Dating the Surya Siddhanta : Different Views

The ”’Surya Siddhanta”’ is one of the earliest astronomical treatises of [[India]], but the form in which it has come to us is generally believed 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 be 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 revolving round an equant is the most important Surya Siddhantic device used for 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 proved to be a result of Greek teaching. No detailed examination of mathematical systems was undertaken. Equations of Surya Siddhantic true planet were a secret, and that was why modern commentators 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 innovations, because an internally coherent system cannot evolve as a result 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 prove 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. If sidereal Sun is chosen to be a criterion for dating, we get a date nearabout 2000 AD or 150000 BCE ! Other planets gives various dates, showing vast differences. There is no period in history when the descrepancy between 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 method. Hence, this method is highly questionable. But it has been accepted because it neatly fits into the currently believed dates for Vedic and post-Vedic history. But to accept the result a doubtful method just because it supports a premise is tantamount to prove a premise on the basis of premise itself.

The most ancient date for Indian astronomy was 1400 BCE (Colebrooke), which was supposed to be the date of original observations cited in Vedanga Jyotisha. Rgvedic and Yujurvedic treatises of Vedanga Jyotisha mention that Uttarayana (winter solstice) coincided with the simultaneous entry of Sun and Moon into Dhanishtha in the beginning of bright half of lunar month of Magha. Beginning of Dhanishtha means sidereal 293°:20′, which is equal 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 observations 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 bothers to wonder that the beginning of bright half of lunar month of Magha,which is explicitly mentioned as a condition in original texts, was totally impossible around 1400 BCE from any system of reckoning. A comprehensive understanding of Indian astronomy was not the objective of these scholars. That is why no modern commentator even raised the question 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 coincide with aforementioned event.

Every almanac maker of India knows that the Kali Age began with Magha, when siddhantic sidereal Mean Sun stood at 360°. Now-a-days, an average of 60 years 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 began. But tropical Uttarayan needed tropical Sun at 270°. Colebrooke’s computations showed an error of about 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 2451900.067257, when Tithi *smile emoticon* Moon minus Sun, the result divided by 12) was equal 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 20.11363426 scientifically and 19.7426117 siddhantically. Difference in scientific and siddhantic Tithis was 0.08424213 in 2000 AD and 0.37102256 in 1400 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 month 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 neglected by Indian and Western scholars alike for centuries, because they have lost 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 demands 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 reckoning 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 equations of Surya Siddhanta, we find that pre-historic astronomers of India had a highly complex and organic system of astronomy and mathematics which was forgotten during the post Christian era, especially during 1500-2000 AD. Commentators like G.Thibaut have described Paitamaha Siddhanta as an underdeveloped system, but there are tangible proofs to the contrary,shown in subsequent sections here,which these scholars neglected.

During 400-800 AD, Sury Siddhantic and scientic positions of planets show differences amounting 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 moving, otherwise Brahma will not know that His night has elapsed. Hence,Surya Siddhantic planets were believed to be divine and therefore distinct from material planets. The main purpose of astronomy was predictive astrology 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 Siddhantic 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 examination of the original scheme of Surya Siddhanta was deemed necesasary. But in the light of many new facets of this mysterious text unearthed in a Hindi book (Vinay Jha,2006), dating the 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 distorting the facts.

So-called Old and New Versions of Surya Siddhantas

In his famous treatise Panchsiddhaantika (Five Theories),Varah Mihira concluded that Surya Siddhanta was the most accurate and clear among all theories known to him. But in his version of Surya Siddhanta the revolutions of planets during a mahayuga of 4320000 years (known as Yuga-bhagan) does not tally with the extant version of Surya Siddhanta. This descrepancy induced European scholars to call the Panchsiddhaantic version of Surya Siddhanta as the old one, and the extant version as the modern one. This 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 (so-called modern) Suryasiddhaanta :

