SURYA SIDDANTHA
This article aims at providing a thorough (but not verse by verse) expo sition of most important topics of and problems related to Surya Siddhanta in its relation to modern p hysical astronomy and its true or faulty interpretations by commentators, together with its use in astrology. Concrete proofs are provided in this article concerning many c ardinal problems in the field of ancient astronomy. In ancient India 18 original theoreticians were frequently mentioned in the field of theoretical theoretical astronomy known as SIDDHANTA , but Varah Mihir could could get tangible proofs of only five, which he mentioned in his Pa nch-siddhantika nch-siddhantika ('Of Five T heories'), among which Surya Siddhanta was t he only theory which was complete in itself and therefore h ighly regarded by Varah Mihir as the m ost accurate among all theories about heaven s. In India, the practical formulae of Surya Siddhanta are orally preserved a nd are regarded as sacrosanct by traditional scholars of this field, and are never fully published, because because it is believed that the practical method of using this text ought to be giv en only to worthy persons, who do not make a living out of it (-Manusmriti, Mahabharata). No commentator has ever published the practical methods of making actual planetary computations computations from ancient Surya Siddhantic formulae. These modern commentators themselves did not know these ancient formulae. The Makaranda Tables (with zero date of AD 14 78) are Surya Siddhantic, made from some approximate formulae of Surya Siddhanta, which implies that Makarandacharya posses sed the approximate formulae and made the tables made from those formulae, but did not made public those formulae. There is error in mean Mars of Makaranda because either Makarandacharya forgot to undertake beej-samskara (see later sections and the page on be eja corrections) in Mars, while the Surya Siddhantic commentary of Aryabhata contained beej corrections for Mars too as corroborated by Graha Laghava. The Surya Sidd hantic commentary of Aryabhata was therefore the only reliable commentary of Surya Siddhanta for at least over a millenium which had any practical utility for theoreticians and almanac-makers. This was the real reason behind immense prestige accorded to Aryab hata, but this Aryabhata was different from Ary abhata abhata I or Aryabhata II, as Al Beruni rightly believed. Unfortunately, this excellent Surya Siddhantic commentary by Aryabhata was lost during or after 16th century, and now most of pe ople wrongly believe that this Aryabhata was the same as the author of Aryabhatiya. All other ancient and modern c ommentaries of Surya Siddhanta are useless as far as their utility for actual computations is concerned, and all of them contain incomplete formulae of making true planets, but the author of Grahalaghava (Ganesh Daivajna,1519 AD) explicitly mentions that he used the be ej corrections of Aryabhata for outer planets,whose value tally with those of Surya Siddhantic tables of Makarandacharya and not with those of Aryabhatiya. This topic is discussed in the section 'Siddhantic 'Siddhantic Beej Samskaara'. Author of Aryabhatiya was not a follower of Surya Siddhanta, and differs from the latter in all major practical aspects, e.g, number of revolutions per mahayuga, sizes of e picycles, sequence of corrections to be made in the mean planet planet to get true one, etc. Aryabhatiya was widely criticised
by supporters of canonical astronomy in India, esp ecially by Brahmagupta and his followers. It is noteworthy that the philosophical and astronomical or astrological statements made by ep ic and puranic authors of India conform t o Surya Siddhantic views . Hence, Surya Sidd hanta is the sole book which can be said to co nstitute the bedrock of India's traditional astronomical/astrological mathematics. Other traditional text are are e ither incomplete or inconherent. Recently, many governmental a nd non-governmental non-governmental organisations in I ndia have started publishing annual almanacs based upon a freely distributed Surya Siddhantic software (Vinay Jha, 2006). It is still claimed by many astrologers of India that predictions based upon Surya Siddhanta are absolutely perfect. In 2006, a b ook was published in Hindi in which all major constants of modern astronomy were mathematically deduced, b y means of theorems, from Surya Siddhanta! But the author stated that Surya Siddhantic Siddhantic planets occupy different po sitions in heaven than material planets (Vinay Jha, 2006),which amounts to stating that there are at least two universes, one phenomenal univers e of matter open to human s enses (bhoo-loka), and the other noumenal universe of gods (bhuva-loka) who are presiding deities of material planets of ph enomenal world (martya-loka or the world of mortals). Surya Siddhanta is said to describe this noumenal world, whose planetary deities control the destinies of creat ures living in the the material world. Any attempt to confuse Surya Siddhanta with the phenomenal world lead s to misinterpretation of this mystic text (Surya Siddhanta is described as a secret text in its last stanza, whose knowledge i s said to be equivale nt to Brahma-jnana or omniscience,i.e., "rahasyam-brahma-sammitam"!). "rahasyam-brahma-sammitam"!). Indian astrologers used to worship Surya Siddhanta till the first half of 20th century (Pt Sudhakar Dwivedi mentions this practice in the introduction to his commentary of Surya Siddhanta),when Western scholars and modernised scholars of India started criticizing Surya Siddhanta as an outdated and inaccurate text and gradually its worth declined. None of these commentators of Surya Siddhanta possessed any knowledge of the formulae of Surya Siddhanta, yet they they posed as experts of this text and wrote worthless commentaries, which fail to elucidate how to compute actual positions of Surya Siddhantic planets according to ancient methods (proofs of this fact are provided i n subsequent sections). The problem with Surya Siddhanta is that its masters preserved its practical formulae and crucial concepts as closely guarded secrets, be cause the text itself ordered so. No attempt was ever ma de to refute the false commentaries of ignorants, because supporters of Surya Siddhanta Siddhanta believe that it is futile to argue in favour of a divine Non-Sensory Universe during a materialistic Kali Age. This article provides proofs showing that there were g enuine scholars of Surya Siddhanta, e.g., Aryabhata the Elder (prior to the author of Aryabhatiya) Aryabhatiya) in ancient India and M akarandacharya in mediaeval India. After Aryabhata, no one tried to write down any g enuine commentary of Surya Siddhanta showing practical methods of computations. The lost Surya Siddhantic commentary by Aryabhata the Elder was the source of those practical manuals of almanac making in India for millenia which followed Vedic-Puranic tradition (see the section "Lost Surya Siddhantic Commentary of Aryabhata: New Lig hts").
