Modern Equations On Ancient Principles

Deduction of Exact Equations of Modern Astronomy

through Ancient texts of Siddhānta Jyotisha


Sage Vyasa has clearly said in Vishnudarmottara Purāna (विष्णुधर्मोत्तरपुराण) that in examining perceivable events like eclipses etc, where an actual observation is needed, the position of the planets should be further corrected using Drika-Karma corrections so that they can be used in determining the actual event, but these Drik-corrections should never be made use of in computation of Tithis etc :

यन्त्रवेधादिनाज्ञात यद्बीजं गणकैस्ततः। ग्रहणादि परीक्षेत न तिथ्यादि कदाचन।।

Nirnaya Sindhu also states that Suryasiddhānta should be used for knowing invisible results ("Adrishta" or Fortune) :

अदृष्ट-फल-सिध्यर्थ यथार्कगणितं कुरु। गणितं यदि दृष्टार्थ तद्दृष्ट्युद्भव तस्सदा।।

The mathematics of Suryasiddhānta is given in the Narada Purāna too. In all other Purānas too, Suryasiddhānta has been made use of for the purpose of computation and its ideas have been presented at many place. But since the time of Graha-lāghava (cir.1440 AD), materialists have begun to dominate the scene gradually. They consider physical planets to be exactly same as the astrological planets.
Drika-Karma correction (दृक्कर्म-संस्कार) is an essential part of ancient Siddhānta skandha of Jyotisha. But Drika-Karma corrections are never used in finding True Longitudes of planets (Graha-spashtikarana or ग्रह-स्पष्टीकरण) in any ancient Siddhānta text. It is used only when perceivable phenomena like eclipses, heliacal risings and settings (शुक्रादि उदयास्त), etc are needed. Two chief components of Drika-Karma correction are Āksha and Āyana Drika-Karma corrections (आक्ष-दृक्कर्म-संस्कार and आयन-दृक्कर्म-संस्कार) which are explained in ancient siddhāntas, chief of which is Suryasiddhānta. But these two Drika-Karma corrections give only that position of a planet which is needed for predictive astrology, e.g. udayāsta of Jupiter and Venus is needed for determining muhurtas of auspicious events like marriage, sacred thread ceremony, etc. Positions of physical planets as perceived by our eyes is not given by the equations given in any Siddhāntic texts. For this reason, many mediaeval scholars like Ganesha Daivajna of Graha-lāghava or Divākara Daivajna of Makaranda-vivarana declared that Suryasiddhānta has become obsolete and some changes are needed in its formulations or methods. They advocated removal of mandaphalārdha (मन्दफलार्ध) from four corrections made in Mean Longitude of a planet to get True Longitude, forgetting that the fundamental theory of siddhānta texts will become distorted if any one of four corrections is removed. Unfortunately, no siddhānta text or its commentator ever explained the fundamental theory involved in those four corrections of siddhānta texts, namely sheeghra-phalārdha, manda-phalārdha, manda-phala and sheeghra-phal (शीघ्रफलार्ध, मन्दफलार्ध, मन्दफल, शीघ्रफल). Rev Eveneger Burgess, the translator and commentator of Suryasiddhānta, candidly accepted that he could not understand the rationale behind these four corrections even after spending eight years among Indian experts to learn Suryasiddhānta. Other commentator are worse, they neither explained nor admitted their inability to explain. All ancient siddhāntas and Purānas which deal with graha-spashtikarana are unanimous in the applicability and order of aforementioned four corrections, but none of them explain the mathematical reasons and related geometry. Although two madiaeval so-called experts, namely Ganesha Daivajna and Diwakara Daivajna, rejected the applicability of mandaphalārdha, they did not bother to go into the rationale behind either mandaphalārdha or the other three corrections. If mandaphalārdha was rejected, what is the mathematical reason of sheeghra-phalārdha ? Manda-phala and Sheeghra-phala are accepted in modern astronomy too, as equation of centre and reduction of heliocentric to geocentric position respectively. But what about their halves : manda-phalārdha and sheeghra-phalārdha ? Modern astronomy knows no such things as manda-phalārdha and sheeghra-phalārdha. Nobody understands them, but they are taught by Jyotisha departments of Sanskrit universities. Here, a question arises : if no commentator has ever succeeded in unravelling the mathematical logic behind the most essential aspects of siddhānta texts, is not something mysterious about siddhānta texts ? Either all siddhānta texts are wrong or all mediaeval and modern "experts" are ignorants in the field of siddhānta skandha of Jyotisha. A false excuse is invented by some "experts" : these ancient siddhānta texts were accurate in ancient times but have become outdated now. This false logic was first invented by the author of Graha-lāghava, Ganesha Daivajna and is flaunted by majority of modernisers of astrology. Here is the irrefutable proof of falsity of such statements in tabular form, which shows there was no period in known history during which difference between Drik (i.e., perceived, or physical planets) and Saura (i.e., of SuryaSiddhānta) tended towards any minimum value. First table gives the planetary longitudes from both methods, and the second table 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 Drik 343:33:59 001:39:24 304:06:20 320:29:20 238:48:12 310:08:09 050:58:12
Saur 344:09:44 002:18:18 306:00:04 317:26:27 236:14:05 307:10:43 058:18:51
482 Drik 344:18:44 318:25:11 347:52:07 319:15:50 025:16:49 027:27:47 209:22:01
Saur 344:47:48 319:25:52 350:42:50 324:10:33 021:03:18 025:40:02 214:40:16
582 Drik 345:03:34 253:57:54 029:03:14 335:51:57 188:46:46 325:47:33 337:17:06
Saur 345:25:49 258:28:12 031:42:36 343:39:19 185:05:00 322:54:50 342:03:42
682 Drik 345:48:00 215:27:37 073:50:27 358:38:34 342:03:44 028:07:06 128:39:19
Saur 346:03:50 214:34:27 076:53:20 000:13:16 338:05:47 031:01:54 138:56:21
782 Drik 346:33:23 152:21:34 157:55:10 357:25:17 136:30:39 342:28:19 272:56:05
Saur 346:41:49 154:02:50 165:14:47 350:55:52 132:22:37 340:03:29 276:49:23
882 Drik 347:18:01 109:07:50 260:33:02 322:29:25 298:43:55 323:44:48 044:58:58
Saur 347:19:46 107:58:29 261:48:04 320:02:06 295:40:57 335:09:06 051:04:16
982 Drik 348:02:48 052:09:32 311:52:48 324:01:45 085:44:25 359:21:07 205:23:02
Saur 347:57:41 052:17:24 312:05:43 328:07:58 081:53:55 357:30:27 209:48:18
1082 Drik 348:48:22 000:17:10 355:34:55 341:21:32 253:17:16 302:24:10 335:41:00
Saur 348:35:35 000:24:57 356:47:17 347:45:54 251:39:09 301:33:34 337:05:04