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 from the beginning of Creation. 499 AD was 1955883600 years after Creation according to Surya Siddhaanta, which was equal to 452.7508 Mahayugas. A difference of 60 revolutions during one mahayuga means a difference of 452.75 * 60 = 27165.05 revolutions since Creation ! Such a difference makes a mockery of everything. 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 4320000 years implies a difference of 18° during 3600 years ,i.e., between the onset of Kali Age and AD 499 , when trepidation or ayanamsha was zero and therefore the author of Aryabhatiya chose this year for his reference point,which was near the time of composition of Aryabhatiya. Varah Mihira is believed to have written his texts nearlt five decades later. An error of 18° could not be accepted by anyone. Since the modern Surya Siddhanta is the basis of a large number of Indian almanacs,being not much removed from actual positions of material planets as well, it is the Old Surya Siddhaanta of Varah Mihir which must contain errors upto 18° in the 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 year 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 but a Karana text. This last possibility is really significant,because it has some remote 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 never reversed. Hence, we must conclude that Varah Mihira had access to some almanac making Karana text supposedly 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 essential 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 period. 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 been 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 to find out the values of mahayuga-bhagans from some almanac making karana text, he failed to notice that Karana texts contain 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 nuance of traditional Indian astronomy, which has always 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 tables, 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 wrong values in his treatise. No good almanac for any period 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 possess 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 and 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 version ever available, and whatever Varah Mihir quoted was not from Surya Siddhanta but from a wrong interpretation of some almanac making text supposedly based upon Surya Siddhanta.(These sentences are being written by a person who is the maker of six governmental and non-governmental Surya Siddhantic almanacs in different states of India at present. Cf. Vinay Jha,2006).

The table of Mahayuga-bhagans shown above also shows the figures of Aryabhatiya, which apparently seem to be even more spurious than those of Varah Mihir,because the figures of Aryabhatiya have signs inverted in the case of all planets. The only plausible explanation behind such a blunder by Aryabhata is that he substracted beej corrections instead of adding them to mean planets. Even if this view is accepted, the values viven in 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 good results even if comparison with modern scientific methods are made. Moreover,the sequence of corrections made in mean planet to get 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 ‘Lost Surya Siddhantic Commentary of Aryabhata : New Lights ‘ should be viewed as well.

Many crucial aspects of Surya Siddhanta have not been thoroughly researched as yet by anyone. For instance, Surya Siddhantic equatorial radius of Earth is stated to be 800 yojanas, one yojana equalling 7.97274625 kilometres. On this basis, the distance from Girivraja (prehistoric 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 7.97274625 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 by Bhaskaracharya in 11th century and nearly 4000 by Ganesh of Grahalaghava in AD 1519. The implication is that the author of Mahabharata knew how to compute the diameter 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 such values of yojana which are incompatible with Surya Siddhanta. Such portions must be interpolations,because they are not related to the main story. Narada Purana gives a detailed explanation 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 that Margashirsha was the foremost month. Etymologically, it means “at the head of Sun’s Path”. Another popular ancient name of the month 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 was 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 relations of Metonic Cycle with prehistoric India when month-names were being discovered makes it clear that Metonic Cycle was known to Indian astronomers in very remote prehistoric ages. These formulae are discussed in the section ” Surya Siddhantic Time-Cycles and Age of Universe”.

Lost Surya Siddhantic Commentary of Aryabhata : New Lights

Aryabhata the Elder is reputed for having written the first known commentary of Surya Siddhanta, which had been mentioned by many ancient authorities but is no longer available. The author of Aryabhatiya (of Kusumpur) is believed by many to be the same as this Surya Siddhantic commentator. The author of Aryabhatiya does not seem to 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 motions 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 according to some. Varaha Mihir did not clarify a major part of Surya Siddhanta or parts of Panchsiddhantika are lost. But Aryabhata was a highly respected astronomer and renowned for his commentary upon Surya Siddhanta in ancient India. The Mahasiddhanta of Aryabhata II adheres to the crucial concepts of Surya Siddhanta but differs in some 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 later period because he was known to ancients. Hence, the commentator of Surya Siddhanta must have existed long before Aryabhata I ( the author of Aryabhatiya) : this is the view of Al Beruni and some others. But careful examination of Aryabhatiya proves thatit is merely an Audiyika version of Ardharaatrika Suryasiddhanta, but details of this intricate Karana techniques cannot explained here due to its intricacy and details.