Surya Siddhantic 'Sun' is stated to be a deity, only 5.5 million kilometres from Earth (p hysical sun is 149.6 million kms away). A deity cannot be see n by ordinary senses, argue the prop onents of Surya Siddhanta. The only proof of Surya Siddhanta is astrological prediction based upon it, which are held to be perfect. Since astrology based upon modern astrononomy has already accepted to be a pseudoscience b y mainstream scientists, Surya Siddhantic astrology needs t o be tested by scientists. Another proof of Surya Siddhanta is a series of secret theore ms which show that major constants of modern astronomy can be a ccurately deduced from Surya Siddhantic notions and equations (see the section "Deduction of Modern Astronomical Constants from Surya Siddhanta"). Some of these Surya Siddhantic or Vedic theorems suggest solutions of many unresolved cardinal problems of modern astronomy, and therefore deserve serious attention. The problem with western commentators is that Surya Siddhantic system has many similarities with that of Almagest, on account of which Surya Siddhanta is declared to be influenced by Almagest. But detailed investigation of Surya Siddhantic system does not support this view. There seems to be a long history of distortions through translations, which may place original Surya Siddhanta in distant prehistory. Many secret ideas of Surya Siddhanta were indirectly exported to Greece, but could not be fitted into the ge neral framework of Western astronomy and were subsequently forgotten. The concept of Philolaus that Earth and all h eavenly bodies rev olve round a ce ntral fire which could never be see n since there was a counter earth between the earth and this fire was related to Puranic and Surya Siddhantic tradition of a heavenly Meru which was away from the centre of Earth and was related t o a terrestrial Mt Meru (see the section "Meru: Centre of All 14 Universes"). The idea of trepidation originated from Surya Siddhanta, in which 360° w as multiplied with 30% to get 108°, which h ad four parts of 2 7° each, in b oth positive and ne gative phases. Some pr ehistoric translator erroneously multiplied this 27° with 30% again and deduced t he maximum value of trepidation to be 8° only, which was current in Greece a nd Europe till 15th century AD, when modern astronomy prove d that material universe d oes not manifest any to and fro o scillation or trepidation of equinoxes at all. But Surya Siddhantic system cannot work without trepidation ( = ayanamsha ), and Indian astrology will die if ayan aamsha is removed. If astrology has any merit at all, it must be based upon Surya Siddhantic system , because this system has a complete and coherent system as well as a complete parallel u niverse of gods who regulate the dest inies of living creatures. Those commentators who confuse Surya Siddhantic planets to be same as material planets observed by astronomers declare this text to be imprecise, and such commentators do not even try to te st the validity of Surya Siddhantic system for astrology based upon Parashara. There are many facets of Surya Siddhantic system which were highly esteemed by ancients but are now regarded t o be false notions,e.g., the idea of trepidation or of Meru as Centre of Cosmos. Therefore, no serious attempt is made to u nderstand the original logic behind such ideas which captured their imagination for millenia. Such exotic ideas are discussed in d etail in subsequent sections, and they prove to be right provided we do not judge them out of context.
Surya Siddhanta gives the locations of several stars other than the lunar nakshatras, which are not the stars of material universe according to proponents of Surya Siddhanta. Later Indian mathematicians and astronomers such as Aryabhatta and Varaha Mihira made references to this text, while later Arabic and Latin translations were very influential in the Mid dle East and Europe.
Dating the Surya Siddhanta : Different Views The '''Surya Siddhanta''' is one of the earliest astronomical treatises of [[India]], but t he form in which it has come to us is generally believe d to date after circa 400. It has rules laid down to determine the true motions of the luminaries, which do not exactly conform to the positions of material objects in the sky. It is not known who wrote the ''Surya Siddhanta'' or when it was first compiled. It is stated in Surya Siddhanta that it was given by the Sun-God to an Asura named Maya in 2163101 BCE. Such a date cannot be accepted by modern scholars,but we do not have definite alternatives. On the basis of concurrence of Surya Siddhantic tropical True Sun with that of modern astronomy, 782 AD is the date for such a concurrence in mean sun, and 908 AD is for true sun. Since Varah Mihir had stated around 550 AD that Surya Siddhanta was the most accurate and prominent of all theories, 800 or 900 AD cannot b e the date of composition of original Surya Siddhanta. It is,therefore, proposed that 1° of error in Surya Siddhantic True Sun may place it around 400 AD. A deferrent epicycle rev olving round an equant is the most important Surya Siddhantic device used f or accurate description of true planets, and it is same as that in Almagest. Hence Surya Siddhanta's date had to be placed subsequent to that of Ptolemy's, so that Indian astronomy could be prove d to be a result of Greek teaching. No detailed ex amination of mathematical systems was undertaken. Eq uations of Surya Siddhantic true planet were a secret, and that was why modern comme ntators could not realize that Surya Siddhantic sysytem was not only internally coherent but was vastly different from that of Almagest in crucial respects also. These peculiarities of Surya Siddhantic system could not have been innov ations, because an internally coherent system cannot evolve as a re sult of haphazard patchworks of borrowings plus improvisations. Hence the causes behind superficial similarities between Surya Siddhanta and Almagest needed to be investigated more thoroughly. Important original facts had to be deliberately forgotten or distorted in order to prov e posterity of Surya Siddhanta with respect to Almagest.Some of these misconceptions are examined here. While declaring that scientific investigation into Surya Siddhantic positions of tropical Sun revealed that it was composed around 800 AD (±400 years if 1° error is assumed),it was not mentioned that other planets do not fit into this scheme. I f sidereal Sun is chosen to be a criterion f or dating, we get a date nearabo ut 2000 AD or 150000 BCE ! Other planets gives v arious dates, showing vast differences. There is no period in h istory when the descrepancy betwee n Surya Siddhantic and scientific values of true positions of all planets fall within tolerable margins. Around 400 to 900 AD,all five planets show differences widely fluctuating bewteen ±12°,which is too much to enable any dating based on this met hod. Hence, this method is highly questionable. But it has been accepted because it neatly fits into the currently belie ved dates for Ved ic and post-Vedic history.
But to accept the result a doubtful method just because it supports a prem ise is tantamount to prove a premise o n the basis of premise itself. The most ancient date for Indian astronomy was 1400 BCE (Colebrooke), which was suppose d to be the date of original observations cited in Ve danga Jyotisha. Rgvedic and Yujurvedic treatises of Vedanga Jyotisha mention that Uttarayana (wi nter solstice) coincided with the s imultaneous entry of Sun and Moon into Dhanishtha in the begin ning of bright half of lunar month of Magha. Beginning of Dhanishtha means sidereal 293°:20', which is eq ual to tropical 316° now-a-days(due to +23° ayanamsha). Around 1400 BCE, sidereal 293 °:20' was equivalent to tropical 270° due to 23°:20' ayanamsha. Since, tropical 270° was tropical Uttarayana,Colebrooke concluded that it was the date when observ ations were originally noted dowmn which were later used in the treatises of Vedanga Jyotisha. To date, all scholars are using this conclusion of Colebrooke as a proven fact, and no one b others to wonder that the beginning of b right half of lunar month of Magha,which is explicitly mentioned as a condition in original texts, was t otally impossible around 1400 BCE from any system of reckoning. A comprehe nsive understanding of Indian astronomy was n ot the objective of these scholars. That is why no moder n commentator even raised the que stion that original equations of Surya Siddhanta need to be re-discovered. They had to prove an Aryan Invasion Theory at any cost,and they proved it at the cost of facts.It was deliberately forgotten that beginning of bright half of lunar month of Magha should c oincide with aforementioned event. Every almanac maker of India k nows that the Kali Age began with Magha, when siddhantic sidereal Mean Sun stood at 360°. Now-a-days, an average of 60 ye ars has shown that Magha starts when siddhantic sidereal Sun stands at 293°(Dhanishtha),which is believed to be Sidereal Uttarayana by Indians. Hence, in 1400 BCE, siddhantic sidereal Sun stood at 338° nearly, and tropical Sun was at 315° when Magha bright half beg an. But tropical Uttarayan needed tropical Sun at 270°. Colebrooke's computations showed a n error of ab out 45° in Sun's longitude, which is not a small error. Colebrooke and his followers, therefore,decided that Indian system of reckoning should not be considered at all. But even with modern system of reckoning, beginning of Magha cannot be proven around 1400 BCE. At the meridians of New Delhi, winter solstice ( tropical Sun at 270°)occurred on 21 Dec,2000 AD at 19:06:51 PM, Julian date 24 51900.067257, when Tithi (= Moon minus Sun, the result divided by 12) was eq ual to 26.08875 scientifically and 26.00450787 siddhantically. Same event of winter solstice took place on Jan 1,1400 BCE at 17:04 PM when Tithi was 20.1136342 6 scientifically and 19.7426117 siddhantically. Difference in scientific and siddhantic Tithis was 0.08424213 in 2 000 AD and 0.3 7102256 in 1 400 BCE. It is a marginal difference compared to the error of 45° in Sun's longitude at the stsrt of Magha found in Colebrooke' s reckoning,which is equivalent to an error of nearly 45. 7 tithis, or of 15.7 tithis if one lunar month is substracted !