Tropical longitudes have been chosen for this comparison so that the controversies related to ayanāmshas do not intervene. The differences are clearly due to Manda-phalārdha and Sheeghra-phalārdha, because the difference in mean value of longitudes will result in a linear increase in difference with time which is not the case, while the differences in manda-phala plus sheeghra-phala will also show another line of linear increase in difference with time, because both Drik and Saura systems use Mandaphala as well as Sheeghraphala. Even if Mandaphalārdha is discarded, as Ganesha Daivajna proposed, this non-linear anomaly does not vanish, because differences due to sheeghraphalārdha are much more than those due to mandaphalārdha.

Difference in Tropical Planetary Longitudes : Drik 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 siddhāntic values of mandaphala-paridhi or sheeghra-phala-paridhi can reduce this anomaly, because those changes will be linear while actual difference is highly non-linear, ranging from over +6 degrees to less than -11 degrees, which is an unacceptably high anomaly because Aryabhata or Varahamihira and all other scholars could not be so great fools to have failed to notice such errors. Had Suryasiddhānta 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 planets also have very high divergences. Actually, it is around 2000 AD when sidereal differences in longitudes of Drik and Saura planets become minimum (whatever be the value of ayanāmsha), 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 Suryasiddhānta was not created on the basis of observation of physical planets. This result conforms with the statements in Suryasiddhānta and all other available siddhāntas and texts like Nārada Purāna mentioned above, which say Drik positions should not be used in Phalita Jyotisha.
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 siddhāntas, what is the rationale and what is the use of such siddhāntas ? The utility aspect is very simple to answer : predictive astrology, although this utility of siddhāntas 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 and 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 Suryasiddhānta on the criterion of predictive astrology. Not only anti-astrologers, but even supporters and users of Vedic Astrology using Drik astronomy are not ready to test Suryasiddhāntic astrology without any bias. During past few decades, I have found only a handful of Drik-supporters ostensibly ready to test Suryasiddhāntic 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 interest in Jyotisha. Therefore, Suryasiddhāntic astrology is used by a few among internet astrologers. But even today, overwhelming majority of traditional panchāngas are made with some mediaeval tables which have been either directly created by means of Suryasiddhānta (such as Makaranda Tables) or were indirectly based on some earlier source derived from Suryasiddhānta (such as South Indian Vākya texts). For those who are not ready to test the validity of Suryasiddhānta just because its planetary positions do not tally with physical planets, is not any method available to prove the validity of Suryasiddhānta? The following sections outline some of the answers to this question.