Grahalaghava of Ganesh Daivajna was written around AD 1519, and in it Ganesh says that his mean Mars, Jupiter and Saturn are based upon 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 (except in the case of Mars, in which Makarandacharya forgot beej corrections but Aryabhata the Elder did not err). Mean motions of Aryabhata I or Aryabhata II do not conform to those of Grahalaghava. Hence, the author of Grahalaghava was certainly referring to the Surya Siddhantic Aryabhata, whose commentary was extant around AD 1519. Grahalaghava is among the most popular treatise from which traditional almanacs are still being made in a large part of India, and the statement of its author carries much weight.

Deduction of Modern Astronomical Constants from Surya Siddhanta

Kamlakara Bhatt(author of Siddhant-tattva-viveka,as yet untranslated),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 material planets. In the beginning of 20th century,terms like Drik-paksha and Saur-paksha came into vogue in India, to distinguish planets and phenomena of Sensory World from that of Surya Siddhanta. Drik-paksha meant the world perceived by means of sense organs, and therefore it denoted the field of modern astronomy, while Saurpaksha denoted the gods of Next World bearing same name as the material 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 anyone.Unfortunately, after the disappearance of the Surya Siddhantic commentary of Aryabhata the Elder, even the Saurpakshiya mathematics became obscure, and all the commentators kept on repeating hackneyed phrases whose practical significance was clear to none. Ranganath, Kamlakar Bhat, Sudhakar Dwivedi, Kapileshwar Shashtri, etc wrote voluminous commentries on Surya Siddhanta, elucidating everything except the practical ways of using the formulas 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).

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Theorem of Drikpakshiya Sidereal and Tropical Years and of Precessional Period

Saurpakshiya eccentricity of Sun’s elliptic orbit round the centre of Cosmos (Mt Meru) is exactly equal to 1/60 *smile emoticon* ε),although saurpakshiya equation of centre requires an equant,which will be elaborated in the section ‘The True Places of Surya Siddhantic Planets’. Let us denote 1/60 by ε and ‘pi’ by π . Then,

(1)

Ys′=[1π2∗ε2+12(1+ε2)]=[3600π2+0.5+17200]=365.25640000130486608685495644391days

This is the limiting value of scientific sidereal year by means of Vedic (i.e.,Surya Siddhantic) equation. The Vedic (i.e.,Surya Siddhantic) theorem of scientific Tropical Year Yt (=365.24219878125) will be demonstrated later, let us first get the value of mean sidereal year with the help of following equation :

(2)

Ys=(Ys′+1)(1+1Yt)=366.2564000013048660868551+1365.24219878125=365.25636122581667241689259003252668days

Now we can get the Period of Precession PP :

(3)

PP=Yt(Ys−Yt)=25789.488323276570161593347095778years

This mean value needs two complex correction which are too intricate to be shown 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 :

(4)

Ms=Ys(YsMss−1)=29.53058780664716371374days.

Metonic Year Ym is equal to :

(5)

Ym=235Ms19=365.246743924320182775185653635days

Precessional Period due to Moon’s effect (PPM1) :

(6)

PPM1=1(YsYm)−)=37978.09022183997109169737years

Precessional Period due to Sun’s effect (PPS1), intermediate term :

(7)

PPS1=11PP−1PPM1=80356.674413324332490977057144470years

Precessional Period due to Sun’s effect from alternative equation (PPS2) , intermediate term :

(8)

PPS2=1Ys(1Yt−1Ym)=80356.674413324332490977057250561years

The difference between PPS1 and PPS2 is due to computer’s errors and is equal to a negligible quatity :

(9)

Difference=1.320251252∗10−27years

Intermediate terms are :

A1 = PPS1 / PPM1 = 2.1158692799964388041303958720096.

A2 = PPS2 / PPM1 = 2.1158692799964388041303958748028.

Precessional Period due to Sun’s effect (PPS) , final value :

PPS = PPS1 + A1 = 80358.790282604328929781187540342

PPS = PPS2 + A2 = 80358.790282604328929781187646436

There is difference in two values of solar precessional period shown above (PPS) in 27th digit only. Hence, the computations are highly reliable.

There are three equations for obtaining scientific Tropical Year (in days) :

(10)

Yt.1=Ym1+1(PPS1+A1)=365.24219878124999999999999999999638527125

(11)

Yt.2=YmPPS=365.24219878124999999999999999999638595267

(12)

Yt.3=Ym1+1(PPS2+A2)=365.2421987812499999999999999999999999972349

Drikpakshiya Tropical Year is the most precise constant known to modern astronomy, whose empirical value is 365.24219878125 ± 0.00000000058 days.

