises and planetarium softwares as an observable astronomical phenomenon. Indian National Ephemeris mentions both Vyatīpātam and Vaidhrtam but the times given have no observational relevance as the computation is not according to the procedure outlined in Siddhāntas. An astronomical phenomenon having detailed exposition in Siddhāntas for obervation but failing to have any reference in modern astronomy and ignored of the astronomical rationale even in the modern Indian National Ephemris (Rāstrīya Pancāňga)1, Pātams i.e. Vyatīpātam and Vaidhrtam as such are unique by origin, development of computational procedure in ancient times and the obscurity in modern times. Present paper is an attempt to examine the different facets of the phenomenon and its relevance vis-a-vis factors that made the observation obscure in the Indian tradition where the times of these occurrences have been regarded as highly inauspicious since very early times. 2. Vyatīpātam and Vaidhrtam in Siddhāntas Pancasiddhāntikā, which is a compilation of the earliest of five Siddhāntas by Varāhamihira, under the Pauliśasiddhānta gives the following rationale of the phenomenon.

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I 20 I2

"When the sum of the longitudes of sun and moon i.e. yogasphuta is 3600 Vaidhrtam occurs and yogasphuta increased by ten naksatras (=133020') is 3600, there is Vyatīpātam. Time of occurence is to be found using the sum of the daily motions of sun and moon"

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I 22 I

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When the sum of the longitudes of sun and moon i.e. yogasphuta is 1800 and the sun and moon are in different solstitial halves Vyatīpāta happens by parallel declinations of sun and moon. This ancient prescription of Pauliśa came down to us through Varāhamihira has undergone varied interpretations at the hands of erstwhile scholars. Verses as emended by Sarma given

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above only do justify the observed phenomena and computation of the same. In elaborating on the subject Sarma says – "...the day on which the sun and moon rise almost at the point, one moving southward and the other moving northward, coming to meet each other as it were, that day is the Vyatīpāta. Because they cross each other moving in different directions, the phenomenon is called Vyatīpata or Vyatipāta"

Varied Interpretations and Observation It is interesting to take a look at the varied interpretations of the verses 20 and 22 in the light of the observable phenomena and the computational method handed down to us since the early times of Āryabhata and other siddhāntic astronomers. (a) Sastry and Sarma explain the verse 20 as description of Vyatīpātam and Vaidhrtam, two out of the 27 classical pancāňga yogas, durations of yogasphuta equal to 13020' in which the 17th one (yogasphuta = 17x13020' = 226040') is Vyatīpātam and 27th (yogasphuta = 27x13020' = 360040') is Vaidhrtam. Apparently, this interpretation makes sense when we look against the background of later descriptions of the pancāňga yogas. But then the question comes as to why only the computation of the 2 out of 27? Sastry and Sarma observe that the two have been given separately because Pauliśa did not have the 27 Yogas which is one of the Pancāňgas. Here another question arises – if the 27 yogas of 13020' of nirayana-yogasphuta did not exist, what meaning the 17th and 27th onees had in Pauliśa's times? In fact the confusion can be tide over if we take the 20 and 22 verses together for interpretation. 21st verse Āślesārdhādāsīt... etc is out of place there and have led the commentators to date the method to a solstitial position of 113020' -293020' belonging to 1500 BC. 21st verse is only a reference to ancient solstitial line as introduction to the subsequent discussions on the solstices and equinoxes in verses 23-25.4 (b) 22nd verse taken alone has to be interpreted as some different Vyatīpātam happening when the yogasphuta is 1800. In fact yogasphut
a as such has no meaning unless we are led to some observation in the vicinity of the same. This is true whether the yogasphuta is 360, 226040' or 1800. Further some of the longitudes as such has no observational relevance unless the same was to lead other computations which facilitated the observation of a phenomena. Therefore the interpretation that the verse 20 implied the 17th and 27th of the nirayana-pancāňga yogas cannot be correct.

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(c) A Malayalam commentary interprets the verse 20 by assuming an ayanāmśa of 23020' from verse 21 which speaks of Āśles
ārdhādāsīt yadā nivr
tti... meaning the solstice was at 113020'. As the ayanāmśa was (+) 23020', the nirayana yogasphuta was less by 46040' and 1800- 46040' = 133020' and so the mistaken interpretation that Vyatīpātam occurred when the yogasphuta is ten naksatras or 133020'. (d) Sastry's work5 in elaborating the meaning of verse 22 says that Vyatīpāta getting again mentioned for yogasphuta of 1800 is not a contradiction of the earlier reference in verse 20 to yogasphuta of 226040' as the zero point of verse 22 is winter solstice which was at (-) 900 to the equinox and thus causing a deduction of 1800 in the yogasphuta. No evidence is available for a longitude measurement at any time from the winter solstice. Account as above is illustrative of the confusions prevailing in respect of what actually the phenomenon is and how the same may be precisely computed. When we enter the period of later Siddhāntas we can see that the classical astronomers were quite clear in their minds and have instructed precise computation of the phenomenon viz. sparśa, madhya and moksa based on the rationale that no point on moon's disc shall have krāntisāmyam with sun. 3. In Later Siddhāntic Works We can make an attempt to decipher the right interpretation of the above verses 20 and 22 and by referring to the discussion on Pātas in later Siddhāntic works. In texts like Sūryasiddhānta, Brahmasphutasiddhānta, Siddhāntaśiromanī etc full chapters have been devoted to explain the phenomenon. Mahābhāskarīya, the crest of the Āryabhata tradition speaks of Vyatīpāta and Vaidhrta as – 6

