Modern Equations On Ancient Principles

Deduction of Exact Equations of Modern Astronomy through Ancient texts of Siddhnta Jyotia

Vinay Jha

Disclaimer from uploader:

I feel that this paper presented herein as authored by Vinay Jha has a lot of merits and, only for aesthetic reasons, the presentation (layout) has been altered as well as corrections were made while some (unnecessarily) wordings have been struck out wherein it was deemed necessary in order to maintain the simplicity of this great research for the sake of ease in digesting such a sagaciously-written scientific writeup.

Contents INTRODUCTION ............................................................................................................................................................... 2

Comparison of Tropical Planetary Longitudes for Ujjain on March 3 .................................................................... 4

Difference in Tropical Planetary Longitudes : Dk vs Saura, in Arc-Sec ................................................................. 5

DECLINATION: Deduction of Modern Equation from Srya-Siddhnta .................................................................... 7

LATITUDE OF MOON ....................................................................................................................................................... 9

Exact Differential Equation Of Physical Moon .............................................................................................................. 10

Evidence Of Lost Portions Of Srya-Siddhnta ............................................................................................................. 12

Deduction of Modern Astronomical Constants from Srya Siddhnta ..................................................................... 20

Theorem of Dk-Pakya Sidereal and Tropical Years and of Precessional Period .............................................. 21

Vedic (ie, Srya-Siddhntika) Theorem of Lunar month ........................................................................................ 23

Lunar Binomial Theorem : .......................................................................................................................................... 24

Srya Siddhntika Theory of the Rotation of Material Universe ................................................................................ 25

Ancient Cosmogony and Geography .............................................................................................................................. 27

The Cycles of Lord Brahm ......................................................................................................................................... 28

INTRODUCTION

Viu Dharmottara Pura of Vedavysa

yantra vedhdi njta yad bja gaakaistata grahadi parketa na tithydi kadcana

Sage Vysa has clearly said in Viudharmottara Pura ( ) that in examining perceivable

events like eclipses etc ., where an actual observation is needed , the position of the planets should be

further corrected using Dk -Karma corrections (i.e., adding the Ayan a to get the Tropical longitude) so

that they can be used in determining the actual event , but these Dk -corrections should never be made use

of in computation of Tithis and others.

Nir aya Sindhu

- -

ada phala sidhyartha yathrka gaita kuru gaita yadi drtha tad dy udbhava tassad

Nir aya-Sindhu also states that Srya -Siddhnta should be used for knowing invisible results ("Ad a

Phala" i.e., things like Destiny or Fortune).

The mathematics of Srya -Siddhnta is given in the Nrada Pur a too. In all other Puras too, Srya -

Siddhnta has been made us e of for the purpose of computation and its ideas have been presented at

many place. But since the time of Graha -lghava (cir.1440 AD) , materialists have begun to dominate the

scene gradually. They consider physical planets to be exactly same as the astrol ogical planets.

dk-karma correction ( - ) is an essential part of ancient Siddhnta skandha of Jyoti a. But dk-karma saskra are never used in finding True Longitudes of planets ( graha-spa-karaa | - ) in any ancient Siddhnta text It is used only when perceivable phenomena like eclipses , heliacal risings

& settings ( skrdi udaysta | ) etc ., are needed. Two chief components of dk-karma correction are

1. ka & yana dk-karma saskra (corrections ) ( - - ) and 2. ayana-dk-karma saskra ( - - )

both of which , are explained in ancient siddhntas , chief of which is Srya -Siddhnta.

But these 2 dk-karma corrections give only that position of a planet which i s needed for phalita astrology, e.g. udaysta of Jupiter & Venus is needed for determining Muhrta s of auspicious events like Vivha|marriage , Upanaya| sacred thread ceremony , etc. Positions of physical planets as perceived by our

naked -eyes is not given by the equations given in any Siddhntika texts.

It is for this reason , many medieval scholars like Ga ea Daivaja of Graha -lghava or Divkara

Daivaja of Makaranda -Vivaraa have all declared that the Srya -Siddhnta treatise has now b ecome

obsolete and some changes are needed in its formulations or methods. They advocated removal of manda-phalrdha | from the 4 corrections made in Mean Longitude of a planet to get the True Longitude , while ignoring completely that, if such a thing were to be indulged, the very fundamental theory of

siddhnt ika texts likewise will become distorted. Unfortunately , no any siddhnt ik a text or its commentator

n ever explained the basis of the fundamental t heory involved in those 4 corrections of siddhnta texts ,

namely

1. ghra -phalrdha | ,

2. manda -phalrdha | ,

3. manda -phala | and,

4. ghra -p hala |

Rev . Eveneger Burgess , the translator & commentator of Srya -Siddhnta , candidly accepted that he could

never understand the rationale behind these 4 corrections in spite of having spent 8 years among Indian

experts to learn the Srya -Siddhnta. Other commentator s of this text were even worse , they neither

explained nor had the humility to admit their inability to explain the WHY s behind these calculations . All

ancient S iddhntas and Puras which deal with graha-spa-karaa are unanimous in the applicability and order of aforementioned 4 corrections , but none of them explain the mathematical reason ing and

related geometry.

Although 2 medieval so-called Indian experts , namely Ga ea Daivaja and Divkara Daivaja ,

rejected the applicability of manda-phalrdha, they did not bother to go into the rationale behind either manda-phalrdha or even the remaining 3 corrections.

If manda-phalrdha was rejected , what is the mathematical reason of ghra-phalrdha then ? manda & ghra phala are accepted in modern astronomy too , as equation of centre and the reduction of heliocentric to geocentric position , respective ly. But what about their halves manda & ghra phalrdha?

Modern astronomy knows NO SUCH THINGS as manda & ghra phalrdha. Nobody understands them , but surprisingly enough they are taught by Jyoti a departments of Sanskrit univer sities.

Here , a question arises if no commentator has ever succeeded in unravelling the mathematical logic

behind the most essential aspects of siddhnta texts , dont you think there is something m ysterious about

siddhnta te xts ? Either all siddhnta texts are wrong or , all medieval and modern experts are ignorants in the field of siddhnta skandha of Jyoti a.

A false excuse is invented by some experts claiming that these ancient siddhnta texts were then -accurate in ancient times but as of now have become outdated. This false logic was first invented by

the author of Graha-lghava, Ga ea Daivaja and is flaunted by majority of modernisers of astrology. Here is the irrefutable proof of falsity of such stat ements in tabular form , which shows there was no period

in known history during which difference between

1. Dk and, i.e., perceived, or physical planets

2. Saura, i.e., of Srya-Siddhnta

tended towards any minimum value.

The First table (below) gives the planetary longitudes from both methods , and the second table following

this gives differences , at regular intervals of 100 years.