The detailed equations of finding lunar m onth in distant eras is discussed in the section "Surya Siddhantic Time-Cycles and Age of Universe". These equations are not very intricate, but have been negle cted by Indian and Western scholars alike for centuries, because they have l ost interest in deciphering the methods of the ancient astronomers. But these equations are essential for
traditional almanacs of India,because observance of many religious rites dem ands an accurate determination of tithis for all manvantaras and yugas ! A careful examination of these equations reveals an organic relationship between the Surya Siddhantic system of reck oning and the general body of Vedic-Puranic tradition, which is helpful in determining the date of composition of Surya Siddhanta as well. When we delve into intricate e quations of Surya Siddhanta, we find that prehistoric astronomers of India had a highly complex and or ganic system of astronomy and mathematics which was forgotten during th e post Christian era, especially during 1500-2000 AD. Commentators like G.Thibaut have described Paitamaha Siddhanta as an underdev eloped system, but there are tangible proofs to the c ontrary,shown in subsequent sections here,which these scholars neglected. During 400-800 AD, Sury Siddhantic and scientic po sitions of planets show differences a mounting upto ±12°. It is inconceivable that errors of 12° went unnoticed by all ancient astronomers ! The reason is different,which is deliberately neglected by all modern commentators. Surya Siddhanta explicitly states that its planets are various incarnations of God and are therefore deities. According to Surya Siddhanta, the whole material universe vanishes during the night of Brahma when Surya Siddhantic Sun(and other planets) continues movin g, otherwise Brahma will not know that His night has elapsed. Hence,Surya Siddhantic planets were believed to b e divine and therefore distinct from material planets. The main purpose of astronomy was predictive a strology in all ancient societies, hence actual position of material bodies in the sky was not a matter of primary concern to most of the ancient Indians. Modern commentators assume Surya Sidd hantic planets to be same as material objects of the sky, and therefore deduce that Surya Siddhanta is an inaccurate text as far as physical astronomy is concerned. No detailed ex amination of the original scheme of Surya Siddhanta was deemed necesasary. But in the light of many new facets of this mysterious text une arthed in a Hindi bo ok (Vinay Jha,2006), dating t he Surya Siddhanta needs a reevaluation. If we fail to find out a definite date, we should state it explicitly and should not enforce a fictious date by deliberately di storting the facts.
Old
and New Versions of Surya Siddhantas
In his famous treatise Panc hsiddhaantika (Five T heories),Varah Mihira concluded that Surya Siddhanta was the most accurate and clear among all theories kn own to him. But in his version of Surya Siddhanta the revolutions of planets during a mahayuga of 432 0000 years (k nown as Yugabhagan) does not tally with the extant version of Surya Siddhanta. This de screpancy induced European scholars to call the Panchsiddhaantic version of Surya Siddhanta as the o ld one, and the extant version as the modern one. T his nomenclature was used by G.Thibaut,the commentator of Panchsiddhaantika. But this decision was made without any scientific investigation into the causes of this descrepancy. The Mahayuga-bhaganmaana (revolutions per 43200000 years) of five planets in old and modern versions of Surya Siddhanta are as follows (Actual SS implies actual Surya Siddhanta which is elaborated in the section "Siddhantic Beej Samskaara"):
Revolutions per Mahayuga (Bhagans) : differences of various system from extant (socalled modern) Suryasiddhanta :
Planets
Suryasiddhanta
Suryasiddhanta
Differences
Differences
Differences
Old
Extant
Old SS
Actual SS
Aryabhatiya
Mercury
17937000
17937060
+60
+12.58
-40
Venus
7022388
7022376
-12
- 9.43
+12
Mars
2296824
2296832
+8
+ 2.6
-8
Jupiter
364220
364220
0
- 6.29
+4
Saturn
146564
146568
+4
+ 9.43
-4
There were three methods of making almanacs (panchangas) : Siddhanta, Tantra,and Karana. In the siddhaantic method, computations were made fro m the beginning of Creation. 499 AD was 1955883600 ye ars after Creation according to Surya Siddhaanta, which was eq ual to 452.7508 Mahayugas. A difference of 60 revolutions during one mahayuga means a difference of 452.75 * 60 = 27165.05 rev olutions since Creation ! Such a difference makes a mockery of e verything. Hence Varah Mihir's figure cannot be related to Siddhaantic methodology,i.e.,reckoning from the beginning of Creation. In the Tantric Method (which has nothing to do with Tantra of religion or philosophy), difference of 60 revolutions during 432000 0 years implies a difference of 18° during 3600 years ,i.e., between the onset of Kali Age and AD 499 , when trep idation or ayanamsha was zero and therefore t he author of Aryabhatiya chose this year for his reference p oint,which was near the time of composition of Aryabhatiya. Varah Mihira is believed to have written his texts ne arlt five decades later. An error of 18° could not be accepted by anyone. Since the mod ern Surya Siddhanta is the basis of a large number of Indian almanacs,being not much remov ed from actual p ositions of material planets as well, it is the O ld Surya Siddhaanta of Varah Mihir which m ust contain errors upto 18° in t he position of planets(+18° for Mercury,-3.6° for Venus,+2.4° for Mars,zero error for Jupiter,and +1.2° for Saturn).