ºÉÚªÉæxnÖùªÉÉäMÉä SÉGòÉrÇù ´ªÉiÉÒ{ÉÉiÉÉä +lÉ ´ÉèvÉÞiÉ& SÉGäò SÉ ¨ÉèjÉ{ɪÉÇxiªÉä Ê´ÉYÉäªÉ& ºÉÉ{ÉǨɺiÉEò& (4.35) xÉÉxÉɪÉxÉä ´ªÉiÉÒ{ÉÉiɺiÉÖ±ªÉÉ{ÉGò¨ÉªÉÉäºiɪÉÉä& =qäù¶ÉºiɺªÉSÉGòÉræù Ê´ÉIÉä{ÉÉk´ÉÊvÉEòÉäxÉEÆò (4.36) "When the yogasphuta of sun and moon is 3600, 1800 and 226040' the Vyatīpātam happens. When yogasphuta is 1800 Vyatīpātam is called Vaidhrtam and when the sum of longitudes is at the end of Anurādha (226040') then the phenomenon of Vyatīpātam is called śārpamastaka. Vyatīpātam occurs when the sun and moon are in different solstitial halves and their true declinations are equal when yogasphuta is near 1800 subject to the latitude of moon" In commenting on these verses Paramesvara says - iÉjÉ

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Vyatīpātam defined as 'half the circle' is

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approximate only and the true observation happens when the sun and moon equal in true declination. Modern Sūryasiddhānta has elaborately discussed 7 the topic on similar lines and the discussion in classical texts makes it clear that the Vyatīpāta being prescribed for computation are the moments of parallel declinations of sun and moon. This Phenomenon like eclipses have got sparśa, madhya and moksa with sparśa and moksa defined as moments having the declination difference of 32 minutes of arc and the sidereal naksatra division of moon correponding to the above is treated as highly inauspicious. When sparśa or moksa is in a different naksatra it is known as Dantādūnam which too is inauspicious like Vyatīpātam. Pātams given in Rāstrīya Pancāňg Despite the detailed accounts by ancient astronomers and the great importance ascribed by them to Vyatīpātam, the Rās
trīya Pancāňga is giving only the times of mean occurrence or the times at which the sum of longitudes becomes 1800 and 3600. Appendix-I illustrates the computations. These Pātams almost always falls in the same naksatra and quite against the precise instructions that the declinations have to be equal we can see that the declinations are unequal for these mean locations of Pātams. All the results are derivable from the thumb rules: 1. Vaidhrta-pātam = (3600 – 2 x Ayanāmśa – nirayana Sun)/13020' and 2. Vyatī-pātam = (1800 – 2 x Ayanāmśa – nirayana Sun)/13020' Locations where the phenomenon occurs makes a circuit round the heaven in anticlockwise direction as is the case with the nodes (Pātams) of planetary and lunar orbits and hence the nomenclature of Pātam for the phenomenon as Vaidhrta-pātam and Vyatīpātam. It is abundantly clear from the earlier discusson that such mean times and locations given in Rāstrīya Pancāňga have no relevance as observable phenomena and for religious observance as per the scriptures. Most of the Malayālam Pancāngas published in Kerala give the sidereal stellar position of Moon correponding to Vyatīpātam and Vaidhrtam computed as per the krānti-sāmya and the stellar occupation of moon in cases of Dantādūnam. Appendix-II gives the phenomena computed for Malayālam Era years, Kollam 1182 as given in the Malayālam Pancāňga Jyotiścakram8 1182 for illustration purpose. Contrasted with the data of Appendix-I, it is easy to realize that the actual phenomena of occurred from the middle of August 2006 (Kollam begins with solar month of Leo) in sequence of naksatras different from the mean locatons given in columns 3 & 6 below where few examples are reproduced:

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2 3 4 5 6 Naksatra Naksatra Naksatra Naksatra Vaidhrtam Actual Mean Vyatīpātam Actual Mean 28 Aug 2006 Citrā (14) 15 9 Sep 2006 U.Bhadra (26) 27 22 Sep 2006 U.Phālguni (12) 14 5 Oct 2006 P.Bhadra (25) 26 18 Oct 2006 Maghā (10) 13 31 Oct 2006 Dhanisthā (23) 25 12 Nov 2006 Āślesā (9) 11 26 Nov 2006 Śrāvana (22) 24 8 Dec 2006 Pusyā (8) 10 23 Dec 2006 Utrāsādhā 23 Specific example from Rāstrīya Pancāňga 20079 Sāyana Vaidhrti on 19 August 06-26, Naksatra is given as Svāti on the day. Table below shows the data typical of Rāstrīya Pancāňga and the correct data required as per the siddhāntic precepts: Date and time (IST) 19Aug 2007, 06:26 18 Aug 2007, 11:05 18 Aug 2007, 08:53 18 Aug 2007, 13:19

Sun δ & λ

Moon δ & λ

Remarks

Sāyana Vaidhrti according to δm = -17008' Rāstrīya Pancāňga 2007 when λm = 214018' declinations are widely different 0 0 δs = 13 12'50" δm = -13 12'50" Real Vaidhrti madhya and naksatra λs = 144055' λm = 204044' was Citrā δs = 13015' δm = -12045' Beginning of Vaidhrti, sparśa δs = 13011' δm = -13041' End of Vaidhrti. moksa δs =12057' λs = 145042'

It may be noted that – 1. Rāstrīya Pancāňga is citing a time that has no relevance to the phenomena as described in Indian astronomical texts and just meets the criterion of λsun + λ moon =3600/1800 which in itself is only a means to compute the true times. 2. Pātam in fact took place when the sum of the sāyana longitudes of sun and moon was 349040 and happened on the naksatra Citrā which precede the one given in Rāstrīya Pancāňga viz., Svāti. 3. Rāstrīya Pancāňga gives no cognizance to the precepts on sparśa-madhya-moksa which are critical for observance as in the case of eclipses. 4. Further, as will be explained later, the Rāstrīya Panchāňga is giving no cognizance to what is described Sārpamastaka in siddhāntic texts. This anomaly in fact defeats the declared objective of Rāstrīya Pancāňga of achieving a unified calendar computed scientifically all over India. It is well evident from the quoted verses that no justification can be adduced for the wrong values as the siddhāntic texts had 6

devoted separate chapters for the phenomenon under reference to facilitate the true times of krāntisāmyam and also the beginning and end.

4. Three Types of Occurrences -1800, 3600 and 226040' Most of the confusion in modern times in understanding the phenomenon had been due to the modern astronomer's unwillingness to compute the phenomena and see for themselves the reasons underlying classical accounts. To illustrtate the three different cases Vyatīpāta, Vaidhrtam and Sārpamastakam we shall consider a few examples below wherein the sayana geocentric longitudes and true declinations will be used to compute the phenomenon: (a) Vaidhrtam: Yogasphutam = 360 Considering for example 28 Aug 2006, we can understand the phenomenon in terms of the ratioanle - yogasphutam becoming 360 under 'ekāyāna bhinnagati' or ekāyana bhinna golam, giving rise to Vaidhrta-pātam. Yogasphutam 3600 = 28 August 15:26, λsun = 154:58 and λmoon = 205:02 and λsum =360. Both sun and moon are in the same solstitial half Karkkyādi but the declinations are in opposite direction. Observing the declinations in the neighbourhood we can see that: 1. Beginning (sparśam): 28.08.2006, 02:57 IST, δsun = +09052' and δmoon = (-) 09020'. 2. Middle (madhyam): 28.08.2006, 05:11 IST when the magnitude of δ = 09050' in different directions. λsun =154:33 and λmoon = 199:58 and λsum =354:31 i.e. almost half a day behind the mean time of 15:26 when λsum =360. Moon's naksatra can be found by substracting ayanāmśa and as per Rāstrīya pañcāňga moon is at 176000' in Citrā at the middle of Vaidhrtam. Obviously, at the end when the declinations differ by bimbayogārdham of 32' (after nearly 2 hours) the naksatra will be Svāti and the Jyotisa texts ascribe the blemish of Dantādūnam to the particular naksatra. 3. End (moksam): 28.08.2006, 07:24 when δsun =+ +09048' and δmoon = (-) 10020'. (b) Yogasphutam = 180 and bhinnāyana ekagolam Yogasphutam covers1800 on 09.09.2006 and the declinations show up as 1. 09.09.2006, 14:18 IST: δsun = 05019', δmoon = 04047'. 2. At 16:03 IST, δsun = δmoon = 05017' and λsun = 166037 and λmoon =10011'. Obviously, we can understand that sun and moon are in different solstitial halves but in the same hemisphere and λsum ≈1800. Naksatra of moon at this midpoint as per