Comparison of Tropical Planetary Longitudes for Ujjain on March 3

AD Sun Moon Mars Mercury Jupiter Venus Saturn

382 Dk 343:33:59 001:39:24 304:06:20 320:29:20 238:48:12 310:08:09 050:58:12

Saura 344:09:44 002:18:18 306:00:04 317:26:27 236:14:05 307:10:43 058:18:51

482 Dk 344:18:44 318:25:11 347:52:07 319:15:50 025:16:49 027:27:47 209:22:01

Saura 344:47:48 319:25:52 350:42:50 324:10:33 021:03:18 025:40:02 214:40:16

582 Dk 345:03:34 253:57:54 029:03:14 335:51:57 188:46:46 325:47:33 337:17:06

Saura 345:25:49 258:28:12 031:42:36 343:39:19 185:05:00 322:54:50 342:03:42

682 Dk 345:48:00 215:27:37 073:50:27 358:38:34 342:03:44 028:07:06 128:39:19

Saura 346:03:50 214:34:27 076:53:20 000:13:16 338:05:47 031:01:54 138:56:21

782 Dk 346:33:23 152:21:34 157:55:10 357:25:17 136:30:39 342:28:19 272:56:05

Saura 346:41:49 154:02:50 165:14:47 350:55:52 132:22:37 340:03:29 276:49:23

882 Dk 347:18:01 109:07:50 260:33:02 322:29:25 298:43:55 323:44:48 044:58:58

Saura 347:19:46 107:58:29 261:48:04 320:02:06 295:40:57 335:09:06 051:04:16

982 Dk 348:02:48 052:09:32 311:52:48 324:01:45 085:44:25 359:21:07 205:23:02

Saura 347:57:41 052:17:24 312:05:43 328:07:58 081:53:55 357:30:27 209:48:18

1082 Dk 348:48:22 000:17:10 355:34:55 341:21:32 253:17:16 302:24:10 335:41:00

Saura 348:35:35 000:24:57 356:47:17 347:45:54 251:39:09 301:33:34 337:05:04

Tropical (Syana) longitudes have been chosen for this comparison so that the controversies related to

Ayan a s do not intervene. The differences are clearly due to manda & ghra phalrdha, because the difference in mean value s of longitude will result in a linear increa se in difference with time which is not the

case , while the differences in manda-phalrdha plus ghra-phalrdha will also show another line of linear increase in difference with time , because both dk & saura systems use manda as well as ghra phala. Even if manda-phalrdha is discarded , as Ga ea Daivaja once proposed , still, this non -linear anomaly does not vanish , because differences due to ghra-phalrdha are much more than those due to manda-phalrdha.

Difference in Tropical Planetary Longitudes : Dk vs Saura, in Arc-Sec

AD Sun Moon Mars Mercury Jupiter Venus Saturn

382 -2145 - 2334 - 6824 +10973 + 9247 +10646 -26439

482 -1744 - 3641 -10243 -17683 +15211 + 6465 -19095

582 -1335 -16218 - 9562 -28042 +13306 +10363 -17196

682 - 950 + 3190 -10973 - 5682 -21723 -10488 -37022

782 - 506 - 6076 -26377 +23365 +14882 + 8690 -13998

882 - 105 + 4161 - 4502 + 8839 +10978 -41058 -21918

982 + 307 - 472 - 775 -14773 +13830 + 6640 -15916

1082 + 767 - 467 - 4342 -23062 + 5887 + 3036 - 5044

This highly irregular non -linearity proves that no changes in Siddhntika values of manda-phala-paridhi or ghra-phala -paridhi can reduce this anomaly , because those changes will be linear while actual difference is highly no n -linear , ranging from over +6 to less than -11 , which is an unacceptably high

anomaly because ryabha a or Varhamihira and all other scholars could not be so great fools to have

failed to notice such errors.

Had Srya -Siddhnta been created around 400 AD or on any other date through sensory observations , this

anomaly should be minimum around that date. The fact is that there is no such period in history. Sun's

anomaly is minimum around 900 AD , but the anomaly of Venus is maximum then and other plane ts also

have very high divergences.

Actually , it is around 2000 AD when sidereal differences in longitudes of D k and Saura planets become

minimum ( regardless of the Ayan a value), although these differences still remain huge. All these

findings cannot be presented here. There are handy softwares freely available online through which anyone

can check these conclusions.

Therefore , it is clear that Srya-Siddhnta was not created on the basis of observation of physical planets. This result conforms with t he statements in Srya -Siddhnta and all other available siddhntas and texts like Nrada Pura mentioned above , which say D k positions should not be used in

Phalita Jyoti a.

Now , the problem gets intensified instead of being solved. If physical planetary positions and the

astronomy of modern scientists cannot explain the equations of our ancient siddhntas , what is the rationale

and wha t is the use of such siddhntas ?

The utility aspect is very simple to answer predictive astrology , although t his utility of siddhntas

is unpalatable to modern secularists who cannot tolerate the very mention of " astrology". But whether astrology is a true or a false science , it is a fact that all known societies had great faith in and reverence for

astrology in ancient ages and astrology was the mother of modern astronomy too. Scientists deliberately

omit to mention that not only ancient astronomers like Ptolemy but even the forerunners of modern

astronomy like Copernicus and Kepler were practising astrologers an d the motivating force behind their

interest in astronomy was to find better means for predictive astrology.

The problem with materialists is that they cannot agree to test the validity or falsity of Srya -Siddhnta on

the criterion of predictive astrology. Not only anti -astrologers , but even supporters and users of Vedic

Astrology using D k astronomy are not ready to test Srya -Siddhntika astrology without any bias. During

past few decades , I have found only a handful of D k -supporters ostensibly ready to test Srya -Siddhntika

astrology , but they push their own habits and biases and therefore could not test it in its own frame of

reference. This is a common problem with all materialists. On the other hand , most of the spiritualists have

no intere st in Jyoti a.

Therefore , Srya -Siddhntika astrology is used by a few among internet astrologers. But even

today, overwhelming majority of traditional Pac ga s are made with some medieval tables which have

been either directly created by means of Srya -Siddhnta (such as Makaranda Tables) or were indirectly

based on some earlier source derived from Srya -Siddhnta (such as South Indian Vkya texts). For those

who are not ready to test the validity of Srya -Siddhnta just because its planetary positions do not tally

with physical planets , isnt there any method available to prove the validity of Srya -Siddhnta? The

following sections outline some of the answers to this question.

DECLINATION: Deduction of Modern Equation from Srya-Siddhnta

The apparent srya vth the ecliptic which is the path of the Sun is slanted on the projection of Equatorial Plane by a variable amount which is about 23.4393 at present according to modern astrono my

but this value is exactly equal to 24 according to Srya -Siddhnta. If both modern astronomy and Srya -

Siddhnta describe the same Sun , then Srya -Siddhnta is certainly a wrong text. But if the integral Srya -

Siddhntika values give the results obtain ed through modern astronomy with a very high degree of precision

through simple D k -karma correction , what should we deduce ? As cited above , Sage Vysa sai d that

perceived positions of planets should be obtained by means of finding proper bja-corrections. Let us take

the case of Declination of Sun for any given date , for which the Srya -Siddhntika equation is thus :

Sin D = Sin L x Sin P

where ,

D is Declination for a given time , L is Tropical Longitude of Sun for that given time , and P is the maximum possible value of Declination.