DECLINATION: Deduction of Modern Equation from Suryasiddhānta

The apparent path of Sun (Ecliptic) is slanted on the projection of Equatorial Plane by a variable amount which is about 23.4393 degrees at present according to modern astronomy but this value is exactly equal to 24 degrees according to Suryasiddhānta. If both modern astronomy and Suryasiddhānta describe the same Sun, then Suryasiddhānta is certainly a wrong text. But if the integral Suryasiddhāntic values give the results obtained through modern astronomy with a very high degree of precision through simple Drik-karma correction, what should we deduce ? As cited above, Sage Vyāsa Ji sais that perceived positions of planets should be obtained by means of finding proper beeja-corrections. Let us take the case of Declination of Sun for any given date, for which the Suryasiddhāntic 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 siddhāntic 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 siddhāntic equation mentioned above can be comfortably used to create modern table of solar declination,provided we replace siddhāntic 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 siddhāntic equation cited above with reference to Lahiri's table below. Out of 180 entries in the table at intervals of one degree, 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 siddhāntic equation of declination was
absolutely correct, excepting the effect of nutation which was never used in any siddhānta. Has any historian of science ever credited Suryasiddhānta 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" Suryasiddhānta which is supposedly lost, while so-called "modern" Suryasiddhānta is of a much later unspecified date. But it has been shown in this paper that the so-called modern Suryasiddhānta 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-siddhānta was capable of finding such a fine formula for computing declination, why the value of maximum 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 : Suryasiddhāntic equation of Declination can give exact modern values of solar declination down to the limit of less than one arc-second. Two beeja corrections are needed. The major correction is simple : multiply the Suryasiddhāntic 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 degrees which is only 16 arc-seconds more than modern value obtained by NASA scientists. Its geometric implication is that Drik ecliptic is exactly 12 degrees slanted to Saura ecliptic, which means Drik Sun is a completely different entity than the Saura Sun. Now comes the second beeja-correction

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

where 'M/2' is maximum possible value of siddhāntic manda-phalārdha, which Ganesha Daivajya and his followers tried foolishly to expel from traditional astronomy without understanding its significance. Maximum mandaphala is equal to 2°:10':32" according to Suryasiddhānta. 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 siddhāntic values are changeless which scientists may like to explain as long-term average. This siddhāntic value is equal to NASA's value for 2000 AD, which confirms another major finding that with proper ayanāmsha the period of minimum difference between sidereal siddhāntic solar longitude with sidereal Drik longitude was 2000 AD, as mentioned in previous section. Here only summarized results of many important themes are shown.


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

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

Here, Lm" is the latitude of Moon to be known, Lm is the maximum possible Latitude of Moon, while 'Moon' and 'Rahu' are their longitudes, tropical or sidereal. The only problem is Lm, whose value in modern astronomy is higher than in Suryasiddhānta. In Suryasiddhāntic system, planets are not physical bodies, hence have no masses and gravitation. Therefore, there is no effect of barycentre. Second effect is of Meru. Suryasiddhāntic astronomy is Merucentric and not geocentric (Ptolemaic astronomy was also not geocentric ; geocentricity is a wrong propaganda of mediaeval Church). If we take these two effects into account, it is easy to compute Lunar latitude of modern astronomy from Suryasiddhāntic terms.
Suryasiddhānta has maximum lunar latitude equal to 4.5 degrees. Multiply its sine with the distance of Earth's centre to the tip of Mt Meru (Mt Kenta) at equator, which is 6383.362 Kms. We get 500.8328 Kms which is equal to 0.001302891538 multiplied with Moon's average distance from Earth. Substract it from Sine of 4.5 degrees which is siddhāntic maximum latitude of Moon, and get the arc-sine of the result. Thus we get the reduced latitude due to effect of Merucentricity 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 Drik 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 explanation is lengthy and tedious.
This is a crude method, taking help from mass ratio, which is un-siddhāntic. Siddhāntic corrections in Saura latitude to get Drik lunar latitide is easy, but requires such terms whose explanation is highly complicated. Even the crude method given above is enough to show that siddhāntic terms are neither wrong nor outdated, but need Drik corrections to make Saura entities visible.
The complicated geometrix around a few yojanas around the tip of Mt Meru (Mt Kenya) is required to get the Drik corrections to get Drik Sunrise from siddhāntic equations of Sunrise. (This was published in a Hindi book by me in 2005 AD.)

Maximum mandaphala of Moon is 5°02'48" in Suryasiddhānta, but 6°17'19.7" or 22639.7" in modern astronomy (cf. NC Lahiri's Panchanga Darpana). Take the difference of sine of mandaphalārdha of both, which is same as difference of Saura and Drik eccentricies. Multiply it with distance of Moon and add the Meru correction of 500.8328 Kms deduced above, the resultant will be barycentre with 83 Km anomaly whose reason lies again in the intricate mathematics around the tip of Mt Meru. If this small anomaly is neglected, Drik mandaphala of Moon can be thus deduced from Saura Moon's terms. Adding effects of barycentre to Meru's effect, we get Drik Mandaphala of Moon.
Hitherto, some simple terms were being discussed, but now let us get something out of Suryasiddhānta 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 terms 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 Ākāsha), and therefore these equations need revisions after few years. The above equation deduced siddhāntically conforms with Lahiri's and later equations admirably, and perfectly satisfies the procedures of differential calculus perfectly for 2000 AD when Drik and Saura universes coincided (it happens at intervals of 42000 years). Here is the siddhāntic explanation of the most troublesome equation of modern physical astronomy, the equation of Mean Moon (converted into Nirayana following NC Lahiri's method) :
The siddhāntic equation for deducing any term in the above equation is this :

