Modern Equations On Ancient Principles Deduction of Exact Equations of Modern Astronomy through Ancient texts of Siddhānta Jyotiṣa 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 : Dṛk vs Saura, in Arc-Sec ................................................................. 5 DECLINATION: Deduction of Modern Equation from Sūrya-Siddhānta .................................................................... 7 LATITUDE OF MOON....................................................................................................................................................... 9 Exact Differential Equation Of Physical Moon.............................................................................................................. 10 Evidence Of Lost Portions Of Sūrya-Siddhānta............................................................................................................. 12 Deduction of Modern Astronomical Constants from Sūrya Siddhānta ..................................................................... 20 Theorem of Dṛk-Pakṣīya Sidereal and Tropical Years and of Precessional Period .............................................. 21 Vedic (ie, Sūrya-Siddhāntika) Theorem of Lunar month ........................................................................................ 23 Lunar Binomial Theorem : .......................................................................................................................................... 24 Sūrya Siddhāntika Theory of the Rotation of Material Universe ................................................................................ 25 Ancient Cosmogony and Geography .............................................................................................................................. 27 The Cycles of Lord Brahmā ......................................................................................................................................... 28
INTRODUCTION Viṣṇu Dharmottara Purāṇa of Vedavyāsa — य
वेधा द ना ात य ीजं गणकै ततः । हणा द परी ेत न ित या द कदाचन ॥
yantra vedhādi nājñāta yad bījaṃ gaṇakaistataḥ । grahaṇādi parīkṣeta na tithyādi kadācana ॥ Sage Vyāsa has clearly said in Viṣṇudharmottara Purāṇa (िव णुधम
रपुराण) that in examining perceivable
events like eclipses etc., where an actual observation is needed, the position of the planets should be further corrected using Dṛk-Karma corrections (i.e., adding the Ayanāṁśa to get the Tropical longitude) so that they can be used in determining the actual event, but these Dṛk-corrections should never be made use of in computation of Tithis and others.
Nirṇaya Sindhu — अदृ -फल-िस यथ यथाक गिणतं कु । गिणतं य द दृ ाथ त दृ
ु व त सदा॥
adṛṣṭa phala sidhyartha yathārka gaṇitaṃ kuru । gaṇitaṃ yadi dṛṣṭārtha tad dṛṣṭy udbhava tassadā ॥ Nirṇaya-Sindhu also states that Sūrya-Siddhānta should be used for knowing invisible results ("Adṛṣṭa Phala" i.e., things like Destiny or Fortune). The mathematics of Sūrya-Siddhānta is given in the Nārada Purāṇa too. In all other Purāṇas too, SūryaSiddhānta 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.
dṛk-karma correction (दृ म-सं कार) is an essential part of ancient Siddhānta skandha of Jyotiṣa. But dṛkkarma saṃskāra are never used in finding True Longitudes of planets (graha-spaṣṭī-karaṇa | ह- प ीकरण) in any ancient Siddhānta text — It is used only when perceivable phenomena like eclipses, heliacal risings & settings (sūkrādi udayāsta |शु ा द उदया त) etc., are needed. Two chief components of dṛk-karma
correction are
1. ākṣa & āyana dṛk-karma saṃskāra (corrections) (आ -दृ म-सं कार) and 2. ayana-dṛk-karma saṃskāra (आयन-दृ म-सं कार) both of which, are explained in ancient siddhāntas, chief of which is Sūrya-Siddhānta. But these 2 dṛk-karma corrections give only that position of a planet which is needed for phalita
astrology, e.g. udayāsta of Jupiter & Venus is needed for determining Muhūrtas of auspicious events like Vivāha|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 Siddhāntika texts. It is for this reason, many medieval scholars like Gaṇeśa Daivajña of Graha-lāghava or Divākara Daivajña of Makaranda-Vivaraṇa have all declared that the Sūrya-Siddhānta treatise has now become obsolete and some changes are needed in its formulations or methods. They advocated removal of manda-
phalārdha |म दफलाध 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 siddhāntika texts likewise will become distorted. Unfortunately, no any siddhāntika text or its commentator never explained the basis of the fundamental theory involved in those 4 corrections of siddhānta texts, namely— 1. śīghra-phalārdha | शी फलाध, 2. manda-phalārdha |म दफलाध, 3. manda-phala |म दफल and, 4. śīghra-phala |शी फल Rev. Eveneger Burgess, the translator & commentator of Sūrya-Siddhānta, 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 Sūrya-Siddhānta. Other commentators of this text were even worse, they neither explained nor had the humility to admit their inability to explain the WHYs behind these calculations. All ancient Siddhāntas and Purāṇas which deal with graha-spaṣṭī-karaṇa are unanimous in the applicability and order of aforementioned 4 corrections, but none of them explain the mathematical reasoning and related geometry. Although 2 medieval so-called Indian experts, namely Gaṇeśa Daivajña and Divākara Daivajña, rejected the applicability of manda-phalārdha, they did not bother to go into the rationale behind either
manda-phalārdha or even the remaining 3 corrections.