Modern value of maximum declination is less than the Siddhntika value by 2018.6" arc -seconds. If we

neglect the effect of nutation whose maximum value ~17 is negligible in respect to this huge difference ,

then the Siddhntika equation mentioned above can be comfortably used to create modern table of solar

declination , provided we replace Siddhntika value of P (maximum declination) with modern value.

Thus , we can create the modern scientific table of solar declination , as given in N . C . Lahiri 's book

Advance Ephemeris, shown in the picture below. Using a scientific calculator , anyone can check the Siddhntika equation cited above with reference to Lahiri's table below. Out of 180 entries in the table at

in tervals of 1 , a difference of one arc -minute will be noticed at a handful of places , which is due to effect

of nutation which is always less than 17.23 (arc -seconds ) but sometimes results in 1 (arc -minute )

difference when value are rounded off in arc -minutes as given in Lahiri's Table. It proves that the

Siddhntika equation of declination was absolutely correct , excepting the effect of nutation which was never

used in any siddhnta.

Has any historian of s cience ever credited Srya -Siddhnta with invention of the correct equation of solar

declination which is used by even modern scientists ? No.

All of them insist that Ptolemy preceded the date of composition of Old Srya -Siddhnta which is

supposedly lo st, while so -called modern Srya -Siddhnta is of a much later unspecified date. But it has been shown in this paper that the so -called modern Srya -Siddhnta cannot be ascribed to any date of

known history without accepting very high amounts of errors in all planets , which will result in declaring all

ancient Indians as idiots who made such errors.

Now , the real question is this if the author of Surya -siddhnta was capable of finding such a fine

formula for computing declination , why the value of maxi mum declination could not be measured within

tolerable limits of inaccuracy ?

Historians of science have a handy answer : Indians stole the equation from Greeks , but could not

measure planetary positions accurately. They can never accept the reality which is much more astounding

than anyone can ever imagine Srya -Siddhntika equation of Declination can give exact modern values

of solar declination down to the lim it of less than one arc -second. Two bja corrections are needed. The

major correction is simple : multiply the Srya -Siddhntika declination P with the cosine of its exactly half -

value :

Sin D' = Sin D x Cos P/2

It gives a maximum value of 23.443745 which is only 16 arc -seconds more than modern value obtained

by NASA scientists. Its geometric implication is that D k ecliptic is exactly 12 slanted to Saura ecliptic ,

which means D k Sun is a completely different entity than the Saura Sun. Now comes th e second bja-

correction

Sin D" = Sin D' x Cos M/2

where 'M/2' is maximum possible value of Siddhntika manda -phalrdha , which Ga ea Daivajya and his

followers tried foolishly to expel from traditional astronomy without understanding its significance. Max imum

manda-phala is equal to 2 10 32 according to Srya -Siddhnta. Thus we get a final value of 23 26 22.27 , nearly equal to 23 26 22.27 which is the value given by latest DE -series ephemerides from

NASA's JPL , the difference is merely of 0.8654 (arc -second ). Here it must be noted that NASA's values

change with time , while Siddhntika values are changeless which scientists may like to explain as long -

term average. This Siddhntika value is equal to NASA's value for 2000 AD , which confirms another major

finding that with proper Ayan a the period of minimum difference between sidereal Siddhntika solar

longitude with sidereal D k longitude was 2000 AD , as mentioned in previous section. Here only

summarized results of many important themes are show n.

LATITUDE OF MOON

The page from Lahiri's Advance Ephemeris given above gives table for lunar latitude. Its formula is simple:

Sin Lm" = Sin (Moon - Rhu) x Sin Lm

Here , Lm is the latitude of Moon to be known , Lm is the maximum possible Latitude of Moon , while Moon

& Rhu are their longitudes , tropical or sidereal. The only problem is Lm, whose value in modern astronomy is higher than in Srya -Siddhnta.

In Srya -Siddhntika system , planets are not physical bodies , hence have no masses and gravitation.

Therefore , there is no effect of barycentre. Second effect is of Meru. Srya -Siddhntika astronomy is Meru -

Centric and not geocentric ( Ptolemaic astronomy was also not geocentric; geocentricity is a wrong propaganda of medieval Church). If we take these tw o effects into account , it is easy to compute Lunar latitude of modern astronomy from Srya -Siddhntika terms. Srya -Siddhnta has maximum lunar latitude

equal to 4.5 . Multiply its sine with the distance of Earth's centre to the tip of Mt. Meru ( Mt. Ken ya) at

equator , which is 6383.362 KM s. We get 500.8328 KM s which is equal to 0.001302891538 multiplied with

Moon's average distance from Earth. Substract it from Sine of 4.5 which is Siddhntika maximum latitude

of Moon , and get the arc -sine of the result. Thus we get the reduced latitude due to effect of Meru -Centric ity

versus geocentricity. Now , add 'Moon / Earth' mass ratio (nearly 1/81) to the sine of this reduced latitude in

order to get the effect of barycentre , and get arc -sine of the resultant , which is the maximum D k latitude of

Moon , equal to slightly more than 5 08 . Accuracy needs correct Earth:Moon ratio. A very small correction

is further needed due to effect of finer motions around Mt. Meru , but its expl anation is lengthy and tedious.

This is a crude method , taking help from mass ratio , which is un -Siddhntika . Siddhntika corrections in

Saura latitude to get D k lunar latitide is easy , but requires such terms whose explanation is highly

complicated. Even the crude method given above is enough to show that Siddhntika terms are neither

wrong nor outdated , but need D k corrections to make Saura entities visi ble. The complicated geometrix

around a few yojanas around the tip of Mt. Meru ( Mt. . Kenya ) is required to get the D k corrections to get

Dk Sunrise from Siddhntika equations of Sunrise . (This was published in a Hindi book by me in 2005 AD.)

Maximum Manda -Phala of Moon is 5 02 48 in Srya -Siddhnta , but 6 17 19.7 or 22639.7 in modern

astronomy (cf. NC Lahiri's Pacga Darpaa). Take the difference of sine of manda-phalrdha of both , which is same as difference of saura & dk eccentricies. Multiply it with distance of Moon and add the Meru correction of 500.8328 KM s deduced above , the resultant will be barycentre with 83 KM anoma ly

whose reason lies again in the intricate mathematics around the tip of Mt. Meru. If this small anomaly is

neglected , dk manda-phala of Moon can be thus deduced from Saura Moon's terms. Adding effects of barycentre to Meru's effect , we get dk manda-phala of Moon. Hitherto , some simple terms were being discussed , but now let us get something out of Srya -Siddhnta which is beyond the reach of modern

science.

Exact Differential Equation Of Physical Moon

Setting up an empirically correct planetary differential equation is most difficult part of modern astronomy.