There is a third possibility of Karana Method, in which any neighbouring ye ar is chosen as reference point and Yuga-bhagans are readjusted accordingly in order to facilitate the task of almanac-makers. If the Old Surya Siddhanta had a Karana reference point only a few centuries before Varah Mihira, the error in mean planets will vastly decrease. Hence, it may be argued that the Old Surya Siddhanta quoted by Varah Mihira was actually quoted from not a Sidhhanta b ut a
Karana text. This last possibility is really significant,because it has some rem ote connections with actual Beej-samskaara for AD 499 as shown in the table above. Although Varah Mihira's figures show large errors in magnitude, the sign of differences are n ever reversed. Hence, we m ust conclude that Varah Mihira had access to some almanac making Karana text suppo sedly based upon Surya Siddhanta, which used wrong values of beej-samakaara (See the section 'Siddhantic Beej Samskaara' for further details on Beej-Samskaara, which are esse ntial corrections in mean planets). The figures given by Varah Mihira are certainly related to some lost Surya Siddhantic Karana text, but the values are wrong, which will result in a very faulty almanac for any peri od. For instance, Mercury will show a beej-samskaara of +8°,while its actual beej-samskaara ought to be a little over 6° during the age of Varah Mihira. An error of 12° could not have bee n accepted by anyone. Had Varah Mihira possessed any idea of beej samskaara, he must have elucidated it by differentiating the Siddhantic bhagans(e.g.17937060 for Mercury) from beej samskaara (+12.6 or roughly +13 for Mercury). When he tried t o find out the values of mahayuga-bhagans from some almanac making karana text, he failed to notice that Karana texts c ontain not the Siddhantic bhagans but beej-corrected bhagans(i.e.,corrections already made in the tables for mean planets).Varah Mihir was not an almanac maker, and therefore could not discern this nuan ce of traditional Indian astronomy, which has a lways remained a trade secret of almanac-makers. It is intereasting to note in this respect that all modern Surya Siddhantic almanac makers of India are using tables made in AD 1478 (known as Makaranda Tables), because these almanac makers do not know how to update the t ables, and therefore refuse to accept the views of those who actually know the secret. Hence, it is not surprising that Varah Mihir did not know this closely guarded secret and therefore gave wro ng values in his treatise. No good almanac for any per iod can be made from the values given by Varah Mihira. Hence, it is wrong to label his version as Old Surya Siddhanta, because he did not po ssess any version of Surya Siddhanta at all and merely tried to get something out of karana text which he failed to understand properly. Thibaut was totally in the wrong in proposing manes like Old a nd Modern versions of Surya Siddhanata. He did not try to understand the actual practices of traditional almanac making. The socalled modern Surya Sidhhanta is the only ver sion ever available, a nd whatever Varah Mihir quoted was not from Surya Siddhanta but from a wrong interpretation of some almanac making text supp osedly based upon Surya Siddhanta.(These sentences are being written by a person who is the maker of six governmental and n on-governmental Surya Siddhantic almanacs in different states of India at present. Cf. Vinay Jha,2006). The table of Mahayuga-bhagans shown above also s hows the figures of Aryabhatiya, which apparently seem to be ev en more spurious than those of Varah Mihir,because the figures of Aryabhatiya have signs inverted in the c ase of all planets. The only plausible exp lanation behind such a blunder by Aryabhata is that he substracted b eej corrections instead of adding them to mean planets. Eve n if this view is accepted, t he values viven i n Aryabhatiya will lead to a faulty almanac, containing errors of 6° in the case of Mercury if comparison with Surya Siddhanta are made. Aryabhatiya does not show go od results even if comparison with modern scientific methods are made. Moreover,the sequen ce of corrections made in mean planet to g et true planet is wrong
in Aryabhatiya, which is discussed in the section 'Corrections in Mean Planet to Make True Planet'.In this connection, the section 'Lo st Surya Siddhantic Commentary of Aryabhata : New Lights ' should be viewed as well. Many crucial aspects of Surya Siddhanta have not been t horoughly researched as yet by anyone. For instance, Surya Siddhantic equatorial diameter of Earth is stated to be 800 y ojanas, one yojana equalling 7.972 74625 kilometres. On this basis, the distance from Girivraja (pre historic capital of Magadha) to Mathura comes out to be 98.51 yojanas. In Mahabharata, it is stated that Mathura was 99 yojanas from Girivraja ! This story of Jarasandha of Girivraja is part of the basic story of Mahabharata and cannot be brushed aside as an interpolation. Moreover, only the Surya Siddhantic value of one yojana equalling 7.9 7274625 kilometres satisfies the statement in Mahabharata. During 500-600 AD, Earth's circumference was stated to be 3200 to 3300 yojanas by Aryabhata and Varah Mihira, 6600 yojana by Aryabhata II later, 4867 b y Bhaskaracharya in 11th century and nearly 4 000 by Ganesh of Grahalaghava in AD 1519. The implication is that the author of Mahabharata knew how to compute the d iameter and other aspects of Earth, and possessed an accurate value of pi ! There are,however, some sections in Mahabharata which do not form part of the main story and give s uch values of yojana which are incompatible with Surya Siddhanta. Such portions must be interpolations,because they are not related to the m ain story. Narada Purana gives a detailed exp lanation of mant topics of astronomy,which are in harmony with Surya Siddhantic framework. Intricate equation of determining lunar month od distant age confirms the statement of Bhagvat Gita t hat Margashirsha was the foremost mo nth. Etymologically, it means "at the head of Sun's Path". Another popular ancient name of the m onth of Margashirsha is Agra-hayana, which etymologically means " at the start of Year". Surya Siddhantic month-equation shows that Agrahayana was the first month of Creation. If etymological meanings confirm actual meanings, they must belong to a very early period when language w as itself taking shape and names of months were being worked out. The month-formula which make these computations possible are related to the so-called Metonic Cycle, which was borrowed by Greece from Babylon. But the re lations of Metonic Cycle with prehistoric India whe n month-names were being discovered m akes it clear that Metonic Cycle was known to Indian astronomers in very remote prehistoric ages. The se formulae are d iscussed in the section " S urya Siddhantic TimeCycles and Age of Universe".