If manda-phalārdha was rejected, what is the mathematical reason of śīghra-phalārdha then?
manda & śīghra phala are accepted in modern astronomy too, as equation of centre and the reduction of heliocentric to geocentric position, respectively. But what about their halves—manda & śīghra phalārdha? Modern astronomy knows NO SUCH THINGS as manda & śīghra phalārdha. Nobody understands them, but surprisingly enough they are taught by Jyotiṣa 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, don’t you think there is something mysterious about siddhānta texts? Either all siddhānta texts are wrong or, all medieval and modern “experts” are ignorants in the field of siddhānta skandha of Jyotiṣa. A false excuse is invented by some “experts” — claiming that these ancient siddhānta 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-lāghava, Gaṇeśa Daivajña 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 —
1. Dṛk and, i.e., perceived, or physical planets
2. Saura, i.e., of Sūrya-Siddhānta 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 382
Sun Dṛk
Moon
Mars
Mercury
Jupiter
Venus
Saturn
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
Dṛk
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
Dṛk
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
Dṛk
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
Dṛk
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
Dṛk
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
Dṛk
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 Dṛk
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 (Sāyana) longitudes have been chosen for this comparison so that the controversies related to Ayanāṁśas do not intervene. The differences are clearly due to manda & śīghra phalārdha, because the difference in mean values of longitude will result in a linear increase in difference with time which is not the case, while the differences in manda-phalārdha plus śīghra-phalārdha will also show another line of linear increase in difference with time, because both dṛk & saura systems use manda as well as śīghra phala. Even if manda-phalārdha is discarded, as Gaṇeśa Daivajña once proposed, still, this non-linear anomaly does not vanish, because differences due to śīghra-phalārdha are much more than those due to manda-
phalārdha.