Statistically arranged empirical data are analyzed through various statistical tools and Fourier Transforms

to find out proper differential equations , but after few years the constants term s and co -efficients in these

equations change due to reasons not known to modern astronomers (real reason in rotations and

revolutions of physical entities and the whole physical Universe in the permanently fixed k a), and

therefore these equations need revisions after few years. The above equation deduced Siddhntika ally

conforms with Lahiri's and later equations admirably , and perfectly satisfies the procedures of differential

calculus perfectly for 2000 AD when dk & saura universes coincided (it happens at intervals of 42000 years). Here is the Siddhntika explanation of the most troublesome equation of modern physical

astronomy , the equation of Mean Moon (converted into Nirya a following NC Lahiri's method):

The Siddhnt ika equation for deducing any term in the above equation is this

Ys is Siddhntika Niryaa year equal to 365.258756481481481 Svana days, Yd is Dk tropical year equal to 365.24219878125 days , n is the number of term in the following differential equation of Nirya a Mean Moon , t is Julian centuries of 36525 days , T = Julian years of 365.25 days , 261 10 1.24 is Mean Moon on Zero date of 1900 AD (Greenwich Noon 31 Dec , 1899)

387 is the total number of revolutions of Siddhntika mandoccha (apogee) in one Kalpa (1 Kalpa = 4320

million years)

K is deduced Siddhnti c ally in following manner :

K = [{(Ys-Yd) / Ys} - (1/42000)]-1 x (Ys / t) = 464.65408706471303027753666827

Then the wanted term in the Siddhntika equation of D k Nirya a Mean Moon is

Mn = [360 / (n - 1)! ] x [ t x [{ 1 + ( 1 / 387 ) } / K ] n ]

Following is my Siddhntika Dk formula of Niryaa Mean Moon created from above equation , published in Hindi in 2005 , built from purely Srya -Siddhntika terms using Taylor's and Lagrange's

formulas of modern differential calculus :

(1)

NiryaaMeanMoon=261:10:1.24"+(17325593.803064287678"T)

(2)

+1006.0337456626113312731046134872458"t2

(3)

+1036.5095055710038624734367"t3

(4)

+1064.681852716188407032"t4

(5)

+1092.525508037859365516483207"t5

(6)

+10121.0898575817626111529246014535145"t6

(7)

+10150.39193089427273663825034568365639"t7

(8)

+10180.12080988126146805887553801248113"t8

(9)

+10210.03258393040897135345673870555868"t9

(10)

+10240.0078118151691312247782389032276435"t10+......

The equation above can be extended upto infinite number of terms , although there is no use of higher

terms because of impossibility of empirically verifying the higher terms.

Now , here is NC Lahiri's formula of Mean Moon published by him in Bengali book " Pac ga Darpa a".

Latest equations do not differ significantly.

(11)

NiryaaMeanMoon=261:10:1.24"+(17325593.8031"T)+(6.03"t2)+(0.0067"t3)

It is clear that the modern scientific formula is a crude form of the exact Siddhntika equation. Even after

supercomputers and other sensitive instruments used by NASA scientists , they have not been able to

discover any equation approaching this Vedic equatio n. Vedic here means based on Vedic -Purnic -

Siddhntika traditions and being eternal , changeless , perfect.

Materialist cannot digest such things and start abusing , instead of studying the mathematics and trying to

prove it wrong on the basis of pure mathema tics or pure science. They are guided by their materialist

prejudices. But following section is a concrete proof of the fact that the entire Srya -Siddhnta has never

been written down.

Evidence Of Lost Portions Of Srya-Siddhnta

Modern Value of Precession in Bhskarcrya 's Work based on Srya -Siddhnta

In the chapter Direction, Place and Time (Srya -Siddh nta , Ch. 3 ), E . Burgess writes

(bracketed words are mine) :

The (Srya Siddhntika) theory which the passage (verses 9-12), in its present form, is

actually intended to put forth is as follows : the vernal equinox librates westward and

eastward from the fixed point, war Piscium, assumed as the commencement of the

sidereal sphere the limits of the libratory movement being 27 in either direction

from that point, and the time of a complete revolution of libration being the six-

hundredth part of the period called the Great Age (ie, Mahyuga as defined by Burgess

in chapter i, 15-17, where he gave it a span of 4320000 years), or 7200 years; so that

the annual rate of motion of the equinox is 54.

This is the interpretation of existing version of Srya Siddhnta (triatktyo yuge bhn cakre prkparilambate | , SS , iii.9) in own words of E. Burgess

[as it is actually intended to put forth] by all traditional commentators.

This is exactly what I illustrated with example in the illustrated example of computation of ayanamsha.

The moot point is this : Burgess knew the traditional interpretation ( bhn cakre | .., ie pendulum

like motion of nak atra orbit itself) , but gave his own meaning based upon modern concept of precession

of equinoxes , and tried to create doubts about the authenticity of these verses ( Ch.3. 9 -12) by putting forth

deliberately false arguments.

Let us examine Burgess. In verse -9 (Srya -Siddhnta , Ch. 3.9 ), he translates pari-lambate as falls back , although he says lambate means lag, hang back, fall behind and pari means about, round about.

Therefore , pari-lambate should have been translated as fall back roundabout and not me rely as fall back according to own logic of Burgess. If the circle of asterisms lags roundabout any fixed point (whether Revat

or C itr), it is a to and fro motion as all traditional commentators accepted. Modern concept of precession

is something different from the original concept of Ayan a . Theon in West had mentioned this oscillating

motion , Arab astronomers also accepted it , and almos t all Europeans accepted it upto Renaissance , after

which Hipparchus was rediscovered and modern concept of precession became a well established fact in

astronomy. But this concept of equinoctial precession (as well as anomalistic precession) was also know n

to ancient Indians and Greeks.

Burg ess wrongly quotes Bhskara -II, because he relied upon a wrong translation of Bhskara by

Colebrooke (As. Res. , xii 209 ; Essays , ii, 374 , etc) and did not try to examine Siddhnta iromai which

was wrongly translated by Lancelot Wilkinson due to Colebrooke's influence.

Bhskara -II did not give his own opinion at all , and merely quoted Srya Siddhnta and Muj la (elsewhere

Muj la and Manjula) , saying

Srya-Siddhnta gives -30000 revolutions of sampt or equinoctial point per Kalpa while ayana has a motion of +199669 revolutions per Kalpa (of 4320 million years).

Bhskara's own opinion was that these should be followed , which means both Srya Siddhnta and Muj la

were correct in Bhskara's opinion. Colebrooke , Burge ss, Wilkinson , etc ., have misquoted Siddhnta

iromai and created an impression that ancient Indians were inept in astronomical observations , as

Whitney shamelessly declared in his prologue to Burgess , but the Hindi translation by Satyadeva Sharma

is corr ect , although he could not get the real meaning.