Ys is siddhāntic nirayana year equal to 365.258756481481481… saavana days,
Yd is Drik tropical year equal to 365.24219878125 days,
n is the number of term in the following differential equation of Nirayana 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 siddhāntic mandochcha (apogee) in one Kalpa
(one Kalpa is of 4320 million years),
K is deduced siddhāntically in following manner :
K = [{(Ys-Yd) / Ys} - (1/42000)]-1 x (Ys / t)
= 464.65408706471303027753666827
Then the wanted term in the siddhāntic equation of Drik Nirayana Mean Moon is
Mn = [360° / (n - 1)! ] x [ t x [{ 1 + ( 1 / 387 ) } / K ] n ]
Following is my siddhāntic Drik formula of Nirayana Mean Moon created from above equation, published in Hindi in 2005, built from purely Suryasiddhāntic terms using Taylor's and Lagrange's formulas of modern differential calculus :

\begin{equation} Nirayana Mean Moon = 261:10':1.24" + (17325593.803064287678" * T) \end{equation}
\begin{equation} +{10^{0}} * 6.0337456626113312731046134872458" * {t^2} \end{equation}
\begin{equation} +{10^{-3}} * 6.5095055710038624734367" * {t^3} \end{equation}
\begin{equation} +{10^{-6}} * 4.681852716188407032" * {t^4} \end{equation}
\begin{equation} +{10^{-9}} * 2.525508037859365516483207" * {t^5} \end{equation}
\begin{equation} +{10^{-12}} * 1.0898575817626111529246014535145" * {t^6} \end{equation}
\begin{equation} +{10^{-15}} * 0.39193089427273663825034568365639" * {t^7} \end{equation}
\begin{equation} +{10^{-18}} * 0.12080988126146805887553801248113" * {t^8} \end{equation}
\begin{equation} +{10^{-21}} * 0.03258393040897135345673870555868" * {t^9} \end{equation}
\begin{equation} +{10^{-24}} * 0.0078118151691312247782389032276435" * {t^{10}} + ... ... \end{equation}

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 "Panchānga Darpana". Latest equations do not differ significantly.

\begin{equation} Nirayana Mean Moon = 261:10':1.24" + (17325593.8031" * T) + (6.03" * {t^2}) + (0.0067" * {t^3}) \end{equation}

It is clear that the modern scientific formula is a crude form of the exact siddhāntic equation. Even after supercomputers and other sensitive instruments used by NASA scientists, they have not been able to discover any equation approaching this Vedic equation. Vedic here means based on Vedic-Purānic-Siddhāntic 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 mathematics or pure science. They are guided by their materialist prejudices. But following section is a concrete proof of the fact that the entire SuryaSiddhānta has never been written down.

Evidence Of Lost Portions Of Suryasiddhānta

Modern Value of Precession in Bhāskaracharya's Work based on Suryasiddhānta

In the chapter "Direction, Place and Time" (Suryasiddhānta, Ch.iii), E Burgess writes ;
Quote: (bracketed words are mine) : The (Surya Siddhāntic) 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 degrees 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, Mahāyuga 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".Unquote:
This is the interpretation of existing version of Surya Siddhānta ( त्रिंशत्कृत्यो युगे भानां चक्रे प्राक्परिलम्बते…, 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 (भानां चक्रे.., ie pendulum like motion of nakshatra 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 (iii, 9-12) by putting forth deliberately false arguments. Let us examine Burgess.
In verse-9 (Suryasiddhānta, Ch.iii), 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 merely as "fall back" according to own logic of Burgess. If the circle of asterisms lags roundabout any fixed point (whether Revati or Chitrā), it is a to and fro motion as all traditional commentators accepted. Modern concept of precession is something different from the original concept of ayanāmsha. Theon in West had mentioned this oscillating motion, Arab astronomers also accepted it, and almost 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 known to ancient Indians and Greeks.
Burgess wrongly quotes Bhāskara-II, because he relied upon a wrong translation of Bhāskara by Colebrooke (As. Res., xii 209 ; Essays, ii,374, etc) and did not try to examine Siddhānta Shiromani which was wrongly translated by Lancelot Wilkinson due to Colebrooke's influence. Bhāskara-II did not give his own opinion at all, and merely quoted Surya Siddhānta and Mujjāl (elsewhere Munjāla and Manjula), saying Suryasiddhānta gives -30000 revolutions of sampāt or equinoctial point per Kalpa while ayana has a motion of +199669 revolutions per Kalpa (of 4320 million years). Bhāskara's own opinion was that these should be followed, which means both Surya Siddhānta and Mujjāla were correct in Bhāskara's opinion. Colebrooke, Burgess, Wilkinson, etc have misquoted Siddhānta Shiromani 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 Sharmā is correct, although he could not get the real meaning.