Difference in Tropical Planetary Longitudes : Dṛk vs Saura, in Arc-Sec AD
Sun
382 482
Moon
Mars
Mercury Jupiter Venus
-2145 - 2334
- 6824
+10973
-1744 - 3641
-10243 -17683
+ 9247
Saturn
+10646 -26439
+15211 + 6465
-19095
582
-1335 -16218 - 9562
682
- 950
+ 3190 -10973 - 5682
-21723
-10488
-37022
782
- 506
- 6076
+14882 + 8690
-13998
882
- 105
+ 4161 - 4502
+ 8839
+10978 -41058
-21918
982
+ 307 - 472
- 775
-14773
+13830 + 6640
-15916
- 4342
-23062
+ 5887
- 5044
1082 + 767 - 467
-28042
-26377 +23365
+13306 +10363 -17196
+ 3036
This highly irregular non-linearity proves that no changes in Siddhāntika values of manda-phala-paridhi or śīghra-phala -paridhi can reduce this anomaly, because those changes will be linear while actual difference is highly non-linear, ranging from over +6° to less than -11°, which is an unacceptably high anomaly because Āryabhaṭṭa or Varāhamihira and all other scholars could not be so great fools to have failed to notice such errors. Had Sūrya-Siddhānta 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 Dṛk and Saura planets become minimum (regardless of the Ayanāṁśa 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
Sūrya-Siddhānta was not created on the basis of observation of
physical planets. This result conforms with the statements in Sūrya-Siddhānta and all other available siddhāntas and texts like Nārada Purāṇa mentioned above, which say Dṛk positions should not be used in Phalita Jyotiṣa. 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 Sūrya-Siddhānta on the criterion of predictive astrology. Not only anti-astrologers, but even supporters and users of Vedic Astrology using Dṛk astronomy are not ready to test Sūrya-Siddhāntika astrology without any bias. During past few decades, I have found only a handful of Dṛk-supporters ostensibly ready to test Sūrya-Siddhāntika 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 Jyotiṣa. Therefore, Sūrya-Siddhāntika astrology is used by a few among internet astrologers. But even today, overwhelming majority of traditional Pañcāṅgas are made with some medieval tables which have been either directly created by means of Sūrya-Siddhānta (such as Makaranda Tables) or were indirectly based on some earlier source derived from Sūrya-Siddhānta (such as South Indian Vākya texts). For those who are not ready to test the validity of Sūrya-Siddhānta just because its planetary positions do not tally with physical planets, isn’t there any method available to prove the validity of Sūrya-Siddhānta? The following sections outline some of the answers to this question.
DECLINATION: Deduction of Modern Equation from Sūrya-Siddhānta The apparent sūrya vīthī — 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 astronomy but this value is exactly equal to 24° according to Sūrya-Siddhānta. If both modern astronomy and SūryaSiddhānta describe the same Sun, then Sūrya-Siddhānta is certainly a wrong text. But if the integral SūryaSiddhāntika values give the results obtained through modern astronomy with a very high degree of precision through simple Dṛk-karma correction, what should we deduce ? As cited above, Sage Vyāsa said that perceived positions of planets should be obtained by means of finding proper bīja-corrections. Let us take the case of Declination of Sun for any given date, for which the Sūrya-Siddhāntika 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 Siddhāntika 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 Siddhāntika equation mentioned above can be comfortably used to create modern table of solar declination, provided we replace Siddhāntika 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 Siddhāntika equation cited above with reference to Lahiri's table below. Out of 180 entries in the table at intervals 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 Siddhāntika 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 Sūrya-Siddhānta 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” Sūrya-Siddhānta which is supposedly lost, while so-called “modern” Sūrya-Siddhānta is of a much later unspecified date. But it has been shown in this paper that the so-called modern Sūrya-Siddhānta 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 — Sūrya-Siddhāntika equation of Declination can give exact modern values of solar declination down to the limit of less than one arc-second. Two bīja corrections are needed. The major correction is simple : multiply the Sūrya-Siddhāntika declination P with the cosine of its exactly halfvalue :
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 Dṛk ecliptic is exactly 12° slanted to Saura ecliptic, which means Dṛk Sun is a completely different entity than the Saura Sun. Now comes the second bījacorrection
Sin D" = Sin D' x Cos M/2 where 'M/2' is maximum possible value of Siddhāntika manda-phalārdha, which Gaṇeśa Daivajya and his followers tried foolishly to expel from traditional astronomy without understanding its significance. Maximum
manda-phala is equal to 2° 10’ 32” according to Sūrya-Siddhānta. 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 Siddhāntika values are changeless which scientists may like to explain as longterm average. This Siddhāntika value is equal to NASA's value for 2000 AD, which confirms another major finding that with proper Ayanāṁśa the period of minimum difference between sidereal Siddhāntika solar longitude with sidereal Dṛk longitude was 2000 AD, as mentioned in previous section. Here only summarized results of many important themes are shown.