Lost
Surya Siddhantic Commentary of Aryabhata : New Lights Aryabhata the Elder is reputed for having written the first known c ommentary of Surya Siddhanta, which had been mentioned by many ancient authorities but is no longer available. The author of Aryabhatiya (of Kusumpur) is wrongly believed by many to be the same as this Surya Siddhantic commentator. But the author of Aryabhatiya does not accept the system of Surya Siddhanta in many crucial fields. For instance, mean motions of planets in Aryabhatiya differ widely from the socalled Old as well as Modern versions of Surya Siddhanta and the values as well as sighs of seed
corrections ( beej samskaara ) in mean m otions also differ widely. Epicycles also show differences, and the sequence of four corrections made in mean planet to get true one in different from that of Surya Siddhanta ; all other theories of ancient India follow the sequence of Surya Siddhanta. Aryabhata's concept of moving Earth also keeps him apart. Hence the original commentator of Surya Siddhanta was a different Aryabhata. Varaha Mihir did not possess e ither a good version of Surya Siddhanta or a good commentary on it. But Aryabhata was a highly respecterd a stronomer and renowned for his commentary up on Surya Siddhanta in ancient India. The Mahasiddhanta of Aryabhata II adheres t o the crucial concepts of Surya Siddhanta but differs in s ome significant details. Hence the commentatator of Surya Siddhanta cannot be identified either with Aryabhata I or with Aryabhata II, but cannot be placed in a lated peri od because he was k nown to ancients. Hence, the commentator of Surya Siddhanta must have existed long before Aryab hata I ( the author of Aryabhatiya). Grahalaghava of Ganesh Daivajna was written around AD 1519, and in it Ganesh says that his mean Mars, Jupiter and Saturn are based upo n those of Aryabhata. Actual computations show that the mean positions of Mars, Jupiter ans Saturn according to Grahalaghava for different periods broadly conform to those of Surya Siddhanta of Makarandacharya (ex cept in the case of Mars, in which Makarandacharya forgot bee j corrections but Aryabhata the Elder di d not err). Mea n motions of Aryabhata I or Aryabhata II do not conform to those of Grahalaghav a. Hence, the author of Grahalaghava was certainly referring to the Surya Siddhantic Aryabhata, whose commentary was extant around AD 151 9. Grahalaghava is among the most popular tre atise from which traditional almanacs are still being made in a large part of I ndia, and the statement of its author carries much weight. G. Thibaut expressed surprise that the Aryabhata enjoyed great fame which cannot be satisfactorily accounted for (G.Thibaut and Sudhakar Dwivedi,Panchasiddhantika, 1888). But he was confusing the famed commentator of Surya Siddhanta with the author of Aryabhatuya who was renounced by many renowned a stronomers, notably Brahmagupta. The commentator of Surya Siddhanta must be placed in an unknown era, well before 500 AD. Al Beruni was right in assuming that the author of Aryabhatiya was a different person than the Aryabhata the Elder (who wrote a commentary of Surya Siddhanta). Al Beruni was merely expressing what he heard, but modern scholars are willing to forget the greatest and most renowned a stronomer of India, mainly because be belonged to t he mainstream of Indian tradition, unlike the author of Aryabhatiya. Proofs of Aryabhata the Elder are provided in the section " Siddhantic Beej Samskaara".
Deduction of Modern Astronomical Constants from Surya Siddhanta Kamlakara Bhatt(author of Siddhant-tattva-viveka,as yet u ntranslated),an ardent supporter of Surya Siddhanta and an opponent of Bhaskara II,had strongly advocated in 16th century that Surya Siddhantic planets are to be distinguished from the matererial planets. In the b eginning of 20th century,terms like Drik-paksha and Saur-paksha came into vog ue in India, to distinguish planets and phenomena of Sensory World fr om that of Surya Siddhanta. Drik-paksha meant the
world perceived by means of sense organs, and therefore it denoted the foeld of modern astronomy, while Saurpaksha denoted the gods of Next World bearing same name as thematerial planets but being non-material. Ketaki system of almanac used these concepts in actual practice. But the Surya Siddhantic viewpoint of Drikpaksha was never elaborated by a nyone.Unfortunately, after the disappearance of the Surya Siddhantic commentary of Aryabhata the Elder, even the Saurpakshiya mathematics became obscure, and all the comme ntators kept on repeating hackneyed phrases whose practical significance was clear to none. Ranganath,Kamlakar Bhat,Sudhakar Dwivedi, Kapileshwar Shashtri, etc wrote voluminous commentories on Surya Siddhanta, elucidating everything except the practical ways of using the f ormulas and the Merucentric geometrics. Let us examine some orally transmitted occult theorems of Surya Siddhantic school which show that Drikpaksha can be deduced from Saurpaksha mathematically, without the aid of any observatory(Vinay Jha,2006).
Theorem
of Drikpakshiya Siderea l Year
Saurpakshiya eccentricity of Sun's elliptic orbit round the centre of Cosmos(meru) is exactly equal to 1/60,although saurpakshiya equation of centre req uires an equant,which will be elaborated in the section 'The True Places of Surya Siddhantic Planets'. Let us denote 1/ 60 by . Then, Ys' = [1/(^2 * ^2)] + [(1/2)(1+^2)] = (3600 / ^2) + 0.5 + (1/7200) = 365.256400001304866086855 days This is the limiting value of scientific sidereal year. The Vedic (i.e.,Surya Siddhantic) theorem of scientific Tropical Year Yt (=365.24219878125) will be de monstrated later,let us first get the value of mean sidereal year with the help of following equation : Ys = (Ys'+1) / (1+ (1/Yt)) = 366.256400001304866086855 / (1+ (1/365.24219878125)) = 365.2563612258166724169 days
Now we can get the Period of Precession PP : PP = Yt / ( Ys - Yt ) = 25789.4883232765701616 years This mean value needs two complex correction which are too intricate to be s hown here. Let us deduce the value of scientific Tropical Year first.We will not explain all the intermediate terms here, which can be easily recognised by students of modern astronomy. Let sidereal lunar month be equal to : Mss = 27. 321660641391789747802454274321 days, which will be proven later. Then, synodic month Ms will be : Ms = Ys / [ (Ys / Mss) -1 ] = 29.53058780664716371374 days. Metonic Year Ym is equal to : Ym = 235 Ms / 19 = 365.246743924320182775185653635 days. PPM1 = 1 / [(Ys / Ym)-1] = 37978.09022183997109169737 years. PPS1 = 1/[(1/PP ) - (1/PPM1 )] = 80356.674413324332490977057144470 years. PPS2 = 1/[Ys * (1/Yt ) - (1/Ym )] = 80356.674413324332490977057250561 years. A1 = PPS1 / PPM1 = 2.1158692799964388041303958720096.
A2 = PPS2 / PPM1 = 2.1158692799964388041303958748028. PPS1 + A1 = 80358.790282604328929781187540342 PPS = 80358.790282604328929781187540342 PPS1 + A1 = 80358.790282604328929781187540342 There are three e quations for obtaining scientific Tropical Year : Yt.1 = Ym / [ 1 + { 1 / ( PPS1 + A1 )}] = 365.24219878124999999999999999999638527125 Yt.2 = Ym / PPS = 365.24219878124999999999999999999638595267 Yt.3 = Ym / [ 1 + { 1 / ( PPS2 + A2 )}] = 365.2421987812499 99999999999999999999997234 9 Drikpakshiya Tropical Year is the most precise constant known to mod ern astronomy,whose empirical value is 365.24219878125 ± 0.00000000058 days.
Vedic (ie, Suryasiddhantic)
Theorem
of Lunar month.