The startling fact is that Siddhānta Shiromani 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 Suryasiddhānta, while Mujjala's value of ayana's motion is +199669, and both (Suryasiddhānta and Mujjala ) must be added to get the final motion (of the equinox ). Hence, we get +169669 revolutions per Kalpa, which gives (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 Siddhānta Shiromani'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 Siddhānta Shiromani is still being misinterpreted by foreigners, and if a true rendering is offered by Indian scholars, they are abused, esp by those who do not care to consult the originals and declare the forign missionaries to reliable. Bhāskara-II neither excluded Suryasiddhānta, nor Mujjāla, but mentioned the both must be used, which is clear from verse-19, where he clearly asks to add Mujjāla's ayana-chalam to Suryasiddhāntic sampāt-chalanam (this sampāt-chalanam is anomalistic precession with a period of 144000 years per cycle, not far from modern value).
Another startling fact is that Bhāskara-ii differentiates sampāt-chalanam of Suryasiddhānta from ayana-chalanam of Mujjāla, and says both must be added before computing phenomena like declension, ascensional differences, etc. But modern commentators like Colebrooke misinterpret Bhāskara-II deliberately, and imply that sampāt-chalanam of Suryasiddhānta quoted by Bhāskara-ii was an erroneous thing which must be forgotten, while ayana-chalanam of Mujjāla was a crude approximation of modern precession. But this interpretation is falsified by Bhāskara's original verses (and his own commentary Vāsanābhāshya) as shown above. The root of this problem lies in the fact that sampāt-chalanam of Suryasiddhānta is a distinct phenomenon from ayana-chalanam of Mujjāla according to Siddhānta Shiromani, but readers are not informed of the real meaning of Siddhānta Shiromani and false quotation from Siddhānta Shiromani was quoted by Colebrooke and Burgess (12th verse, chap.iii). This is a sign of intellectual incompetence and dishonesty of Western "experts" who are blindly followed by brown sāhibs of India. Those who do not consult the original texts cited above will not believe me.
Siddhānta-tattva-viveka by Kamlākara Bhatt is a medieval text, which clearly states that Saurpaksha is distinct from Drikpaksha. Saurpaksha (astronomy of bhuvaloka) is Suryasiddhānta as it exists. Drikpaksha (astronomy of Bhooloka or physical/material/sensory world) is that version of Suryasiddhānta which was not preserved because it was useless in astrology. Siddhānta Shiromani uses many concepts of Drikpakshiya astronomy, as the instance cited above proves. Saurpakshiya Suryasiddhānta does not contain any refence to 30000 cylces per Kalpa mentioned by Bhāskara-II. He was quoting from Drikpakshiya Suryasiddhānta which as a text had been lost ; Bhāskara-II said in his own Vāsanābhāshya commentary of Siddhānta-shiromani that Suryasiddhānta is "āgama". Modern commentators confuse both variants of Suryasiddhānta. Siddhāntatattvaviveka is prescribed in post-graduate (Ganitāchārya) syllabus of Sanskrit universities, but no modern commentator has ever tried to translate it or comment on it.
According to Bhāskara-ii , negative sampāt-chalanam of Drikpakshiya Suryasiddhānta should be added to positive ayana-chalanam of Mujjāla to get final Drikpakshiya precession, which is very close to modern value. Ayana-chalanam of Mujjāla is also Drikpakshiya, because Saurpakshiya entities are not used in Drikpakshiya astronomy, and vice versa. I have put some of the most important extant theorems of Drikpakshiya Suryasiddhānta 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.
Mujjāla's ayana-chalanam, as mentioned in Siddhānta Shiromani, gives a period of (4320 million / 199669 = ) 21636 years per cycle. Siddhānta Shiromani says that it is ayanachalanam according to Munjala & his followers but it was not accepted as precession by Bhaskara, precession is obtained after substracting (Saurpakshiya) Suryasiddhāntic sampātchalanam. If this 21636 year cycle is not precession, what is it ??
Readers should read a Wikipedian article Milankovitch cycles ( ) 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." (at some sites of NOAA of USA, 22000 is mentioned instead of 21000)
Ayana-chalanam of Mujjāla 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 Siddhānta Shiromani, the aforementioned Wikipedian clause can be rewritten 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.
Siddhānta Shiromani also says that Mujjāla's ayana-chalanam (21,636 years per cycle) is opposite to sampāta-chalanam. Bhāskara-ii clearly defines sampāta-chalanam as "the point of intersection of equatorial plane and ecliptic" (which is the very definition of equinox). Hence, what Siddhānta Shiromani says is exactly what Wikipedia informs us, the only difference is that Siddhānta Shiromani is misinterpreted and declared to be obscurantist, and the great cycles mentioned in Siddhānta Shiromani is "discovered" by 20th century scientists. But we must remember Bhāskara-ii did not discover these things, he acknowledged Suryasiddhānta and Munjāla.
Bhāskara-ii knew Drikpakshiya Suryasiddhānta, which has not survived because it was not useful in astrology. In his formula of precession, Bhāskara-II used a figure 30000 cycles per Kalpa. Bhaskara-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 Purānic verse which proves knowledge of equinoctial precession in Purānic times :