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Rastrīya Pañcāňga will be 346014', Uttarabhadra and therefore the blemish Vyatīpatam gets ascribed to Uttarabhadra. 3. Pātam ends at 18:20 IST when δsun = 05015' and δmoon = 05057'. Naksatra of moon as per Rastrīya Pañcāňga will be 347039' and in this case Dantādūnam will be ascribed to Revatī. It may be noted that the Dantadūnam is possible also at the beginning of the Pātam and the religious observance as per the scriptural prescriptions of calendar is possible only if the Pātam is computed using true declinations of sun and moon with times of sparśa, madhya and moksa. Examples given above are typical of Vaidhrtam and Vyatīpātam and they fully meet the descriptions given in texts from earlier times like Pañcasiddhāntikā to later ones like modern Sūryasiddhānta or Grahalāghava. But these cases in no way render any explanation to the reference available in verse 20 viz., daśarksa sahite tu i.e. yogasphuta near about the end of Mitra or Anurādha at 226040 which has led modern scholars into varied interpretations of the Pañcasiddhāntikā verses. As we noted earlier, Bhaskara-I has named this particular case as Sārpamastakam. (c) Sārpamastakam: Yogasphutam = 2260:40' A careful examination of the phenomenon has led the present author to 28th June 02:22 IST when the declinations were equal and met the conditions of Pātam. 1. Beginning: 28.06.2006, 02:22 IST. λsun = 96°04' λmoon =121°56', λsum = 2180 and δsun = 23°18' and δmoon = 23°50'. 2. Middle at 06:04 when δsun = +23°17' = δmoon. λsun = 96°13' λmoon =123°51' and λsum = 220004'. 3. End at 09:38 IST, δsun = 23°17' and δmoon = 22°45'. λsun = 96°21' and λmoon = 125°41'. λsum = 222002'. 4. λsun + λmoon =226040' at 18:01 IST on the same date when the true declinations were δsun = 23°16' and δmoon = 21°24' i.e. differed by 01052'. It is evident from the above that in this particular case when the sun and moon are in the same solstitial half and their declinations have the same direction, i.e. ekāyanagola, contrary to the rationales of ekāyana bhinnagola and ekagola bhinnāyana, krānti sāmyam occurs near about the sum of longitudes equal to 226040' which completes circle on the addition of 10 naksatras. Reference to mitrantam in verse 35 of Mahābhāskarīya is meant to convey the magnitude of 17 naksatras = 226040' and has nothing to do with the sidereal naksatra zodiac as the phenomenon is related to declination and tropical longitudes are relevant in the discussion. Of course it is possible that Bhāskara-I used the word mitrantam

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to convey the above longitude because of the coincidence of sidereal zodiac and tropical zodiac during his times or as the ayanāmśa was little in his time and the phenomenon could be computed with the siddhāntic sidereal longitudes. In giving the mean location of the phenomenon sum of longitudes could be given as sidereal as ayanāmśa of a few degrees did not mattered much in the definition of the locality of naksatra where the Pātam occurred. Reason for the name Sārpamastakam It is interesting to notice that in the above case where λsun+λmoon =226040', the sun's longitude is in Ārdra while moon is at the end of Pusyā. Āślesā or Sarpa was at the head of this strange phenomenon which happened against the rationales of ekāyana bhinnagola and ekagola bhinnāyana. Pātam may therefore have been given the name Sārpamastaka in ancient times. Astronomical reason for this rare occurrence may be understood as follows. Inclination of the lunar orbit reaches its maximum value of 05017' when the sun conjoins one of the nodes. Geocentric declination of moon is given by Sinδmoon = [Cosω ω*Sinβ + Sinω ω*Cosβ*Sin λmoon, where ω is obliquity, β is the latitude and λ is the longitude of moon]. Therefore when the sun's declination is near the extreme and moon is declining in latitude after crossing Rahu(Ω)+900 then the declinations can become equal in the same solstitial half circle and declinations having the same direction. As for example in the case when Ω is in conjunction with the vernal equinox (00), λsun+λmoon = 1800 shall be the point of extreme declination of moon as it happened in 2006. North node of moon (Ω) transited over equinox near about solstice and moon conjoined Ω on 19.06.2006 at 00:40 IST at λ = 00010'. Obviously moon had the extreme declination of 28°26'42" on 25th June 14:08 IST when δsun = 23°23'24". λmoon = 89°55' and latitude βmoon = 05°00', λsun = 93040'. Obviously moon near 900 which yields the sphutayoga of 1800 won't be leading to Pātam. But krāntisāmyam occurs when moon advances towards the south node and the latitude declines to make the δmoon equal that of sun after nearly 3 days to make the yogasphuta increase by 3 naksatras or 45 degrees i.e. 180+45 ≈ 226040'. This advancement need for 3 naksatras for yogasphutam inspired Pauliśa to frame the verse as daśarks
a sahitetu yadi cakram vyatīpāto.... Phenomena observed had the speciality that the moon shall be setting precisely at the same point as the sun before Pātamoksam if the Pātam began in the evening with moon at the head of Āślesā or Sarpa and hence the name Sārpamastaka. Question may here arise as to whether the observation described above was possible 1500 years before in Varahamihira's time or even before in Pauliśa time? This doubt can be cleared by a look at the following data of AD 499:

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Maximum declination of moon = 24June 499 AD, 10:18 IST. δmoon = 28°32' and λsun =92°45' and λmoon = 87°48' and yogasphuta =180. Pātam is not possible untill moon's declination falls to that of the sun and this happens in three days, 27.06.499, 02:12 IST when δmoon =δsun = 23°32'. λsun = 95°18' and λmoon = 121°07' and the yogasphuta was 216025', in Anurādha. It is easy to realize from the above data that moon could have been at the top of Āślesā in similar occurrences depending upon the position of the lunar nodes or ayana-sandhi of moon in relation to the extreme declinations of Sun happening towards the east of Āślesā. Contrary to some interpretations that linked the daśārks
asahitetu verse of Pañcasiddhāntikā10 to the solstitial line passing through Āślesārdham (sidereal λ =113020'), it becomes apparent that the phenomenon may have been initially spotted when the solstitial line passed through the beginning of Āślesā (sidereal λ =106040') when sun obviously came to have the extreme declinations. With the lunar node passing through Bharanī or the middle of sidereal Mesa rasi, the longitudes measured from vernal equinox alone could have met the condition of yogasphutam to be 226040' for the occurrence of Pātam. If the discovery of the phenomena by Pauliśa can be dated to 500-900 BC or the period afterwards when sun was at the head of Sarpa and caused the Pātam as above, the name Sārpamastaka has its origin from the position of sun after the summer solstice. Similar Pātam occurs after the winter solstice as it happened on 23rd December 2006, 06:05 IST, when the declinations became equal (-23°26') in the same solstitial half. λsun = 271°02' and λmoon = 301°35' and yogasphuta was 212037. Sārpamastaka is not possible when the South node is near the equinox as the δmoon will be at the low extreme and krāntisāmya is not possible for the advancing moon. In the light of the above discussion, it is clear that the Rāstrīya Panchāňga data fails to take care of the 3 types of phenomenon as the results given are only mean computations having significant offsets. Identification of Sārpamastakam is not finding a mention in the Rāstrīya Panchāňga 2007-08 as may be understood from the following data.11 Date: 9th January 2008, 19:14 IST. λsun = 288°40' and λmoon = 301°20'. λsun+λmoon = 230000' and thus the sum is around the end of Anurādhā. Declinations are equal at -22008' and thus Sārpaśiras concides with Uttarāsādhā naksatra. No mention of the occurrence of this Vyatīpātam is available on page 78 where it should have been mentioned. Similar is the situation in all cases where naksatras have Dantādūnam. As for examples: (a) 13.09.2007, 00:05 IST, sparśam is on Uttaraphālguni naksatra while Vaidhrtam was on Hasta and thus the naksatra is blemished. Rāstrīya Panchāňga gives Vaidhrti at 12:39 IST which obviously is wrong, unscientific and against the precepts in siddhāntic astronomical texts.

10

(b) 03:11.2007, 07:05 IST, moksam is on Maghā while Vaidhrtam was on Āślesā and thus the Maghā naksatra is blemished because of Dantādūnam. Rāstrīya Panchāňga gives Vaidhrti on 2nd November at 23:24 IST. Rāstrīya Pancāňga is stating some phenomenon when there is no occurrence and suggests religious obseravance by the Hindus and it does not give the phenomenon when it is occurring. In fact the term 'sāyana Vaidhrti' has meaning only if the time corresponds to the occurrence of the phenomenon. If there is no phenomenon, what is the difference between nirayana and sāyana Vaidhrtis at which the sum of the longitudes is 3600 or Vyatīpātam at180? When the whole Pancāňga given is nirayana why the Sāyana-Vaidhrti if it does not correspond to the phenomenon described in authoritative texts?

5. Significance of Pātams in Calendar Observances Muhūrthapadavi12, a Malayalam work on Calendar based observances declares the time of Pātas as highly inauspicious.