The startling fact is that Siddhnta iromai clearly says that the point of intersection of equatorial plane and ecliptic (which is the very definition of equinox) has a negative motion of 30000 revolutions per Kalpa according to Srya -Siddhnta , while Muj la's value of ayana's motion is +199669 , and both

(Srya -Siddhnta and Muj la ) must be added to get the final motion (of the equinox ). Hence , we get

+169669 revolutions per Kalpa , which give s (4320000000 / 169669 =) 25461 years per revolution or 50.9"

per year , which is very near to modern value of about 50.3" per year for precession of equinoxes.

Fuller discussion of Siddhnta iromai's text is given below. We must not forget that Hipparchus had given

a period of 36000 years for precession , which was not corrected by Europeans till the onset of modern age.

It is unfortunate that Siddhnta iromai is still being misinterpreted by foreigners , and if a true rendering

is offered by Ind ian scholars , they are abused , esp by those who do not care to consult the originals and

declare the forign missionaries to reliable. Bhskara -II neither excluded Srya -Siddhnta , nor Muj la, but

mentioned the both must be used , which is clear from verse -19 , where he clearly asks to add Muj la's

ayana -chalam to Srya -Siddhntika sampt -calanam (this sampt -calanam is anomalistic precession with

a period of 144000 years per cycle , not far from modern value). Another startling fact is that Bhskara -ii

differentiates sampt -calanam of Srya -Siddhnta from ayana -calanam of Muj la, and says both must be

added before computing phenomena like declension , ascensional differences , etc. But modern

commentators like Colebrooke misinterpret Bhskara -II deliberately, and imply that sampt -calanam of

Srya -Siddhnta quoted by Bhskara -ii was an erroneous thing which must be forgotten , while ayana -

calanam of Muj la was a crude approximation of modern precession. But this interpretation is falsified by

Bhskara's origina l verses (and his own commentary Vsanbhshya) as shown above. The root of this

problem lies in the fact that sampt -calanam of Srya -Siddhnta is a distinct phenomenon from ayana -

calanam of Muj la according to Siddhnta iromai, but readers are not inf ormed of the real meaning of

Siddhnta iromai and false quotation from Siddhnta iromai was quoted by Colebrooke and Burgess

(12th verse , Ch.3 ). This is a sign of intellectual incompetence and dishonesty of Western "experts" who are

blindly followed by brown shibs of India. Those who do not consult the original texts cited above will not

believe me.

Siddhnta Tattva Viveka by Kamalkara Bha a is a medieval text, which clearly states that Saura -Pak a is distinct from Dk -Pak a. Saura -Pak a (astronomy of Bhuva -Loka ) is Srya -Siddhnta as it

exists. Dk -Pak a (astronomy of Bh -Loka or physical/material/sensory world) is that version of Srya -

Siddhnta which was not preserved because it was useless in astrology.

Siddhnta iromai uses many c oncepts of Dk -Pak ya astronomy , as the instance cited above proves. Saura -Pak ya Srya -Siddhnta does not contain any refence to 30000 cylces per Kalpa mentioned

by Bhskara -II. He was quoting from Dk -Pak ya Srya -Siddhnta which as a text had been lo st ;

Bhskara -II said in his own Vsanbhshya commentary of Siddhnta -iromai that Srya -Siddhnta is

gama . Modern commentators confuse both variants of Srya -Siddhnta. Siddhnta -Tattva -Viveka is

prescribed in post -graduate (Ganit crya ) syllabus of Sanskrit universities , but no modern commentator

has ever tried to translate it or comment on it.

According to Bhskara -ii, negative sampt -calanam of Dk -Pak ya Srya -Siddhnta should be

added to positive ayana -calanam of Muj la to get final Dk -Pak ya precession , which is very close to

modern value. Ayana -calanam of Muj la is also Dk -Pak ya, because Saura -Pak ya entities are not used

in Dk -Pak ya astronomy , and vice versa.

Muj la's ayana-calanam , as mentioned in Siddhnta iromai, gives

a period of (4320 million / 199669 = ) 21636 years per cycle. Siddhnta

iromai says that it is ayana-calanam according to Muj la & his followers but it was not accepted as precession by Bhskara ,

precession is obtained after substracting ( Saura -Pak ya) Srya -

Siddhntika sampt calanam . If this 21636 year cycle is not precession ,

what is it??

Readers should read Milankovitch cycles (wiki ) which informs:

Earth's axis completes one full cycle of precession approximately every 26, 000 years (25771.5 precisely at present, 25789.5 years is long term mean). At the same time, the elliptical orbit rotates, more slowly, leading to a 21, 000-year cycle between the seasons and the orbit This orbital precession is in the opposite sense to the gyroscopic motion of the axis of rotation(cf. anomalistic precession as distinct from equinoctial precession), shortening the period of the precession of the equinoxes with respect to the perihelion from 26, 000 to 21, 000 years.

Note: at some sites of NOAA of USA , 2200 0 is mentioned instead of

21000

I had put some of the most important extant theorems of Dk-Pakya Srya-Siddhnta at a website. I had put parts of it at one of most popular websites, where a German Indologist deleted it and abused me profusely; later I found those deleted materials at an Australian website, without any name of author!! But I am here divulging one important secret of ancient science of India which has been neglected by wrongheaded commentators.

yana-calanam of Muj la is not orbital precession , it is the most important of all components of Milankovitch cycles as this Wikipedian definition shown. If we take cue from siddhnta iromai, the afore-mentioned Wikipedi an clause can be rewri tten thus :

This orbital precession of equinoxes is in the opposite sense to the gyroscopic motion

of the axis of rotation, shortening the period of the precession of the equinoxes with

respect to the perihelion from 25771 to 21, 636 years.

Siddhnta iromai also says that Muj la's ayana-calanam (21 , 636 years per cycle) is opposite to sampta -calanam . Bhskara -ii clearly defines sampta -calanam as,

the point of intersection of equatorial plane and ecliptic (which is the very definition of equinox).

Hence , what Siddhnta iromai says is exactly what Wikipedia informs us , the only difference is that

Siddhnta iromai is misinterpreted and declared to be obscurantist , and the great cycles mentioned in

Siddhnta iromai is discovered by 20th centur y scientists. But we must remember Bhskara -ii did not discover these things , he acknowledged Srya -Siddhnta and Muj la. Bhskara -ii knew Dk -Pak ya

Srya -Siddhnta , which has not survived because it was not useful in astrology. In his formula of

precession , Bhskara -II used a figure 30000 cycles per Kalpa. Bhskara -II got an approximate value of

50.9 per year , which was the most precise value before modern astronomy developed in the West. Here I

quote a Purnic verse which proves knowledge of equ inoctial precession in Purnic times :

uttnapdaputro'sau me hbhto dhruvo divi

sa hi bhraman bhrmayate nitya candrdityau grahai saha

Translation

Uttanapda's son Dhruva is the fixed point in the Heavens, round which all planets including Sun and Moon, but Dhruva himself also moves round.