उत्तानपादपुत्रोऽसौ मेढीभूतो ध्रुवो दिवि । स हि भ्रमन् भ्रामयते नित्यं चन्द्रादित्यौ ग्रहैः सह ।।

It means : "Uttanpāda'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 ? Mt Meru, which is the only fixed point in Cosmos according to Purānic-epic stories. Hence, the bhachakra also librates with respect to this fixed point Meru.
According to Bhāskara-II, orbital precession is derived by substracting anomalistic precession (sampāt-chalanam) from the first component of Milankovitch cycles (Munjāla's ayana-chalanam). Bhāskara-II acknowledged earlier authors. Hence, we must conclude that modern values and concepts of orbital precession, anomalistic precession, Milankovitch cycles, etc were known to ancient Indians well before Bhāskara-ii.
But two things about confusing terminology must be borne in mind : this sampāt-chalanam he finally gets by combining the two quantities mentioned above. According to Bhāskara-II, Suryasiddhāntic sampāt-chalanam is 30000 per Kalpa. He does not give a name for the term which is finally obtained by combining this sampāt-chalanam with Munjāla's ayana-chalanam, but the definition he provides for Suryasiddhāntic sampāt-chalanam is exactly the definition of the final quantity whose name he does not provide. Hence, there were many types of sampāt-chalanams !! This is not a case of confusion of terms. It is a result of Saurpakshiya term with Drikpakshiya terms bearing same names but having different magnitudes and sometimes even having difference in basic properties !
Second confusion is due to use of the term ayana-chalanam for Munjāla's precession. It is quite distinct from Saurpakshiya Suryasiddhāntic ayana-chalanam (trepidation) as mentioned in existing text. Burgess could not digest this theory of libration (oscillation or trepidation, ie, ayanāamsha - motion) and tried to distort the meaning of terms to fit modern view of orbital precession with this Saurpakshiya precession. Bhāskara-ii knew and respected Suryasiddhānta which he cited and used in his computations as shown above, and gave exact value of Drikpakshiya precession. Therefore, it is foolish to impose Drikpakshiya precession (50.9" per year according to Bhāskara-II, 50.3" really) upon Saurpakshiya ayanamsha (54" per year, oscillating within a range of ± 27 degrees). (There are further corrections on Drikpakshiya precession which give a final value of one revolution in 25771.4 years, exactly equal to the value deduced by NASA - 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 Siddhānta Shiromani for those who want first hand proof, followed with discussion on its obscure passages :