M1 = 365.2564000013 04866086855 / (42/ ) = 27.321114831446531255 657 K1 = M1 / ( Mss - M1 ) = 50056.095658915529 K2 = 42000(Ys-Yt) = 594.8226718002415 Now raise (Ys/360) to the power (1/K2): Z1 = (Ys/360)^(1/K2) = 1.014601^(1/594.82267) = 1.000024369635568 degrees. K3 = 1-[(180/) * {(Sin(Z1+1)-Sin(Z1)}] = 1-[ 57.296*{(Sin(2.0000243696355 68)-Sin(1.000024369635568)}] = 0.0003553741530559558546620855628939 K4 = K3 * 1000000 = 355.3741530559558546620855628939 K5 = 1+(1/K1) Now we get the value of Drikpaks hiya synodical or lunar month : Ms = [(K4 / K5)-1}/12 = 29.53058780664716371373841555 days. Sidereal lunar month will be : Mss = Ys / [(Ys/Ms)+1] = 27.321660641391789747802454274321
Now we show some more intricate Vedic (Suryasiddhantic) theorems. First of all, let us see :
Lunar
Binomia l Theorem:
A1 = 12/(K4-1) = 1 / 29.5311794213296538 A2 = Ys / 365.256400001304866086855 A = A1 * A2 * (42/) = 0.45270842758190827172 Ax2 + x - Ys = 0
Roots of this binomial are : M1 = [-1 + Sqr(1-(4A*Ys)] / 2A = -29.5305886713712313156 days. M2 = [-1 - Sqr(1-(4A*Ys)] / 2A = +27.3216613815891770963 days. M2 - Mss = 0.063953054266910187950698752 seconds. This apparent 'error' is equivalent to the error of 104.64 3228673117 years in 4.174 8 billion years ( = 14 manavantara of 71 mahayugas each, each Drikpakshiya mahayuga being of 4.2 million years).This is the value of Drikpakshiya correction in Kalpa-Mandochcha, for which Bhaskaracharya deduced the v alue 93 in Siddhantashiromani an d stated Kalpa-Mandochcha to be equal to 48 0 (= Saurpakshiya Kalpa Mandochcha 387 + 93 Drikpakshiya correction).
Surya Siddhanta states Saurpakshiya period of precession to be of 24000 years exactly, while modern value is near the Drikpakshiya value of PP deduced above ( = 25789.4883233 years). Let us see its logic. 1/K' = (1/24000) - (1/25789.4883233) = 1/ 345879.71975438125 Mt = Mss - (Mss/K') = 27.32158164959469683453 days. This constant Mt is the modern value of tropical sidereal lunar month !
Surya Siddhantic Theory of the Rotation of Material Universe According to modern physical science, material universe cannot be said to be rotating even if it rotates, because all space-time-continuum is intrinsically related to matter as part of a unified whole, and there can be n o space or time outside the realm of matter. Since there is no space or time outside material universe, rotation of this material universe cannot be me asured because there is no e xternal space-time. Let us call the sp ace of time of t his material universe as material-space and material-time. There are 14 universe s (Bhuvanas) in the Multiverse (= Creation or Srishti), and we live i n the middle universe. Since all forms of matter have shown to be associated with SPIN, from galactic to subatomic levels, it is natural that the material universe should also r otate. But it can be measured only with reference to the non-material universe or Bhuvaloka, which is the world of Saurapakshiya Suryasiddhanta. Suryasiddhanta states our universe to be finite, and according to Godel's theorem a finite system cannot be fully ex plained on account of its internal properties and phenomena only. There m ust be something outside this finite universe which should exp lain the workings of this universe and its raison-de-etre. Now we show the Vedi c theorem of Rotation of the Material Universe. Surya Siddantic Kalpa is equal to 4.32 billion years. The Creator (Brahma) took 4 7400 divine yuears to create the Creation, which is equal to 4 7400 * 36 0 human years. Hen ce the total Age of Creation = 4.32 billion (47400 * 360) = 4302936000 years.
4302936000 / 24000 = 179289 is the extra years d ue to Saurpakshiya precession. Hence total number of Saurpakshiya tropical years in one creation is equal to 4302936000 + 179289 = 4303115289 ye ars. Divide this number with (Saurvarsh / Chandravarsh) = (Saurpakshiya Sidereal Year / Twelve Saurpakshiya synodical months) = 365.258756481481481 / (12*29.53058794607) = 1.0307356481481. The result is 4174800101.976788423. In it, 4174800000 is the duration of Drikpakshiya Creation ( = 4200000*71*14), and 101.976 788423 is t he exact v alueof Drikpakshiya correction in KalpaMandochcha, for which we had got a crude value 104.643228673117 above, and Bhaskaracharya had got 93. A quantity of 101.976788423 years in 4.1748 billion years is equal to 0.107065 hours in 500 years. Nirmal Chandr Lahiri was the secretary of Panchanga Reform Committee of Government of India. He analysed the differencebetwee n Drikpakshiya and Saurpakshiya tithi (elongation of moon), and found a difference of 0.11 hours in 500 years,which he assumed t o be due t o error in Surya Siddhantic values(NC Lahiri,1968,p.90). But Surya Siddhantic values do not belong to this physical Universe. This apparent error of 0.107065 h ours in 500 years is a result of extra 102 rotations of the Drikpakshiya solar orbit d uring one Creation : Saurpakshiya value is 387 w hile Drikpakshiya value is 489 (Bhaskaracharya-II gave 48 0 only in Siddhantashiromani). This Drikpakshiya rotation of solar ellipse is in addition to the normal Drikpakshiya rotation per 136 000 years which is the cause behind anomalistic year. ---------²² In the same book NC Lahiri gives data of Surya Siddhantic beej corrections applied to lunar anomaly in comparison to modern scientific values, which shows that beej correction nee ded in lunar anomaly in order to get siddhantic tithi from scientific tithi increases at a rate of one revolution in 42000 years(NC Lahiri,1968,p.90). Difference between mod ern scientific tropical Sun and siddhantic Sun also show 360° change during 42000 years. Sun and moon do not move in same orbits. Hence we must conclude that the physical Universe itself is revolving at the rate of one revolution per 4 2000 years round some point v ery near to Earth's centre,which suggests that the centre of Universe i s not far from Earth's centre. Before dealing with this centre (Meru or Mt Kenya in Africa),let us first elucidate the 42000 year cycle of the Sun. Siddhantic sidereal year (365.258756481481)and Drikpakshiya tropical year(365.24219878125) differ at the rate of one revolution or one year i n 22059.75174 years. But in reality both div urge from each other at the rate of one re volution in 42000 years. For instance,Kaliyuga commen ced at Ujjain midnight 17-18 Feb,3102 BCE,when siddhantic nirayan(=sidereal in Indian system) Mean Sun was at zero longitude. 5106 ye ars later siddhantic zero Sun was to be fou nd on 16 Apr,2005 at 5:03:15 AM (Ujjain). If mean Sun differs by 44.2106 days in 5106 years(taking into account 13 days of Gregorian reform), it should differ by one year in 4 2182.8 years. Due to non-linearity of elliptical paths,we get here 42182.8, the ex act figure is an integer 42000. It raises a question : if mathematically siddhantic year and scientific year should show a difference of one r evolution in 22059 years, why do they differ by one rev olution in 42000 years in reality ? Where doe s 19941.24826 years come from ? We have here compared sidereal siddhantic year with tropical scientific year, hence this extra difference of 19941 y ears must be related to precession.