The error of ± 0.00000000058 days is due to errors in modern instruments. The three values we obtained above through Vedic equations have errors in 34th digit which is due to 34-digit precisiuon of Windows Calculator used to obtain above results. The net result is startling : value of ‘pi’ is the basic term used to deduce exact value of most important astronomical constants, if you know the exact value of ‘pi’ then you can deduce the exact value of astronomical constants. Modern physicists know many such equations, which are called “coincidences” by atheists, and as proofs of Intelligent Design of Universe by believers in God.

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Vedic (ie, Suryasiddhantic) Theorem of Lunar month

M1 = 365.256400001304866086855 / (42/π) = 27.321114831446531255657

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/π)* {(Sin(Z1+1)-Sin(Z1)}]

= 1-[57.296*{(Sin(2.000024369635568)-Sin(1.000024369635568)}]

= 0.0003553741530559558546620855628939

K4 = K3 * 1000000 = 355.3741530559558546620855628939

K5 = 1+(1/K1)

Now we get the value of Drikpakshiya synodical or lunar month :

Ms = [(K4 / K5)-1}/12 = 29.53058780664716371373841555 days.

Sidereal lunar month will be :

Mss = Ys / [(Ys/Ms)+1] = 27.321660641391789747802454274321

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Now we show some more intricate Vedic (Suryasiddhantic) theorems. First of all, let us see :

Lunar Binomial Theorem :

A1 = 12/(K4-1) = 1 / 29.5311794213296538

A2 = Ys / 365.256400001304866086855

(13)

A=A1∗A2∗(42π)=0.45270842758190827172

Here is the Lunar Binomial Equation :

(14)

(A∗M2)+M−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 104.643228673117 years in 4.1748 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 value 93 in Siddhantashiromani and stated Kalpa-Mandochcha to be equal to 480 *smile emoticon* Saurpakshiya Kalpa Mandochcha 387 + 93 Drikpakshiya correction). Its elucidation will be shown later.

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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 !

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Exact Differential Equation of Mean Moon of Modern Physics from Suryasiddhaanta

Here is NC Lahiri’s formula of Mean Moon published by him in Bengali book “Panchaanga Darpana”. Latest equations do not differ significantly.

(15)

NirayanaMeanMoon=261:10′:1.24″+(17325593.8031″∗T)+(6.03″∗t2)+(0.0067″∗t3)

where T = Julian years of 365.25 days,

t = Julian centuries of 36525 days

261:10′:1.24″ is Mean Moon on Zero date of 1900 AD (Greenwich Noon 31 Dec 31, 1899)

Here is my siddhaantic Drik formula of Nirayana Mean Moon on same pattern, published in Hindi in 2005 Shivraatri, built from purely Suryasiddhaantic terms using Taylor’s and Lagrange’s formulas of modern differential calculus (setting up an empirically correct planetary differential equation is most difficult part of modern astronomy or higher mathematics) :

*

(16)

NirayanaMeanMoon=261:10′:1.24″+(17325593.803064287678″∗T)

(17)

+100∗6.0337456626113312731046134872458″∗t2

(18)

+10−3∗6.5095055710038624734367″∗t3

(19)

+10−6∗4.681852716188407032″∗t4

(20)

+10−9∗2.525508037859365516483207″∗t5

(21)

+10−12∗1.0898575817626111529246014535145″∗t6

(22)

+10−15∗0.39193089427273663825034568365639″∗t7

(23)

+10−18∗0.12080988126146805887553801248113″∗t8

(24)

+10−21∗0.03258393040897135345673870555868″∗t9

(25)

+10−24∗0.0078118151691312247782389032276435″∗t10+……

*

This explanation of this theorem is very long, which was published in my Hindi book in 2006 AD. It will soon be translated into English to be uploaded here.

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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 no 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 measured because there is no external space-time.

Let us call the space of time of this material universe as material-space and material-time. There are 14 universes (Bhuvanas) in the Multiverse *smile emoticon*Creation or Srishti), and we live in the middle universe. Since all forms of matter have shown to be associated with SPIN, from galactic to sub-atomic levels, it is natural that the material universe should also rotate. 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 explained on account of its internal properties and phenomena only. There must be something outside this finite universe which should explain the workings of this universe and its raison-de-etre.