vAsanA-bhASHya commentary by Bhaskara-ii on his own work Siddhānta Shiromani has never been translated or explained. Bhaskar-ii knew Siddhānta Shiromani will be misunderstood, hence he wrote its commentary vAsanA-bhASHya himself. This commentary also needs a commentary. In it, Bhaskar clearly writes that "sa evaayam" refers to "krAntipAta" and not to ayanachalanam. If verses 17-19 are taken together, we have six lines, and "sa evaayam" occurs in third line, which says that the ayanachalanam as defined by Munjaala &c is same as krAntipAta defined in first line.
This meaning from vAsanAbhASHya is further reinforced in same passage in vAsanAbhASHya which says that the second line (minus 30000 revolutions per Kalpa) must refer not to krAntipAta but to "motion of apogee" ("tatra mandochcha pAtAnAm gatirasti"). Thus, Bhaskar has made it clear that the definition of krAntipAta as given in first line applies not to -30000 revolutions per Kalpa ( the latter being motion of mandochcha) but applies to +199669 revolutions per Kalpa (="ayam") which is same as the "ayanachalanam" (= "sa") as said by Munjaala and his followers (munjAlAdi means munjAla and others beginning from munjAla, "Adi" means "beginning" ; hence the sense of munjAlAdi is not "munjAla and others" but "munjAla and followers of munjAla").
"tatpakSHe" relates to ayanachalanam. If one Kalpa of 4320 million years is divided with 199669 given by Munjaala, 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 munjAla (read the footnote of Siddhānta Shiromani's photograph given above which gives the verses from munjAla 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 Siddhānta (vAsanAbhASHya of verse 17-18 says : "yadA punarmahatA kAlena mahadantaram bhaviSHyati tadA mahAmatimanto brahmaguptAdinAm samAnadharmANa evotpatsyante"). But this crude figure on one minute per year will give 200000 revolutions per Kalpa and not the figure 199669 said by Munjaala. Rationale for 199669 is unexplained. Now, let me summarize the whole issue :
Verse 17 defines krAntipAta, and then gives a figure "minus 30000 revolutions per Kalpa as said in SuryaSiddhānta" which Bhaskar elaborates in vAsanAbhASHya to be the motion of solar apogee. The next verse mentions +199669 revolutions of ayanachalanam as said by Munjaala &c, and clarifies that the krAntipAta defined in preceding verse in same as ayanachalanam of munjAla. But Bhaskara does not accept munjAla's notion of krAntipAta and says that real motion of krantipAta should be deduced by combining -30000 with +199669 : this is clear in the third verse (19th) :
"tat-samjAtam pAtam kSHiptvA kheTe-apamaH sAdhyaH // krAntivashAt-charam-udayaAsh-charadala-lagnAgame tataH kSHepyaH"
apamaH means krAntipAta ("the declination of a planet" - Monier Williams). kheTa means "planet". Hence, Bhaskara says : "pAta 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. pAta means the intersecting point of two circles. Hence, here the meaning is thus : the pAta born out of intersection of circles / ellipses of mandochcha and ayanachalanam should be used for computing declination of planets, and phenomena like chara, udayamaanas, charadala, lagna, etc should be computed from this final declination. What Bhaskara says is practised by all panchanga makers in India. Chara is a term used for intermediate quantities needed in computation of Sunrise, Lagna (ascendant), etc, and is defined as the difference of rising time a rasi in equatorial plane from the rising time of same rasi in ecliptic.
Bhaskara says pAta born out of "tat" should be used for deducing declination. By definitipon, pAta is a resultant of two entities. Hence, the two entities mentioned in preceding verses must be combimed to give the krAntipAta of Bhjaskar.
Existing SuryaSiddhānta does not give a motion of -30000 per Kalpa of any entity, while Bhaskara claims SuryaSiddhānta says so. But Bhjaskar says SuryaSiddhānta is "Agama" and therefore must be accepted as final proof ("pramANa"). Hence, some version of SuryaSiddhānta available to him mentioned -30000 per kalpa as the motion of SOLAR APOGEE. But SuryaSiddhānta gives a value of only 387 revolutions for solar apogee, and Siddhāntashiromani gives a figure of 480 per Kalpa (verse 5 in bhagaNAdhyAya). Bhaskar's value is +93 more than that given in SuryaSiddhānta. Late NC Lahiri wrote in Advance Ephemeris (page 90) that some corrections were needed in SuryaSiddhāntic 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 Bhaskar's beeja correction in SuryaSiddhāntic mandochcha value. But Bhaskar never said SuryaSiddhānta was incorrect. Hence, there were two versions of SuryaSiddhānta : one was Drik-pakshiya, ie related to the phenomanal world revealed directly to the senses, and the other was Saurapakshiya manifest only astrologically. Astrologers did not preserve the Drikpakshiya SuryaSiddhānta. Bhaskar says SuryaSiddhānta'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. Bhaskar also says SuryaSiddhānta is itself a PROOF and needs no other proof for its correctness because it is aagama. But the figure of -30000 per kapla is never used in SuryaSiddhānta used and preserved by astrologers, and Bhaskar's own value of 480 per Kalpa is also near to this version. Hence, he knew about two versions of SuryaSiddhānta. Bhaskara'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 Surya Siddhānta

Kamlakara Bhatt(author of Siddhānt-tattva-viveka,as yet untranslated),an ardent supporter of Surya Siddhānta and an opponent of Bhaskara II,had strongly advocated in 16th century that Surya Siddhāntic planets are to be distinguished from the matererial 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 Siddhānta. Drik-paksha meant the world perceived by means of sense organs, and therefore it denoted the foeld of modern astronomy, while Saurpaksha denoted the gods of Next World bearing same name as the material planets but being non-material. Ketaki system of almanac used these concepts in actual practice. But the Surya Siddhāntic viewpoint of Drikpaksha was never elaborated by anyone.Unfortunately, after the disappearance of the Surya Siddhāntic 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 commentories on Surya Siddhānta, elucidating everything except the practical ways of using the formulas and the Merucentric geometrics.

Let us examine some orally transmitted occult theorems of Surya Siddhāntic school which show that Drikpaksha can be deduced from Saurpaksha mathematically, without the aid of any observatory.

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 (= 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,

\begin{align} Ys' = [{1\over {π^2} * {ε^2}} + {1 \over 2}(1+ε^2)] = [{3600\over {π^2}} + 0.5 + {1\over 7200}] = 365.25640000130486608685495644391 days \end{align}

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 :

\begin{align} Ys = {({Ys'+1})\over ({1+{1\over Yt}}) } = {366.256400001304866086855 \over {1+ {1\over 365.24219878125}}} = 365.25636122581667241689259003252668 days \end{align}

Now we can get the Period of Precession PP :

\begin{align} PP = {Yt \over ( Ys - Yt )} = 25789.488323276570161593347095778 years \end{align}

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.