Round what ? Ans.: Mt. Meru , which is the only fixed point in Cosmos according to Purnic epic s. Hence ,

the bhacakra also librates with respect to this fixed point Meru. According to Bhskara -II, orbital precession

is derived by substracting anomalistic precession (sampt -calanam ) from the first component of

Milankovitch cycles ( Muj la's ayana-calanam). Bhskara -II acknowledged earlier authors. Hence , we

a

must conclude that modern values and concepts of orbital precession , anomalistic precession , Milankovitch

cycles , etc were known to ancient I ndians well before Bhskara -ii.

But 2 things about confusing te rminology mu st be borne in mind

1. this sampt-calanam he finally gets by combining the two quantities mentioned above. According to Bhskara -II, Srya -Siddhntika sampt -calanam is 30 , 000 per Kalpa. He does not give a name for

the term which is finally obtained by combining this sampt-calanam with Muj la's ayana-calanam , but the definition he provides for Srya -Siddhntika sampt-calanam is exactly the definition of the final quantity whose name he does not provide. Hence , there were many types of sampt -calanam s !!

This is not a case of confusion of terms. It is a result of Saura -Pak ya term with Dk -Pak ya terms

bearing same names but having different magnitudes and sometimes even having difference in basic

properties !

2. Second confusion is due to use of the term ayana -calanam for Muj la's precession. It is quite distinct

from Saura -Pak ya Srya -Siddhntika n ayana-calanam (trepidati on) as mentioned in existing text.

Burgess could not digest this theory of libration (oscillation or trepidation , ie, Ayan a - motion) and tried

to distort the meaning of terms to fit modern view of orbital precession with this Saura -Pak ya precession .

Bhskara -ii knew and respected Srya -Siddhnta which he cited and used in his computations as shown

above , and gave exact value of Dk -Pak ya precession. Therefore , it is foolish to impose Dk -Pak ya

precession (50.9" per year according to Bhskara -II, 50.3" really) upon Saura -Pak ya ayanamsha (54 per

year, oscillating within a range of 27 ). (There are further corrections on Dk -Pak ya precession which

give a final value of one revolution in 25771.4 years , exactly equal to the value deduced by NA SA - JPL ,

but these corrections requires some long theorems to prove).

I do not want to say that all ancient texts are true and should be blindly followed. But it is equally

wrong to deride them as outdated and obscurantist just because they could not be understood by

moderns.We have yet to discover the real Wonder that Is India. Unless and until ancient texts are proven

false, it is suicidal to reject them. Here is the photographed copy of relevant page from Siddhnta iromai

for those who want first han d proof , followed with discussion on its obscure passages :

Vsan s Bh ya (commentary ) by Bhskara -ii on his own work Siddhnta iromai has never been

translated or explained. Bhskara -ii knew Siddhnta iromai will be misunderstood , hence he wrote its

commentary Vsan -Bh ya himself. This commentary also needs a commentary. In i t, Bhskara clearly

writes that ,

sa evyam

refers to kr ntip ta, not to ayana -calanam .

If verses 17 -19 are taken to gether , we have six lines , and sa evyam occurs in third line , which says that the ayanacalanam as defined by Muj la & others [his school of thoughts] is same as Krnti-Pta defined in first line.

This meaning from Vsan -Bh ya is further reinforced in same passage in Vsan -Bh ya which say s

that,

tatra mandoccha ptnm gatirasti

the second line (minus 30000 revolutions per Kalpa) must refer not to K rnti -Pta but t o motion of apogee

Thus , Bhskara has made it clear that the definition of Krnti -Pta as given in first line applies not to -30000

revolutions per Kalpa ( the latter being motion of mandoccha ) but applies to +199669 revolutions per Kalpa

(="ayam") which is same as the ayana-calanam (= "sa") as said by Muj la and his followers ( Muj ldi means Muj la and others beginning from Muj la, di means beginning; hence the sense of Muj ldi is not Mujla and others but , Mujla and his followers).

tat pake relates to ayana-calanam.

If one Kalpa of 4320 million years is divided with 199669 given by Muj la, we get one revolution

in 21635.8 years , which is equal to annual motion of 59.9 seconds of arc which was rounded to one minute

of arc by Muj la (read the footnote of Siddhnta iromai's photograph given above which gives the

verses from Muj la about precession). Karana texts use crude numbers in order to facilitate panchanga

making , and after long time when errors accumulate new Karana texts are made from same Siddhnta

(Vsan -B hya of verse 17 -18 says

yad punarmahat klena mahadantaram bhaviyati

tad mahmatimanto brahmaguptdinm samnadharma evotpatsyante

But this crude figure on one minute per year will give 200 , 000 revolutions per Kalpa and not the

figure 199669 said by Muj la. Rationale for 199669 is unexplained. Now , let me summarize the whole

issue :

Verse 17 defines Krnti -Pta, and then gives a figure ,

minus 30000 revolutions per Kalpa as said in Srya-Siddhnta

which Bhskara elaborates in Vsan -Bh ya to be the motion of solar apogee.

The next verse mentions +199669 revolutions of ayana calanam as said by Muj la & others [his school of

thoughts] , and clarifies that the Krnti -Pta defined in preceding verse in same as ayana calanam of

Muj la. But Bhskara does not accept Muj la's notion of Krnti -Pta and says that real motion of Krnti -

Pta should be deduced by combining -30000 with +199669. T his is clear in the third verse (19th) :

tat-samjtam ptam kiptv khee-apama sdhya

krntivat-caram-uday-caradala-lagngame tata kepya

apama means Krnti -Pta = the declination of a planet . (Monier Williams).

khea means planet .

Hence , Bhskara says Uttanapda's pta born out of that / those should be used to deduce declination of a planet.

tat normally is singular , but in samaasa it is used for dual and plural too. Pta means the intersecting point of two circles. Hence , here the [intended] meaning is thus

The pta born out of intersection of circles / ellipses of mandoccha and ayana-calanam should be used for computing declination of planets, and phenomena like chara, udaya-mnas, caradala, lagna, etc., should be computed from this final declination.

What Bhskara says is in current -practice by all pac ga -makers in India. Cara is a term used for intermediate quantities needed in computation of Sunrise , Lagna (ascendant) & others and , is defined as

the difference of rising time a rasi in equatorial plane f rom the rising time of same rasi in ecliptic.

Bhskara says pta born out of tat should be used for deducing declination.

By definition , a pta is a resultant of two entities. Hence , the two entities mentioned in preceding verses

must be combimed to give the Krnti -Pta of Bhskara .

Existing Srya -Siddhnta does not give a motion of -30000 per Kalpa of any entity , while Bhskara

claims Srya -Siddhnta says so. But Bhjaskar says Srya -S iddhnta is gama and therefore must be

accepted as final proof ( prama). Hence , some version of Srya -Siddhnta available to him mentioned -30000 per kalpa as the motion of SOLAR APOGEE.