Siddhantic period of precession is 24000 ye ars and scientific period is 25789.488323 3 years. Both form cycles of 100000 ± 12 000 years with respect to 19941 in h armonic series. Thus, we are now getting close to constants of Milankowitz,just by means of analysing Surya Siddhantic constants ! The Vedic value for Drikpakshiya period of pre cession is 25789.4883233 year s. But it needs slight modifications due to long term cycles.We had g ot 101.976788423 years p er Drikpakshiya Creation for the exact value of Drikpakshiya correction in Kalpa-Mandochcha, which is equal to 101.976788423/4174800000 per year. Add this correction to 1/257898.488, we get 1/25773.252377 in the harmonic series. Again add 1/(4200000*71) to it and get 1/25771.025002. (4200000*71) is the duration of one Drikpakshiya Manvantara. A period of 25771.025 years is equal to 50.28903584 seconds of arc per sidereal year, or 50.288160017 seconds per Julian Year. Presently, 50.28796195 seconds per Julian Year is the accepted value.
Ancient Cosmogony and Geography Surya Siddhantic system is neither heliocentric nor geocentric. It clearly states in Bhoogoladhyaya that Mt Meru resides at the centre (equator) of gl obe in the region of Zamboodweep. In Africa, Mt Kenya is situated upon equator in a region where many modern place names are reminiscent of Surya Siddhanta : Meru town near Mt Kenya, another Mt Meru slightly southwards, a place named kinyan-giri which means Mt Kinyan or Mt Kenya in sanskrit, river Zamboonadi > *zamboodi > *zambedi > *zambe zi, Mu-zambique, Zambia, Zimb-abwe, Gabon (< *Zambo on), Congo (< *Gongo < *zambo),etc. Homo genus of mankind is known to have evolved in that region around 4 million years ago. Indian Puranic ttreadition also mention that modern races of mankind evolved near Meru in 389 1194 BCE when the present Mahayuga commen ced. Surya Siddhantic formulae of making true planets from mean one s require the use of distance from Earth's centre to a p oint in space 28.913 kilometres above the top of Mt Meru (Mt Kenya), which was believed t o be centre of all universes by puranic authors. Surya Siddhantic universe is much smaller in comparison to material universe, and Sun's distance from Earth is only 86 1.7 times of Earth's equat orial radius. Material Sun's distance is 23455 times of Earth's equatorial radius ! Ptolemy used a figure 1 210, which is not much re moved from Surya Siddhantic figure. Ptolemic system is well kn own, but Surya Siddhantic system is rather obscure, known to a few initiated brahmanas only. Due to lack of kn owledge of orally transmitted and unpublished portions of original Surya Siddhanta, Europea n commentators believe t hat Surya Siddhantic system was influenced by Ptolemy's Almagest. But those who know the secrets of Surya Siddhanta say that its framework is too complex a nd organically self-contrained to have been influenced by any other system. For instance, Surya Siddhantic daily motions of all planets are exactly equal to a constant, but this rule is not followed in Almagest. Surya Siddhantic system is based upon a cosmic centre at Meru, wh ich is absent in Almagest. Surya Siddhantic solar epicycle is equal to 14 yojanas per degree, which is equal to 5040 yojanas for 360 degrees. Its diameter is 1604.3 yojanas, which is 4.3 yojanas more than Earth's equatorial diameter. 4.3 yojanas equals 5.199 kilometres ( height of Mt Meru or Mt Kenya)plus 28.913 kilometres. Solar
epicycle equals to 14 y ojanas, which gets reduced to 13:40 at perigee of this elliptical epicycle, which when divided by 2 gives 2:10:31 degrees, which is the maximum value of equation of centre (mandaphala = difference between mean and true Sun) for Sun. Surya Siddhantic theory, therefore relates yojana to degrees in an intrinsic manner, which makes it clear that it was not borrowed from Almagest. Earth's diameter is an integer 1600 y ojana. Moon's diameter is also an integer 436 yojanas. These rations are per fectly scientific. Such integral values seem to be mysterious when they are confirmed with moder n science. This value of yojana was not only prehistoric, manifest in the story of J arasandha's 99 yojanas cited above, but was also intrinsically related to many native concepts of Surya Siddhanta, discussed in other se ctions of this article. ---------²² ( Untranslated / unfinished Sections : )
Surya Siddhantic Time-Cyc les and Age of Universe The
Mean Motions of the Planets
The True
Places of Surya Siddhantic Planets
Mandaphala Equations (Equation of Centre) Shigraphala Equations Three
Questions : Direction, Place and Time
Eclipse of the Sun Eclipse of the Moon Projection of Eclipses Planetary Conjunctions and Stars Certain Malignant Aspects of the Sun and Moon Sunrise and Sunset Risings and Settings of Planets The
Moon's Risings and Settings
Trigonometry
of Surya Siddhanta
The
''Surya Siddhanta'' contains the roots of modern trigonometry
The
Gnomon and Eight Axia l Regions
Rectification of Epicyc loida l curves in Surya Siddhanta Limits
of Space and Time : inferences from Suryasiddhanta One might wonder at cycles of 42000 and 4200000 years and of their multiples of 71 mahayugas and 14 manvantaras as shown ab ove. Saurapakshiya Suryasiddhanta speaks of a mahayug a of 4320000 years, but Drikpakshiya Suryasiddhanta wor ks with a lesser figure of 4200000 ye ars only, which has 100 equal parts of 42 000 years each. Saurapakshiya Suryasiddhanta has no 42000 year cycles. We shall deal with 42000 year cycle later, which gave rise to the socalled Julian Calendar which is not Julian because it arose in Egypt in 471 3 BCE according to current beliefs. First, let me elaborate the special significance of the number 42 a nd logarithmic scale based on 10 in basic processes of Nature. There are 14 universes (Bhuvanas) according to Vedic-Puranic tradition, and our material (physical) Universe is at the middle level. We can se e 7 universes at a time in a ny one direction, but not all 14 simultaneously. According to Suryasiddhanta 1955885109 years hav e elapsed (in 2009 AD) since the beginning of Creation. When we see seven universes arranged one after another, we see into (19 55885109 * 7 =) 13 691 million years of TIME, and into 13691 million light-years of SPACE. Currently, scientists believe the extent of Universe to be of 1 3.7 billion light years. Divide 13.7 billion years with 10^42 (10 raised to the power 42, or 42 zer oes after 1). 13.7 billion years = (13,691,195,763 ye ars) * (31558149.61 seconds per year) = 4.320 688 * {10^17} seconds This is the largest QUANTUM of TIME. Dividing it with 10^42, we get [1 second / ( 2.3 * {10^24}) ] = 0.432 * {10^-24} seconds The time required f or strong nuclear interactions is { 10^-24} seconds. Quarks r equire slightly lesser time to combine for forming nucleons. This tim e is 0.432-688042 * {10^-24} seconds exactly, not exactly known to scientists but very near their estimates. It is the smallest QUANTUM of TIME. Now, let us compute the smallest QUANTUM of SPACE.