[ Ignoring manvantara-correction for 71 Drik mahayugas of 42 lakh years each, we get Lahiri's erronrous annual precession of 50.25737878" per year (his value was 50.25748 p.a.). ]

Let sidereal lunar month be equal to :

Mss = 27. 321660641391789747802454274321 days, which will be proven later. Then, synodic month Ms will be :

\begin{align} Ms = {Ys\over ({{Ys\over Mss} -1 })} = 29.53058780664716371374 days. \end{align}

Metonic Year Ym is equal to :

\begin{align} Ym = {235 Ms \over19} =365.246743924320182775185653635 days \end{align}

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

\begin{align} PPM1 = {1 \over {{({Ys \over Ym})}-)}} =37978.09022183997109169737 years \end{align}

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

\begin{align} PPS1 = {1\over {{1\over PP} - {1\over PPM1}}} =80356.674413324332490977057144470 years \end{align}

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

\begin{align} PPS2 = {1\over {Ys({{1\over Yt} - {1\over Ym}})}} =80356.674413324332490977057250561 years \end{align}

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

\begin{equation} Difference = {1.320251252 * 10^-27} years \end{equation}

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) :

\begin{align} Yt.1 = {Ym \over { 1 + { 1 \over ( PPS1 + A1 )}}} = 365.24219878124999999999999999999638527125 \end{align}
\begin{align} Yt.2 = {Ym \over PPS}= 365.24219878124999999999999999999638595267 \end{align}
\begin{align} Yt.3 = {Ym \over { 1 + { 1 \over ( PPS2 + A2 )}}} = 365.2421987812499999999999999999999999972349 \end{align}

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.


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


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

\begin{align} A = A1 * A2 * ({42\over π}) = 0.45270842758190827172 \end{align}

Here is the Lunar Binomial Equation :

\begin{equation} {(A*M^2)} + M -Ys = 0 \end{equation}

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 (= Saurpakshiya Kalpa Mandochcha 387 + 93 Drikpakshiya correction). Its elucidation will be shown later.


Surya Siddhanta states Saurpakshiya period of precession to be of 24000 years exactly, while modern value is near the Drikpakshiya value of PP deduced above ( = 25789.4883233 years). Let us see its logic.

1/K' = (1/24000) - (1/25789.4883233) = 1/ 345879.71975438125
Mt = Mss - (Mss/K') = 27.32158164959469683453 days.
This constant Mt is the modern value of tropical sidereal lunar month !


Surya Siddhāntic 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 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 Suryasiddhānta. Suryasiddhānta 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 Siddhāntic values(NC Lahiri,1968,p.90). But Surya Siddhāntic 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 Siddhāntashiromani). 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 Siddhāntic 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 Siddhāntic 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 Siddhāntic 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.

Siddhāntic 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 Siddhāntic nirayan(=sidereal in Indian system) Mean Sun was at zero longitude. 5106 years later Siddhāntic 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 Siddhāntic 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 Siddhāntic year with tropical scientific year, hence this extra difference of 19941 years must be related to precession. Siddhāntic 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 Siddhāntic constants !

An excess of 101.9767884 years of anomaly in 4.1748 billion years as we got above 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. We found precessional period equal to 25789.48832327657 years. Divide the number 36738727.96511627907 obtained in previous paragraph with this value of precessional period, one will get 1424.56211246181876. Now, divide 25789.4883232765702 with 1424.56211246181876 to get 18.1034495426171053 and substract the latter from 25789.48832327657 to get the modern value of precessional period used by scientists : 25771.3848737339530562881748. Modern valus is 25771.4021 years.

Ancient Cosmogony and Geography

Surya Siddhāntic 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 Siddhānta : 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 Purānic ttreadition also mention that modern races of mankind evolved near Meru in 3891194 BCE when the present Mahayuga commenced. Surya Siddhāntic 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 Purānic authors.
Surya Siddhāntic 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 Siddhāntic figure. Ptolemic system is well known, but Surya Siddhāntic 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 Siddhānta, European commentators believe that Surya Siddhāntic system was influenced by Ptolemy's Almagest. But those who know the secrets of Surya Siddhānta say that its framework is too complex and organically self-contrained to have been influenced by any other system. For instance, Surya Siddhāntic daily motions of all planets are exactly equal to a constant, but this rule is not followed in Almagest. Surya Siddhāntic system is based upon a cosmic centre at Meru, which is absent in Almagest. Surya Siddhāntic 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 28.913669 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 Siddhāntic 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 from Girivraja to Mathura proving that siddhantic yojana was prevalent in pre-historic era of Girivraja's kings, as mentioned in Mahabharata, but was also intrinsically related to many native concepts of Surya Siddhānta, discussed in other sections of this article.

The Cycles of Lord Brahmā

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 Brahmā and the other half is Dark Band which is Night of Lord Brahmā. Modern instruments have started to get some faint views of these 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 for 4.32 billion years (one Kalpa). Present universe is 1.95885115 multiplied with 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, but in siddhantic astronomy, everything is constant. Siddhāntic Astronomy is fundamental from which physical (=material = sensorily perceived = Māyā) is ctreated.

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 Brahmā, and Collapse into Cosmic Black Hole is Night of Lord Brahmā. There are 72000 such Oscillations in the life of one Brahmā ji, after which Brahmā ji passes into the navel of Lord Vishnu and next Brahmā ji comes. This is Vedic-Purānic view.

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

-Vinay Jha

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