But Srya -Siddhnta gives a value of only 387 revolutions for sola r apogee , and Siddhnta iromai

gives a figure of 480 per Kalpa (verse 5 in bhagadhyya). Bhskara 's value is +93 more than that given in Srya -Siddhnta. Late NC Lahiri wrote in Advance Ephemeris (page 90) that some corrections were

needed in Srya -Siddhntika figures for making it scientifically correct , and the value of one such term

given by him was equal to nearly 109 revolutions per Kalpa , not too far from Bhskara 's bja correction in

Srya -Siddhntika mandoccha value. But Bhskara never said Srya -Siddhnta was incorrect. Hence ,

there were two versions of Srya -Siddhnta :

1. one was D k -Pak ya, ie related to the phenomanal world revea led directly to the senses , and ,

2. the other was Saura -Pak ya manifest only astrologically.

Astrologers did not preserve the Dk -Pak ya Srya -Siddhnta. Bhskara says Srya -Siddhnta's solar

apogee has a motion of -30000 revolutions per Kalpa , or a period of 144000 years , which is not too far

away from modern value of physical astronomy. Bhskara also says Srya -Siddhnta is itself a PROOF

and needs no other proof for its correctness because it is gama. But the figure of -30000 per kapla is never used in Srya -Siddhnta used and preserved by astrologers , and Bhskara 's own value of 480 per Kalpa

is also near to this version. Hence , he knew about two versions of Srya -Siddhnta. Bhskara 's statement

about gravitational force and its proportionality to distance was also related to sensory (i.e. , material) world.

Deduction of Modern Astronomical Constants from Srya Siddhnta

Kamalkra Bha a (author of Siddhnt -tattva-viveka , as yet untranslated) an ardent supporter of Srya

Siddhnta and an opponent of Bhskara II had strongly advocated in 16 th century that Srya Siddhntika

planets are to be distinguished from the material planets.

In the beginning of 20 th century , terms like Dk -Pak a and Saura -Pak a came into vogue in India ,

to distinguish planets and phenomena of Sensory World from that of Srya Siddhnta .

1. Dk-Paka meant the world perceived by means of sense organs , and therefore it denoted the fo ld of modern astronomy , while ,

2. Saura -Pak a denoted the gods of Next World bearing same name as the material planets but being

non -material.

Ketaki system of almanac used t hese concepts in actual practice. But the Srya Siddhntika viewpoint of

Dk -Pak a was never elaborated by anyone. Unfortunately , after the disappearance of the Srya

S iddhntika commentary of ryabha a, the Elder , even the Saura -Pak ya mathematics bec ame obscure ,

and all the commentators kept on repeating hackneyed phrases whose practical significance was clear to

none. Ranganath , Kam alkar a Bha a, Sudh kar a Dvived, Kapile v ara stri etc ., wrote voluminous

comment aries on Srya Siddhnta , elucidating everything except the practical ways of using the formulas

and the Meru -Centric geometrics.

Let us examine some orally transmitted occult theorems of Srya Siddhntika school which show that Dk -

Pak a can be deduced from Saura -Pak a mathematica lly, without the aid of any observatory.

Theorem of Dk-Pakya Sidereal and Tropical Years and of Precessional Period

Saura -Pak ya eccentricity of Sun's elliptic orbit round the centre of Cosmos ( Mt. Meru) is exactly equal to

1/60 (= ) , although Saura -Pak ya 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 and 'pi' by . Then ,

(12)

Ys=[122+12(1+2)]=[36002+0.5+17200]=365.25640000130486608685495644391 days

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) wil l be

demonstrated later , let us first get the value of mean sidereal year with the help of following equation :

(13)

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

Now we can get the Period of Preces sion PP :

(14)

PP=Yt(YsYt)=25789.488323276570161593347095778 years

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 :

(15)

Ms=Ys(YsMss1)=29.53058780664716371374 days.

Metonic Year Ym is equal to :

(16)

Ym=235Ms19=365.246743924320182775185653635 days

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

(17)

PPM1=1(YsYm))=37978.09022183997109169737 years

Precessional Period due to Sun's effect (PPS1) , inter mediate term :

(18)

PPS1=11PP1PPM1=80356.674413324332490977057144470 years

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

(19)

PPS2=1Ys(1Yt1Ym)=80356.674413324332490977057250561 years

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

(20)

Difference=1.32025125210 27 years

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 27 th digit only.

Hence , the computations are highly reliable.

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

(21)

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

(22)

Yt.2=YmPPS=365.24219878124999999999999999999638595267

(23)

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

Dk -Pak ya 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 34 th digit which is due to 34 -digit precisiuon of Windows

Calculator used to obtain above results. The net result is startling : value of 'pi' i s 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 ,

whic h are called coincidences by atheists , and as proofs of Intelligent Design of Universe by believers in God.

Vedic (ie, Srya-Siddhntika) Theorem of Lunar month

M1 = 365.256400001304866086855 / (42/) = 27.321114831446531255657

K1 = M1 / ( Mss - M1 ) = 50056.095658915529

K2 = 4 2000(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 .

K3 = 1 -[(180/)* {(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 Dk-Pakya synodical or lunar month : Ms = [(K4 / K5) -1}/12 = 29.53058780664716371373841555 days.

Sidereal lunar month will b e :

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

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

Lunar Binomial Theorem :

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

A2 = Ys / 365.256400001304866086855

(24)

A=A1A2(42)=0.45270842758190827172

Here is the Lunar Binomial Equation :

(25)

(AM2)+MYs=0

Roots of this binomial are :

M1 = [ -1 + Sqr(1 -(4A*Ys)] / 2A = -29.5305886713712313156 days.

M2 = [ -1 - Sqr(1 -(4A*Ys)] / 2A = +27.32 16613815891770963 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 Mah yugas each , where each Dk -Pak ya Mah yuga = 4.2 mil lion years).

This is the value of Dk -Pak ya correction in Kalpa -Mandoccha , for which Bhskarcrya deduced the

value 93 in Siddhanta iromai and stated Kalpa -Mandoccha to be equal to 480 (= Saura -Pak ya Kalpa

Mandoccha 387 + 93 Dk -Pak ya correction). Its elucidation will be shown later.

Srya Siddhnta states Saura -Pak ya period of precession to be of 24000 years exactly , while modern

value is near the Dk -Pak ya 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 !

Srya Siddhntika 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 (= Creation or S i), 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 sho uld also rotate. But it can be measured only with reference to the non -material

universe or Bhuva -Loka , which is the world of Saura -Pak ya Srya -Siddhnta. Srya -Siddhnta 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 -detre.