±ÉÉ]õ´ÉèvÉÞiɪÉÉä¨ÉÇùvªÉÆ ªÉoùIÉä iÉnÂù Ê´É´ÉVVÉǪÉäiÉ nùxiÉÉnÚùxÉÆ SÉ ªÉκ¨ÉxÉ ºªÉÉiÉ iÉoùIÉÆ SÉ xÉ ¶ÉÉä¦ÉxÉÆ i.e. the naksatra of moon in which the Pāta occurs must be rejected for all auspicious works. The naksatra in which sparśa or moksa takes place, when the moon gains a difference of declination exceeding 32', is also inauspicious. Further we can see –

+ÉtxiÉEòɱɪÉÉä¨ÉÇùvªÉEòɱÉÉä YÉäªÉÉä³ýÊiÉnùɯûhÉ& |ÉVV´É±ÉV´É±ÉxÉÉEòÉ®ú& ºÉ´ÉÇEò¨ÉǺÉÖ MÉνÇþiÉ& The beginning, middle and end parts are highly inauspicious and have to be rejected for all works. Muhūrthapadavi adds further details by quoting Varāhamihira in the following lines-

iÉjÉ ±ÉÉ]õ´ÉèvÉÞiɪÉäɨÉÇùvªº¡Öò]õiÉÉ®Æú SÉ iÉnÖù¦ÉªÉ{ÉÉ·ÉÇiÉÉ®Æú SÉ <ÊiÉ iÉÉ®újɪÉÆ ´ÉVVÉÇxÉÒªÉÆ <ÊiÉ EäòÊSÉiÉ - iÉlÉÉ SÉ ´É®úɽþʨÉʽþ®ú& B¹ªÉÉä vÉxÉÆ IÉ{ɪÉÊiÉ ´ªÉiÉÒ{ÉÉiÉnùÉä¹ÉÉä ¨ÉÞiªÉÖÆ nùnùÉÊiÉ ÊxɪÉiÉÆ JɱÉÖ ´ÉkÉǨÉÉxÉ& ºÉxiÉÉ{ɶÉÉäEò´ÉvÉnèùxªÉ¦ÉªÉÉxªÉiÉÒiɺiɺ¨ÉÉiÉ ÊnùxÉjɪɨÉÊ{É |ÉVɽþÒiÉ Ê´ÉuùÉxÉ The three days, naksatras at which Pātam occurs and those preceding and succeeding ones have to be rejected for all works as they cause evils like loss of wealth, death, sorrow and fear. Contrasting the Vaidhrtam and Vyatīpātam which happens respectively at yogasphuta of 360 and 180, it is told that - SÉGòÉvÉǪÉÉä´ªÉÇiÉÒ{ÉÉiÉÉä nùÉä¹É®úÉVÉ& ºÉ{ÉÉ·ÉÇnÆù –i.e. among the two, the 11

Vyatīpāta occuring at yogasphuta of 180 is the king of all evils along with the two naksatras on the sides.

ʴɹÉ|ÉÊnùMräùxÉ ½þiɺªÉ {ÉÊjÉhÉÉ ¨ÉÞMɺªÉ ¨ÉÉƺÉÆ ¶ÉÖ¦ÉnÆù IÉiÉÉoùiÉä ªÉlÉÉ iÉlÉè´É ´ªÉiÉÒ{ÉÉiÉ& nÚùʹÉiÉ& IÉhɺiÉÖ ´ÉVVªÉÉæ xÉ iÉÖ ¦ÉÆ xÉ ´ÉÉ ÊiÉÊlÉ Just as the deer's flesh killed using poisonous arrow is evil, the Vyatīpāta is inauspicious and neither the naksatra nor tithi is auspicious. Importance that we see for the topic in Indian astronomical treatises is due to the astrological significance given to the phenomenon. Observation of the phenomenon had little importance as the occurrence was associated with sun and moon with or without simultaneity during day and night times. Modern astronomy has therefore failed to take notice of the phenomenon.

6. Conclusions 1. The phenomenon of Pātam of parallel declinations of the sun and moon has been shown to be of three types viz. krāntisāmya of sun and moon when yogasphuta is 3600 (vaidhrtam), 1800 Vyatīpātam and 226040' Sārpamastakam as expressed in Pancasiddhāntikā by Varāhamihira in the enunciation of Pauliśasiddhānta. 2. Varied interpretations of the verses Pancasiddhāntikā III.20 and 22 taking recourse to far epochs like 900 BC when the solstitial colure passed through the middle of Āślesā are shown to be untenable. 3. Siddhāntic literature call for precise computations but the phenomenon has remained obscure in the era of modern astronomy apparently because of the little observational significance. 4. Deficiency of the data given in Rāstrīya Pancāňga is illustrated with example computation to emphasize the need for appropriate corrections. Also, the irrelevance of the terms Sāyana Vaidhrti and Sayana Vyatipāta have been explained when there is no correspondence with the phenomenon. 5. Significance for the Indian Calendar and religious observances has been explained and in the light of (3) above it is desirable that the Rāstrīya Pancāňga may take lead in giving the precise sparśa-madhya-moksa times of the Pātams so that uniformity and scientific computation can be adopted by the Pancāňga makers.