13.7 billion light years = ( 4.320688 * {10^17} second ) * (299797458 metres per second speed of light) = 1.295331 2 * {10^26 } metres. This is the largest Q UANTUM of SPACE. Now, divide it with {10^42}, we get 1.3 * {10^16} metres. It is the ex act dimension of the smallest QUANTUM of SPACE. Atomic radii of some atoms are as follows (in units of pm or picometres, 1 pm = 10^-12 metres)
Hydrogen = 46 Carbon = 71(graphite) to 77 (diamond) Nitrogen = 71 Boron = 88 Fluorine = 60 Chlorine = 91 Oxygen = 68 Only these seven e lements have atomic radii below 10 0 pm. All the rest have radii ranging from 106 (Sulphur) to 262 (Caesium). Some exa mples are : Sulphur = 106 Silicon = 118 Iron = 123 Copper = 128 Tin = 140 Gold = 144 Silver = 144 Lead = 174 Uranium =138
The ratio of smallest and largest atoms is 262 / 46 = 5.7 times in radius or 185 times in volume, which is roughly equal to the ratios of atomic weights on the a verage. Let us, however, assume the average at omic radius to be around 130 pm for the sake of simplicity. It can be written as 1.3 * {10^10} me tres. It is one million times bi gger than smallest QUANTUM of SPACE. Scientists tell us that the nucleus is 100000 times smaller than the atom in radi us. Hence, the smallest QUANTUM of SPACE is ten times smaller than the r adius of nucleus, or in volume the smallest QUANTUM of SPACE is 1000 times smaller than the average nucleus. This smallest QUANTUM of SPACE is the volume of a quark, not exactly known to modern scientists but near their estimates. Many scientists have already wondered at these ratios of large st and smallest quanta of space and time, but they do not know the exact dimensions. Suryasiddhanta helps us in getting the ex act dimensions. As the both sets of 7 universes are ageing with the passage of time, its extent in space is increasing which gives rise to the apparent phenomena of Expanding Universe and socalled Big Bang.
Many similar computations have been arrived at by advocates of Superstring Theory. Some scientists belittle these phenomena as mere coincidences, but such coincidences are too many to ignore. Here, I am giving another such example. In a previous article, I had ded uced the Limiting Sidereal Year from the value of 'pi' , equal to 365.2564000013048660868549564850172389 days.
Tropical year is equal to 365.24219878125 days. In 25719.07183820440572684682960747 years, both years again coincide with each other. It is a basi c cinstant of Nature. Since there are 14 universes in the Multiverse (=Creation), divide this number with 14 to get an other basic constant of Nature : 1837.0765598717432662033449719622 , which is the weight of most abundant and smallest atom in the material universe in terms of electron masses. substract '1' from it, you get the proton : electron mass ratio of 1836.07 6559871743266203344971962 2 . It is an exact quantity, independent of Heisenberg's Principle of Uncertainty. Principle of Uncertainty works under certain connditions, and has nothing to do with these fundamental constants and ratios of Nature. But Vedic tradition forbids us to unravel the mystery of Nature, it is regarded SINFUL. Our aim ought to Know Ourselves and improve our Karmas in order to get rid of the e ndless cycles of rebirths. among all scientific disciplines, Jyotisha is the only discipline which helps in this direction. In this context, it should be mentioned that 42 protons make the most stable atom by dint of having the highest number of stable i sotopes, and 84 is the lowest proton number w hich does not have a single stable isotope.
Earth is N OT situated centra lly, the centra l point is Divine Meru. Suryasiddhanta once says square root of 10 is value of 'pi', but root of 10 is merely a crude v alue of 'pi' for teaching students and should never be used for any serious purpo se. Any siddhanta must never abuse the basic laws of mathematics. The value of 'pi' is 3.14159265««., and n ot root of 10. In Vedic mathematics, there were formulae for computing 'pi' with 12 or 32 digit accuracy. Fot 12 digits, 'pi' = SQRT {2* (18000^2) / (6565 6565 - OCTAL 666)} ; Octal 666 is nu mber for Satan in Biblical mathematics and is therefore substracted. Earth's equatorial circumference is 1600 * 'pi' = 5026 .5482457« yojanas, whereas Manda-paridhi of sun is 5040 yojanas (5039.990052). One degree (amsha0 of manda paridhi is sun's paridhyamsha (= paridhi + amsha) = 5040 / 360 = 14 yojanas (13.9999723667) per degree. The diameter of manda-paridhi is 5040/pi = 1604.27865 9816 yojanas or 34.112669 km s, which is the distance of the centre of Manda-paridhi from Earth's equatorial surface. it is equal to the height of Mt Meru (Mt Kenya = 5.199 Kms) and a mysterious term equ al to 28.913669002241621530835902160508 Kms. It is equal to sum of four components :
d1 = R * sin(180 degrees / 42000) = 28.6231184335656015« Kms d2 = R * sin(180 degrees / 4200000) = 0.2862311846025405641566« Kms d3 = R * sin(180 degrees / [4200000 * 71]) = 0.004031425135247426«. Kms d4 = R * sin(180 degrees / [4200000 * 71 * 14 ]) = 0.000287958938 Kms The actual centra of all universes is 28.91366 90022416215308359 02160508Kms higher than the tip of terrestrial Mt Meru (Mt Kenya) and is Divine Mt Meru.
Why
the Dripakshiya Mahayuga has 4200000 years, as compared to the Saurapakshiya va lue of 4320000 years? The duration of one Saurapakshiya Creation (Srishti) is 47400 d ivine years less than one Kalpa of 4.32 billion years. Hence, Srishti = 4302936000 years. Add its 2400 0th part (=179289) to it to make Saurapakshiya "tropical" years, and divide the res ultant with the ratio of Suryasiddhantic solar year (365.258756 481481481481« days) and lunar year ( 12 * 29.53058794 607 days), this ratio is equal to 1.0307356481481481481481«, you will get a number which is greater than Drikpakshiya-Kalpa (= 4200000 * 71 * 14 ) by a samall margin of 101.9767884 years. An excess of 101.9767884 years in 4.1748 billion years means an excess of 0.107065 hours in 500 years. Late NC Lahiri found same difference (0.11 hours in 5 00 years) in Siddhantic Tithi with Tithi computed on the basis of physical astronomy ( cf. page 90 in 'Advance ephemeris' by NV Lahiri).
first component of Mi lankovitch cyc les or ayana cha lanam is not a single motion but a combination of two motions : The
(a) anomalistic precession (due to rotation of elliptical orbit of Sun) and (b) orbital precession ( sampat chalanam = precession of equinoxe s, ie, precession of c ontact points of ecliptic and equatorial planes).
Such motions are explained by classical and relativistic mechanics. Even atomic orbits display similar motions. The very fact that "the first component of Milank ovitch cycles" controls long term climatic cycles most profoundly makes it clear that the spatial orientation of Solar Orbit with respect to fixed stars is important and tropical astrology is bogus.
Details of the 42000 year cyc le and its consequences on human destiny may be pub lished on demand. But do not try to unrave l the mystery of Mother Nature, it is sinfu l in Vedic tradition, and a lways kept a secret. Notes :
Fllowing Australian website contains materials copied perhaps by some Australian from the Wikipedian article Surya Siddhanta where it was deleted by a German Eurocentrist residing in Switzerland (most of the matter were plagiarised from my work (published in Hindi) without informing or acknowledging me ; the latter portion of information in following site is from another source which is Western): http://www.nationmaster.com/encyclopedia/Surya-Siddhanta
