true rationale of ss

8/3/2019 True Rationale of SS

1/8

Indian Journal o fHis/ory o f S c i e n C t - ~ 32 (3), 1997

TRUE RATIONALE OF SURYA SmDHANTAK. CHANDRA HARI *

(Received 28 December 1995; after revision 27 November 1996.)The Siiryasiddhiinta perhaps followed a model based on the p r e ~ e s s i o n of the

equinoxes. The sidereal mdia


2/8

184 INDIAN JOURNAL OF HISTORY OF SCIENCE

(b) "It is clear from the text that the compilers of the SilryasiddhiJn/a had noknowledge of the precession of the equinoxes .... "[p.240]

(c) " ...How did the indian savants manage to have such a wrong value for the lengthof the year?The year according to the Silryasiddhiinta, is meant to be clearly tropical, but asthe Indian savants compiling the S.S. were ignorant of the phenomenon ofprecession of the equinoxes, they were unaware of the distinction betwecn thesidereal year and the tropical year. .... (p.240)

(d ) ... the above analysis seems to show that the co-ordinates of stars were determinedat different epochs. The epochs come out to be 340 AD,500 AD and 560 ADrespe


3/8

TRUE RATIONALEOFSORYA SIDDHANTA 185

appproximatcIy the time taken by Sun to cover I 'of arc. In otherwords 360 Savana daysin 21600 years or approximately 200 such revolutions in a Mahayuga of 4320000 years.Tbis aspect o f Hindu sidereal year was known to Muffjala Bbaw. the South Indianastronomer who wrote Lagbu Manasam in Saka 854, or A.D. 932. According to Munjalathe Solstitial points make 199669 revolutions in a KaJpa or 199.669 in a Mabiiyuga i!!roughly 200. This information take us to the true rationale of the extra long sidereal yearand Mabiiyugas-

4320000 =200 x 21600 years i.e. MalJiiyuga is an integral mUltiple of the precessionalCycle of SfiIya Siddbiinta.

Based on the above clue Silry,/ Siddbiinta perhaps followed a Mathematical Modelon the following lines.MATHEM.\TJC\L MODEL OF SDRYA SIDDHrlNTA BASED ON TH E PRECESSION OF TH E EQUINOXES.

The Siliya Siddbiintc1 defines the mean Equinox since the beginning of Killiyug:l bythe following rclation* give exact references of verse from it follows:

(i) Ahargana (Nlh equinox) =N Kali Years + 60 - N (y-y') - (A)= 60 + N.y'

At the expiry of 3623 Kali years (1323332.45 days), N (y-y') = 60 and hence themean Sun 01 Kali 3623 (elapsed) coincided with the vernal equinox. This is evident fromthe zero ay:mfi/psa years of Siddhantic texts like Laghumanasa ( saka 449 or kali 3628 )Grahalaghava (saka 444 or kali 3623 ) etc. It must be noted here that as per the varioustexts of the Kerala School of Astronomy based on Aq,1blw!Jya like'Grc1lwcbiiranibandhanmn' 'Drgg:l1Jita' etc. also the zero aY,lI1iifpSa year is Kali 3623elapsed. According to the CRC report, for the expiry of 3600 Kali years the tropicalmean Sun was only 359" 42' as per modern computation instead of the 36(t required as- - ,per Aryabha!ij'a. The decrement of 18 can be explained as 60-3600 (y-y') =60-3600 xO,()J656 =60-59 days 37 gh,7{is= 23 years for the precessional model of Sillya Siddhfinlil.For the true sidereal year this amounts to only 18' of arc so that the mean tropical Suncoincided with the vernal equinox in Kali 3623 (elapsed). In short, 3623 =3600 x .71738.71600 whne 21738 is the period required as pcr SS- sidereal year for 360 days precessionso that there is 60 days precession in 3623 years.

(ii) Mean tropical SUIl (N''' Kali) = 360 - 60+N (y-y')Where N = Kali years elapsed = 300 + N (y-y) ...........(B )for N (y-y') = 6(). Mean tropical Sun of SS coincided with the vernal equinox.

*Apparcntly nil 'lIch ruk is c,itlcnt in the SS (hiltor\.


4/8


(iii) Me,m SMerea/ Sun o fSurya SiddhiinlaTo understand the relation that governs the Sidereal Mean longitude of SS, wemust know the iiyanii1!1sa of the great epoch of Hindu astronomy viz. the beginningof KajjYl.'ga - Midnight of 17/18 February 3102 B.c. N.C. Lahiri5 Secretary ofthe Calendar Reform Committee gives the value as 46"35'. Slight modificationis suggested to the above value based on the following arguments.