Now we show the Vedic theorem of Rotation of the Material Universe. Surya Siddantic Kalpa is equal to 4.32 billion years. The Creator (Brahma) took 47400 divine yuears to create the Creation, which is equal to 47400 * 360 human years. Hence the total Age of Creation = 4.32 billion – (47400 * 360) = 4302936000 years.

4302936000 / 24000 = 179289 is the extra years due to Saurpakshiya precession. Hence total number of Saurpakshiya tropical years in one creation is equal to 4302936000 + 179289 = 4303115289 years. 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 101.976788423 is the exact value of Drikpakshiya correction in Kalpa-Mandochcha, 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 differencebetween Drikpakshiya and Saurpakshiya tithi (elongation of moon), and found a difference of 0.11 hours in 500 years,which he assumed to be due to 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 hours in 500 years is a result of extra 102 rotations of the Drikpakshiya solar orbit during one Creation : Saurpakshiya value is 387 while Drikpakshiya value is 489 (Bhaskaracharya-II gave 480 only in Siddhantashiromani). This Drikpakshiya rotation of solar ellipse is in addition to the normal Drikpakshiya rotation per 136000 years which is the cause behind anomalistic year.

—————

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 needed 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 modern 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 42000 years round some point very near to Earth’s centre,which suggests that the centre of Universe is 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 in 22059.75174 years. But in reality both divurge from each other at the rate of one revolution in 42000 years. For instance,Kaliyuga commenced at Ujjain midnight 17-18 Feb,3102 BCE,when siddhantic nirayan(=sidereal in Indian system) Mean Sun was at zero longitude. 5106 years later siddhantic zero Sun was to be found 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 42182.8 years. Due to non-linearity of elliptical paths,we get here 42182.8, the exact figure is an integer 42000. It raises a question : if mathematically siddhantic year and scientific year should show a difference of one revolution in 22059 years, why do they differ by one revolution in 42000 years in reality ? Where does 19941.24826 years come from ? We have here compared sidereal siddhantic year with tropical scientific year, hence this extra difference of 19941 years must be related to precession. Siddhantic period of precession is 24000 years and scientific period is 25789.4883233 years. Both form cycles of 100000 ± 12000 years with respect to 19941 in harmonic 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 precession is 25789.4883233 years. But it needs slight modifications due to long term cycles.We had got 101.976788423 years per 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 globe 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 > *zambezi, Mu-zambique, Zambia, Zimb-abwe, Gabon (< *Zamboon), 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 3891194 BCE when the present Mahayuga commenced. Surya Siddhantic formulae of making true planets from mean ones require the use of distance from Earth’s centre to a point in space 28.913 kilometres above the top of Mt Meru (Mt Kenya), which was believed to 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 861.7 times of Earth’s equatorial radius. Material Sun’s distance is 23455 times of Earth’s equatorial radius ! Ptolemy used a figure 1210, which is not much removed from Surya Siddhantic figure. Ptolemic system is well known, but Surya Siddhantic system is rather obscure, known to a few initiated brahmanas only. Due to lack of knowledge of orally transmitted and unpublished portions of original Surya Siddhanta, European commentators believe that 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 and 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, which 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 yojanas, which gets reduced to 13:40 at perigee of this elliptical epicycle, which when divided by 2π 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 yojana. Moon’s diameter is also an integer 436 yojanas. These rations are perfectly scientific. Such integral values seem to be mysterious when they are confirmed with modern science. This value of yojana was not only prehistoric, manifest in the story of Jarasandha’s 99 yojanas cited above, but was also intrinsically related to many native concepts of Surya Siddhanta, discussed in other sections of this article.

————

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 above. Saurapakshiya Suryasiddhanta speaks of a mahayuga of 4320000 years, but Drikpakshiya Suryasiddhanta works with a lesser figure of 4200000 years only, which has 100 equal parts of 42000 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 4713 BCE according to current beliefs.

First, let me elaborate the special significance of the number 42 and 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 see 7 universes at a time in any one direction, but not all 14 simultaneously. According to Suryasiddhanta 1955885109 years have elapsed (in 2009 AD) since the beginning of Creation. When we see seven universes arranged one after another, we see into (1955885109 * 7 *smile emoticon* 13691 million years of TIME, and into 13691 million light-years of SPACE. Currently, scientists believe the extent of Universe to be of 13.7 billion light years.