7. References 1

Rāstrīya Pancāňga 2006, Controller of Publications, Civil Lines, New Delhi.

2

Pancasiddhāntikā, Sastry, TSK, Sarma, KV, Pancasiddhāntikā, III.20, p.58. PPST Foundation, Adyar, Madras

3

Ibid p.62

12

4

Ibid p.64

5

Ibid p.63 –"One may think that we are making contradictory statements by saying in the history of the origin of the Vyatīpata that it occurs at the sum being full revolutions and here that it occurs at half revolutions. There is no contradiction because the origin from which the longitudes are measured is different in the two cases. In the former the winter solstice was taken as the origin and in the latter the spring equinox"

6

Shukla, KS. Mahābhāskarīya IV.35, p.25, Lucknow University 1960.

7

Sūryasiddhānta, as quoted in Indian Astronomy, A Source Book, p.107. Nehru Centre, Mumbai, 1985.

BEòɪÉxÉMÉiÉÉ躪ÉÉiÉÉÆ ºÉÚªÉÇSÉxpù¨ÉºÉÉè ªÉnùÉ iÉtÖiÉÉè¨Éhb÷±Éä GòÉxiªÉÉä& iÉÖ±ªÉi´Éä ´ÉèvÉÞiÉÉʦÉvÉ& Ê´É{É®úÒiÉɪÉxÉMÉiÉÉè SÉxpùÉEòÉê GòÉÎxiÉʱÉÎ{iÉEòÉ& ºÉ¨ÉɺiÉnùÉ ´ªÉiÉÒ{ÉÉiÉÉä ¦ÉMÉhÉÉræùä iɪÉÉäªÉÖÊÇÖ iÉ BEòɪÉxÉä ʦÉzÉÊnù¶ÉÉä ®ú´ÉÒxnùÉ&ä ¦ÉÖVÉɺɨÉi´ÉÆ ªÉÊnù ´ÉèvÉÞÊiÉ& ºªÉÉiÉ SɱÉÉƶɪÉÖHòÉä ®úÊ´ÉSÉxpùªÉÉäMÉÉä ¦ÉÉræùxÉ SÉGäòhɺɨÉÉä ªÉnùɺªÉÉ ªÉnùÉ +ÊvÉEòÉäxÉÉä MÉiÉMɨªÉʱÉ{iÉÉ& iÉi¦ÉÖÊHòªÉÉäMÉäxÉ ¦ÉVÉäÊqùxÉÉÊnùEÆò ®úÊ´ÉGòÉxiÉä& ¦ÉÖVÉÉSSÉxpùÉä ¨É½þɶSÉäiÉ ºÉ MÉiÉÉä wÉÖ´ÉÆ +±{É& EòÉäÊ]õ¶É¶ÉÒ iÉuùiÉ ʴÉ{É®úÒiÉä Ê´É{ɪÉǪÉ& 8

Jyotiścakram, Explanatory supplement and Pancāňga for Kollam 1182, Sri Sabarigiri Publications, Kadapra, Kumbanad, Kerala 2006

9

Rāstrīya Pancāňga 2007-08, p. 39, Controller of Publications, Civil Lines, New Delhi.

10

Pancasiddhāntikā, Sastry TSK, Sarma KV, Pancasiddhāntikā, III.20, p.58, PPST Foundation, Adyar, Madras

11

Rāstrīya Pancāňga 2007-08, p. 78, Controller of Publications, Civil Lines, New Delhi.

12

Muhūrthapadavi with the commentary of Kānippayyūr Sankaran Namboodhirippad, Panchangam Publishers, Kunnamkulam, Kerala

13

Appendix-I Approximate Computation of Pātam as in Rāstrīya Pancāňga 1 Sun λ1 0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300 315 330 345 360

2 Sun δ1 9.56 14.72 18.95 21.91 23.34 23.10 21.20 17.83 13.30 7.94 2.11 -3.84 -9.56 -14.72 -18.95 -21.91 -23.34 -23.10 -21.20 -17.83 -13.30 -7.94 -2.11 3.84 9.56

3 Moon δ2 17.08 -2.79 -12.70 22.50 -21.20 9.60 6.22 -19.35 23.27 -15.60 0.77 14.38 -23.01 20.21 -7.71 -8.15 20.46 -22.91 14.00 1.24 -15.95 23.33 -19.07 5.77 10.02