(iv) Divi!>ion of" the Ecliptic into Rilsls & Nak$atrasCalendar Reform Committee has frankly admitted their ignorance on this vitalaspect of Hindu Zodiac. A division of the ecliptic into 30" each and 13"20' eachmeans a division of 360" into 108 parts of 3"20' each i.e. the so called four pad,?sor quarters of 27 nc1k$atra divisions.108 x 200' = 21600' = 360".The obvious first step in any such process is a division of 360" into four quadrants.At any point of time, equinoxes and solstices are the most convenient referencesfor a division of the ecliptic into 4 quadrangles of 90" each. l!p't:da (1.155.6)perhaps refers to such a division of the ecliptic by the equinoxes & solstices.As regards division of the ecliptic into 108 parts of 3" 20' each, scriptural evidenceis available in MaitriiyalJa Upani,5ad VI. 14:"The visibility of time is it's increase from the duration of the twinkling of theeye to the year of twelve parts. Of this year, the one half is consecrated to Agniand the other to Varul)u. The movement from Magha upto half of S r a v i ~ t h u Q , itis consecrated to Agni and the northward movement from half of S r a v i ~ t h a h upto Sarpah is consecrated to Soma. Every month of the year consists of ninequarters (fourth parts of the 27 n a k ~ a t r a s ) in conformity with the accompanying( n a k ~ a t r a ) ... "".The cpoch referred to herein correspond to the fall of solsticesalong 120" & 300" and equinoxes at 30"-210'1, around B.C. 1900. This descriptionof the year reflect a division of the ecliptic using the equinoxes and solstices asthe references.On the above basis. Lahiri's value of 46"35' can be modified as 46"40' i.e. thevernal equinox at the beginning of Ka/iyuga was at Rohini Mid-point. Preciselythis is the mathematical definition of Hindu Zodiac popularly known as RiislCakrc1".The unknown Genius created Surya Siddhiinla in such a way that the Yugiidiequinoxes & solstices as weB as the fiducial star 'Mil/if (Lambda scorpii*)

* The pre-eminent position ofLambtla sCllrpii over the zotliac has been alreatly brought oul by motlern astronomy.It IS located near to the galactic centre anti is one of the two yogatarJshaving no proper motion. Hence Miiliiis nlllre appropriate to serve as fiducial rather than Citrii.


5/8

TRUE RATIONALE OF SORYA SIDDHANTA 187

becomes the reference point in the division of the ecliptic into 108 parts. Asvinyadiwas fixed by defining the sidereal longitude of 'Miila' to be 240". The Rfi!>1Cakra is thus implicit in Silrya siddhiinla and the initial point can be decipheredmathematically. According to the above.Sidereal Mean Sun =346" 40' y' + N (y-y')

360= 347d 21 gh + N (y_ys) -----------(C)The function.1! is meaningful since it is used for converting 4640' into equivalentdays. 360

DEFINITION OF THE HINDU ZERO-POINTAs per the Siddhfultic astronomy all the Sidereal Mean longitudes were at the Hindu

zero-point for the beginning of Kaliyuga. The mathematical model described above clearlydemonstrate that Asvinyiidior the zero-point was 60 days East of the tropical mean sun ofYugiidi and 46"40' west of the vernal Equinox.

COINCIDENCE OF SIDEREAL & TROPICAL ZoDIACS(Zero Ayaniimsa Year)Two requirements have to be met:

(a) Tropical & Sidereal Sun described above. (B) & (C) must coincide.(b) The AhargaIJa must correspond to the Mean equinox of the respective year which

is 60 days east of YugiidiTropical Sun.On equating B & C we gct,300 + N (y-y') = 347d 21 gh + N (y-y') -----------(D)i.c. N =47d 21 gh =3339y'-y'i.e. the sidereal and tropical longitudes of Sun as per the SS model coincided atthe expiry of Kali 3339.Ah:lrgalJa of 3339 Kali (elapsed) = 1219599 days. But 3339 x (y-y') = 55d 1 7 ~ h only. Asvinyfidi was 60 days east of. Yugfidi tropical Sun i.e. Sun reaches the

" In the model zodiac of the author the zero point of the wdiac at Yugidihas the anti-Citrii point (and Miila was24()" when:as the text SS demands Miila at 242" 50' and Revati at 359"50'see (a) above, but, at the end ofeal:hKali year, this I.em point shifted towards e ~ t by an amount given by the excess in the SS length of the Sidcrealyear, i.c. the zero point has a slow east-ward motion.This supposition, according to referee. is in violationoflhe concept ofa sidereal wdiac, and none ofthe traditionsof Hindu astronomy like number of revolutionsof planets and their apogee, node etc. can be litted in this modelzodiac with a moving zern point (Editor).


6/8


Hindu zero-point after about 4 days 42 gha{is.i.e. AhargaIJa = 1219599 + 4 ~ 4 2 ~ h =1219603.684 approx.This corresponds to the Mean equinox of AD 238 (23rd March, Friday) andhence the coincidence of Sidereal & tropical zodiac is confirmed.