Divide 13.7 billion years with 10^42 (10 raised to the power 42, or 42 zeroes after 1).

13.7 billion years = (13,691,195,763 years) * (31558149.61 seconds per year) = 4.320688 * {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 for strong nuclear interactions is {10^-24} seconds. Quarks require slightly lesser time to combine for forming nucleons. This time 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) = 1.2953312 * {10^26} metres. This is the largest QUANTUM of SPACE. Now, divide it with {10^42}, we get 1.3 * {10^16} metres. It is the exact 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 elements have atomic radii below 100 pm. All the rest have radii ranging from 106 (Sulphur) to 262 (Caesium). Some examples 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 average. Let us, however, assume the average atomic radius to be around 130 pm for the sake of simplicity. It can be written as 1.3 * {10^10} metres. It is one million times bigger than smallest QUANTUM of SPACE. Scientists tell us that the nucleus is 100000 times smaller than the atom in radius. Hence, the smallest QUANTUM of SPACE is ten times smaller than the radius 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 largest and smallest quanta of space and time, but they do not know the exact dimensions. Suryasiddhanta helps us in getting the exact 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 deduced 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 basic cinstant of Nature. Since there are 14 universes in the Multiverse (=Creation), divide this number with 14 to get another 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 1836.0765598717432662033449719622 . 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 endless 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 isotopes, and 84 is the lowest proton number which does not have a single stable isotope.

Earth is NOT situated centrally, the central point is Divine Meru.

Suryasiddhanta once says square root of 10 is value of ‘pi’, but root of 10 is merely a crude value of ‘pi’ for teaching students and should never be used for any serious purpose. Any siddhanta must never abuse the basic laws of mathematics. The value of ‘pi’ is 3.14159265……., and not 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) / (65656565 – OCTAL 666)} ; Octal 666 is number 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 *smile emoticon* paridhi + amsha) = 5040 / 360 = 14 yojanas (13.9999723667) per degree. The diameter of manda-paridhi is 5040/pi = 1604.278659816 yojanas or 34.112669 kms, 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 equal 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 28.913669002241621530835902160508 Kms 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 value of 4320000 years?

The duration of one Saurapakshiya Creation (Srishti) is 47400 divine years less than one Kalpa of 4.32 billion years.

Hence, Srishti = 4302936000 years.

Add its 24000th part (=179289) to it to make Saurapakshiya “tropical” years *smile emoticon* 4303115289),

and divide the resultant with the ratio of Suryasiddhantic solar year (365.258756481481481481… days) and lunar year ( 12 * 29.53058794607 days), this ratio is equal to 1.0307356481481481481481…, you will get a number which is greater than Drikpakshiya-Kalpa (4174800000 = 4200000 * 71 * 14 ) by a samall margin of 101.97678842286770191552349305499 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 500 years) in Siddhantic Tithi with respect to Tithi computed on the basis of physical astronomy (cf. page 90 in ‘Advance ephemeris’ by NC Lahiri).

Modern Value of Precessional Period

An excess of 101.9767884 years of anomaly in 4.1748 billion years means one year of anomaly in each 40938727.965116279069767363571421 Drik year. Substract one 4200000 Drik years to get another periodic constant of 36738727.965116279069767363571421 years we will need in some computations needed to get modern value of precessional period. It is as follows :

In equation-3 above, we found precessional period equal to 25789.488323276570161593347095778 years. Divide the number 36738727.965116279069767363571421 obtained in previous paragraph with this value of precessional period, you will get 1424.5621124618187600683107379388. Now, divide 25789.488323276570161593347095778 with 1424.5621124618187600683107379388 to get 18.103449542617105305172322575051 and substract the latter from 25789.488323276570161593347095778 to get the modern value of precessional period used by scientists : 25771.384873733953056288174773203 . Modern valus is 25771.4021 years.

The first component of Milankovitch cycles or ayana chalanam is not a single motion but a combination of two motions :

(a) anomalistic precession (due to rotation of elliptical orbit of Sun) and

(b) orbital precession (sampat chalanam = precession of equinoxes, ie, precession of contact 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 Milankovitch 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.

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