4 5 Moon Naksatra λ2 310.64 24 295.64 23 280.64 22 265.64 20 250.64 19 235.64 18 220.64 17 205.64 16 190.64 15 175.64 14 160.64 13 145.64 11 130.64 10 115.64 9 100.64 8 85.64 7 70.64 6 55.64 5 40.64 4 25.64 2 10.64 1 -4.36 27 -19.36 26 -34.36 25 -49.36 27

6 Moon λ2 130.64 115.64 100.64 85.64 70.64 55.64 40.64 25.64 10.64 -4.36 -19.36 -34.36 -49.36 -64.36 -79.36 -94.36 -109.36 -124.36 -139.36 -154.36 -169.36 -184.36 -199.36 -214.36 -229.36

7 Sun δ1 9.56 14.72 18.95 21.91 23.34 23.10 21.20 17.83 13.30 7.94 2.11 -3.84 -9.56 -14.72 -18.95 -21.91 -23.34 -23.10 -21.20 -17.83 -13.30 -7.94 -2.11 3.84 9.56

8 9 Moon Naksatra δ2 -23.01 10 20.21 9 -7.71 8 -8.15 7 20.46 6 -22.91 5 14.00 4 1.24 2 -15.95 1 23.33 27 -19.07 26 5.77 25 10.02 24 -21.40 23 22.36 22 -12.30 20 -3.25 19 17.41 18 -23.45 17 17.78 16 -3.79 15 -11.83 14 22.18 13 -21.63 11 10.52 27

Note: 1. Col. 5 & 9 gives naksatra position of moon as serial number from Aśvini when the sāyana longitudes of sun and moon became 1800 or 3600. 2. λ2 given as negative have the corresponding positive values as 360+λ2.

14

Appendix-II

Vaidhrtam and Vyateepatam for M. E. 1182 No: Dates of 2006

Time

Midpoint Moon

Mid Naksatra

175:17

Citrā Vaidhrtam U. Bhadra Vyatīpatam Revatī Dantādūnam U. Phalguni Vaidhrtam Apamocanam P. Bhadra Vyatīpatam Maghā Vaidhrtam Dhanisthā Vyatīpatam Āślesā Vaidhrtam Śrāvana Vyatīpatam Pusyā Vaidhrtam Uthratam Vyatīpatam Kārttikā Vaidhrtam Viśākha Vyatīpatam Bharanī Vaidhrtam Citrā Vyatīpatam Svāti Dantādūnam Revatī Vaidhrtam Hastha: Vyatīpatam P.Bhadra: Vaidhrtam U.Phalguni: Vyatīpatam Śatabhisak: Vaidhrtam Maghā Vyatīpatam Dhanisthā Vaidhrtam Śrāvana Dantādūnam Pusyā Vyatīpatam Āślesā Dantādūnam Uttarāsādhā Vaidhrtam Srāvanam Dantādūnam Pusyā Vyatīpatam Punarvasu Dantādūnam Viśākha Vaidhrtam Bharanī Vyatīpatam Svātī Vaidhrtam Aśvinī Vyatīpatam Citrā Vaidhrtam

1

28 Aug

Begi. Middle End 02:57 05:11 07:24

2

09 Sep

14:18

16:03

18:20

345:30

3

22 Sep

13:14

15:44

--

153:54

4 5 6 7 8 9 10 11 12 13

5 Oct 18 Oct 31 Oct 12_13 Nov 26 Nov 8_9 Dec 23 Dec 31 Dec 2006 13_14 Jan 2007 26 Jan 2007

16:13 04:03 15:02 18:56 12:33 21:53 02:42 03:00 21:21 09:58

17:55 06:17 17:04 21:32 15:16 01:14 06:05 06:03 00:22 12:18

19:37 08:30 19:05 00:06 17:55 04:26 09:18 09:12 03:28 14:41

324:31 122:36 303:46 114:38 285:31 99:32 276:54 29:03 203:17 15:27

14

8 Feb 2007

18:46

21:12

23:39

185:35

15 16 17 18 19 20

21 Feb 2007 06 March 2007 19 March 2007 31 March 14 April 26 April

07:51 08:29 02:48 20:28 08:28 09:27

09:42 10:38 04:41 22:36 10:19 11:46

11:33 12:47 06:33 00:44 12:09 14:05

355:41 165:04 331:13 144:07 313:12 123:44

21

10 May

05:44

08:06

10:25

293:26

22

22 May

05:26

08:13

10:57

105:32

23

5 June

07:01

10:15

13:21

278:19

24

17/18 June

18:54

22:26

01:44

95:03

25 26 27 28 29

27 June 10 July 23 July 5 Aug 18 Aug

01:22 05:29 12:27 09:42 08:44

05:01 08:17 15:22 11:53 11:06

08:50 11:10 18:21 14:06 13:28

208:48 24:56 197:58 09:32 180:04

15