EQUINOX OF KALI 3623 (EI.APSED)The Calendar Reform Committee could not provide any explanation for rejectingthe zero point of Siddhantic texts like GrahaJiighava that corresponded to themean equinox of KaIi 3623 (elapsed). The model described above explicitlybrings out imbalance of equation (D) for KaIi 3623 in view of the Sidereal meanSun being at 356" for the mean equinox. The real precession since the beginningof KaJiyllga is 50" 38' instead of 46" 40'.

EQUINOXES OF AD 285, AD 500 & AD 576.It is apparent from equation (B) that the SS Mean tropical Sun coincided

with vernal equinox in Kali 3623 (Elapsed) and as a result of the continued useof extra-long sidereal year the zero-point moved towards cast 0.00239 days peryear. Revali ( Zeta Piscium) being on the west of the equinox of Kali 3623, thefall of equinox on Revati was of no consequence to Silrya Siddhiinta.

Alternatively, with Milia at 240" the sidereal longitude of Revali = 355" 17'.Equation (B) suggests that the Mean Sun of S[Jrya Siddhiinta coincided withRevati for KaIi year 3339 (elapsed) i.e. the zero longitude of Revati belong toAD 238 rather than AD 576.

Similar argument holds good for the point opposite Citra. The east-wardprogress of SS zero-point coincided equinox of AD 285 near about A.D. lX85;In fact, had the equinox of AD 285 or AD 576 been of any relevance to S[JlytJSiddhiinta, the year-length would have obviously undergone modification as canbe seen in the case of Brahmagupta. Also we must note that Brahmaguptadiscarded his modification of year-length to compile the K h a l J ~ a Khiidyak


7/8

TRUE RATIONALEOFSORYA SIDDHANTA 189

ASTROLOGICf\L RATIONALE OF THE INITIAL POINT

Mathematically (or geometrically) every point of a circle is on a par with theother to be considered as the zero point. As such the approach of the CakndarReform Committee was that the choice of initial point of the zodiac was a matterof calendaric custom or convention. The Calendar Reform Committee t h u ~ recommended a standard initial point for bringing unifomuty among the thenprevailing regional calendars. Calendar Reform Committee did take note of theAI-Biruni's observation that the astronomical knowledge was a by-product ofth..: astrological knowledge, but the astrological aspect was overlooked whilerecommending the arbitrary point opposite Citra. If the purpose of creation ofthe zodiac was mainly astrological, there must be some astrological rationalethat gives credibility for a point on the ecliptic to become the 'true' zero point ofthe zodiac. For example, in the realm of modem physics, a mathematical resultis meaningless without a physical rationale that explains its relation with thephenomenal Universe. Citra's opposite point has no physical rationale that justifyits choice as the initial point of Rasi Cakra. On the other hand an explicit rationaleis forthcoming from the interpretation of SS based on MUla as fiducial at 240".The basic postulate of fYOl1h.{listra is the 'Principle of Symbolic Equivalence ofMan and Zodiac i.e. Microcosm & Macrocosm'. This principle we can findreflected even in the U p a n i ~ a d s as- 'Aham Brahmlismi'-and this demands anastronomically defined physical point over the human body. Another of theancient Hindu disciplines viz., Tantra has fortunately preserved this informationand the point of symbolic coincidence can be identified as "!vfil/lidhliram ': theseat of KUlJda/inlat the bottom of the Cerebro-Spinal axis which falls at 240"over the human-zodiac. The nomenclature "Mu/lidhiiram" meaning - MU/li thefiducial, infact is a reflection of the sidereal longitude of 240' for MuJli on theRfi:/i-cakra. An initial point becomes the true zero point only if it makes theresulting zodiac an exact replica of the human being. The synonymous phraseologyprevailing in f y o t i ~ a and Tanlra lend further credence to the above bio-cosmicsymbolic interconnection.

CONCLUSIONS

It is apparent from the above that the true zero ay;mlif!1sa year according toS17rya 5iddhiintil is Kali 3339 or AD 238 and the fiducial star is MUla. Yogatiirfishave nothing to do with the division of the ecliptic into 27 equal divisions as thedivision was mathematical using the'equinoxes & solstices of "Yuglidi" asreference points. On this It\ckground the initial point as recommended by CRCstands for scrutiny and re-examination.


8/8


REFERENCES1. Silrya Siddhfinta - English translation by Rev. E. Burgess, 1860.2. Reports of he Calendar Reform Committee M.N. Saha & N.C. Lahiri, CSIR. 1955.3. Paiica Skldhlintikli of Varahamihira by T.S. Kuppanna Sastry, P.P.S.T. Foundation.

Adyar, Madras, 1993.4. Silrya Siddhlinta- English translation by Rev. E. Burgess, 1860.5. Tables olthe Sun by - N.C. Lahiri.6. Sixty Upilfl1{;ads of the Veda by Paul Deussen. Vol. I.7. Silrya SiddhlinLa - English translation by Rev. E. Burgess, 1860.

true rationale of ss

Documents