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 Saura -Pak ya precession. Hence total

number of Saura -Pak ya tropical years in one creation is equal to 4302936000 + 179289 = 4303115289

years. Divide this number with ( Saura -Vara / Candra -Vara ) = ( Saura -Pak ya Sidereal Year / 12 Saura -

Pak ya synodical months) = 365.258756481481481 / (12*29.53058794607) = 1.0307356481481. The

result is 4174800101.976788423. In it , 4174800000 is the duration of Dk -Pak ya Creation ( =

4200000*71*14 ), and 101.976788423 is the exact value of Dk -Pak ya correction in Kalpa -Mandoccha , for

which we had got a crude value 104.643228673117 above , and Bhskarcrya had got 93. A quantity of

101.976788423 years in 4.1748 billion years is equal to 0.107065 hours in 500 years. Nirmala Candra Lahiri was the secretary of Pac ga Reform Committee of Government of India. He analysed the differencebetween Dk -Pak ya and Saura -Pak ya tithi (elongation of moon) , and found a difference of

0.11 hours in 500 years , which he assumed to be due to error in Srya Siddhntika values (NC Lahiri , 1968 ,

p.90 ).

But Srya Siddhntika 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 Dk -Pak ya solar orbit during one

Creation : Saura -Pak ya value is 387 while Dk -Pak ya value is 489 ( Bhskarc rya-II gave 480 only in

Siddhnta iromai). This Dk -Pak ya rotation of solar ellipse is in addition to the normal Dk -Pak ya

rotation per 136000 years which is the cause behind anomalistic year.

In the same book NC Lahiri gives data of Srya Siddhntika 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 Siddhntika 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 Siddhntika 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.

Siddhntika sidereal year (365.258756481481)and Dk -Pak ya 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 r evolution in 42000 years. For instance , Kaliyuga commenced at Ujjain midnight 17 -18 Feb ,

3102 BCE , when Siddhntika nirayan(=sidereal in Indian system) Mean Sun was at zero longitude. 5106

years later Siddhntika 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 i nteger 42000. It raises a question : if mathematically Siddhntika 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 Siddhntika year with

tropical scientific year , hence this extra difference of 19941 years must be related to precession.

Siddhntika period of precession is 24000 years and scientific period is 25789.4883233 years. Both for m

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 Srya Siddhntika constants !

An excess of 101.9767884 years of anomaly in 4.1748 billion year s as we got above means one year of

anomaly in each 40938727.965116279069767363571421 D k year. Substract one 4 , 200 , 000 D k years

to get another periodic constant of 36738727.965116279069767363571421 years we will need in some

computations needed to get modern value of precessional period. We found precessional period equal to

25789.48832327657 years.

1. Divide the number 36738727.96511627907 as obtained in the previous paragraph with this precessional -period value, and one will get 1424.56211246181876.

,,

=

36738727.96511627907

25789.48832327657 = 1424.56211246181876

2. Now , dividing the value of 25789.4883232765702 with the derived-value amounting to

1424.56211246181876 which stands for (lets call it that way) per dk year value per precessional-lapse .

. = 18.1034495426171053

3. and finally, to get the modern precessional value period as used by scientists , you go about to

substract the previously -derived value from 25789.48832327657

. . = = 25771.3848737339530562881748

Modern valu e [abeit slightly differs but having seeming resemblance to the derived one] is

25771.4021 years .

Ancient Cosmogony and Geography

Srya Siddhntika system is neither heliocentric nor geocentric. It clearly states in Bhoogoladhyaya

that Mt. Meru resides at t he 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 Srya Siddhnta

: 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 evol ved in that region around 4 million years ago. Indian Purnic ttreadition also mention

that modern races of mankind evolved near Meru in 3891194 BCE when the present Mahayuga

commenced. Srya Siddhntika formulae of making true planets from mean ones requi re 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 Purnic authors. Srya Siddhntika universe is much

smaller in comparison to mater ial 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 Srya Siddhntika figure. Ptolemic system is well known , but Srya

Siddhntika system is rather obscure , known to a few initiated brahmanas only. Due to lack of knowledge

of orally transmitted and unpublished portions of original Srya Siddhnta , European commentators believe

that Srya S iddhntika system was influenced by Ptolemy's Almagest.

But those who know the secrets of Srya Siddhnta say that its framework is too complex and

organically self -contrained to have been influenced by any other system. For instance , Srya Siddhntika

daily motions of all planets are exactly equal to a constant , but this rule is not followed in Almagest.

Srya Siddhntika system is based upon a cosmic centre at Meru , which is absent in Almagest.

Srya Siddhntika solar epicycle is equal to 14 yojanas per degree , which is equal to 5040 yojanas for

360 . 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 28.913669 kilometres. Solar epicycle equals to 14 yojanas , which gets reduced to 13:40 at perigee of this elliptical epicycle , which when

divided by 2 gives 2 10 31 which is the maximum value of equation of centre ( manda-phala = difference between mean & true Sun) for Sun.

Srya Siddhntika 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 perf ectly 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 from Girivraja to Mathur proving that siddhantic yoja na

was prevalent in pre -historic era of Girivraja's kings , as mentioned in Mahabharata , but was also intrinsically

related to many native concepts of Srya Siddhnta , discussed in other sections of this article.

The Cycles of Lord Brahm

Every Creation is repeated after 60.24 billion years , in which half or 30.24 billion years comprise

the existence of Universe or Day of Lord Brahm and the other half is Dark Band which is Night of Lord

Brahm. Modern instruments have started to get some faint views of thes e distant bands , which are actually

due to illusion : telescopes reveal only the past states of our Universe but scientists imagine these past

states to be co -existent. Each visible band is actually seven concentric rings of seven universes , each

lasting f or 4.32 billion years (= value for one Kalpa). Present universe is 1.95885115 x 7 = 13.7 billion light

years according to scientists.

The dimension of Time is viewed as Space by them , although Einstein had proved that Time is the fourth

dimension of Space . If some star is 1 billion light years away , it means we are viewing something which

existed one billion years ago , not the present state of that thing , Its present state may be very near to us.

In physical astronomy , orbital elements are not constants , b ut in siddhantic astronomy , everything is

constant. Siddhntika Astronomy is fundamental from which physical (= material = sensorily perceived =

My) is created.

The revised version of Steady State Theory originally propounded by Hoyle-Narlikar which now includes Big Bang Theory is the correct theory, which is in tune with Vedic Astronomy : each universe is created, appears to be expanding in a Big Bang manner due to illusion created by the dimension of Time viewed as dimension of Space, and then collapses, in order to give rise to next Big Banga, hence the theory of Oscillating Universe is joined with Big Bang theory to give a Steady State in the long run. Each existence or Big Bang is Day of Lord Brahm, and Collapse into Cosmic Black Hole is Night of Lord Brahm. There are 72000 such Oscillations in the life of one Brahm ji, after which Brahm ji passes into the navel of Lord Vishnu and next Brahm ji comes. This is Vedic-Purnic view.

Only the most simple and easiest aspects of Srya-Siddhntika mathematics has been presented here. The details are highly intricate and difficult. Kaliyuga is not fit for Srya-Siddhnta and therefore calls it obsolete. The extant text of Srya-Siddhntika provides sufficient clues for unravelling its unwritten marvels.

-Vinay Jha