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 - Rāhu) x Sin Lm Here, Lm” is the latitude of Moon to be known, Lm is the maximum possible Latitude of Moon, while Moon & Rāhu are their longitudes, tropical or sidereal. The only problem is Lm, whose value in modern astronomy is higher than in Sūrya-Siddhānta. In Sūrya-Siddhāntika system, planets are not physical bodies, hence have no masses and gravitation. Therefore, there is no effect of barycentre. Second effect is of Meru. Sūrya-Siddhāntika astronomy is MeruCentric and not geocentric (Ptolemaic astronomy was also not geocentric; geocentricity is a wrong
propaganda of medieval Church). If we take these two effects into account, it is easy to compute Lunar latitude of modern astronomy from Sūrya-Siddhāntika terms. Sūrya-Siddhānta 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. Kenya) at equator, which is 6383.362 KMs. We get 500.8328KMs which is equal to 0.001302891538 multiplied with Moon's average distance from Earth. Substract it from Sine of 4.5° which is Siddhāntika maximum latitude
of Moon, and get the arc-sine of the result. Thus we get the reduced latitude due to effect of Meru-Centricity 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 Dṛk 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-Siddhāntika. Siddhāntika corrections in Saura latitude to get Dṛk lunar latitide is easy, but requires such terms whose explanation is highly complicated. Even the crude method given above is enough to show that Siddhāntika terms are neither wrong nor outdated, but need Dṛk 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 Dṛk corrections to get Dṛk Sunrise from Siddhāntika 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 Sūrya-Siddhānta, but 6° 17’ 19.7” or 22639.7” in modern astronomy (cf. NC Lahiri's Pañcāṅga Darpaṇa). Take the difference of sine of manda-phalārdha of both, which is same as difference of saura & dṛk eccentricies. Multiply it with distance of Moon and add the Meru correction of 500.8328KMs deduced above, the resultant will be barycentre with 83KM anomaly whose reason lies again in the intricate mathematics around the tip of Mt. Meru. If this small anomaly is neglected, dṛk manda-phala of Moon can be thus deduced from Saura Moon's terms. Adding effects of barycentre to Meru's effect, we get dṛk manda-phala of Moon. Hitherto, some simple terms were being discussed, but now let us get something out of Sūrya-Siddhānta 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 Ākāśa), and therefore these equations need revisions after few years. The above equation deduced Siddhāntikaally conforms with Lahiri's and later equations admirably, and perfectly satisfies the procedures of differential calculus perfectly for 2000 AD when dṛk & saura universes coincided (it happens at intervals of 42000 years). Here is the Siddhāntika explanation of the most troublesome equation of modern physical astronomy, the equation of Mean Moon (converted into Nirāyaṇa following NC Lahiri's method):
The Siddhāntika equation for deducing any term in the above equation is this —
Ys is Siddhāntika Nirāyaṇa year equal to 365.258756481481481… Sāvana days, Yd is Dṛk tropical year equal to 365.24219878125 days, n is the number of term in the following differential equation of Nirāyaṇa 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 Siddhāntika mandoccha (apogee) in one Kalpa (1 Kalpa = 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 Siddhāntika equation of Dṛk Nirāyaṇa Mean Moon is
Mn = [360° / (n - 1)! ] x [ t x [{ 1 + ( 1 / 387 ) } / K ] n ]
Following is my Siddhāntika Dṛk formula of Nirāyaṇa Mean Moon created from above equation, published in Hindi in 2005, built from purely Sūrya-Siddhāntika terms using Taylor's and Lagrange's formulas of modern differential calculus :
(1) NirāyaṇaMeanMoon=261:10′:1.24"+(17325593.803064287678"∗T) (2) +100∗6.0337456626113312731046134872458"∗t2 (3) +10−3∗6.5095055710038624734367"∗t3 (4) +10−6∗4.681852716188407032"∗t4 (5) +10−9∗2.525508037859365516483207"∗t5
(6) +10−12∗1.0898575817626111529246014535145"∗t6 (7) +10−15∗0.39193089427273663825034568365639"∗t7 (8) +10−18∗0.12080988126146805887553801248113"∗t8 (9) +10−21∗0.03258393040897135345673870555868"∗t9 (10) +10−24∗0.0078118151691312247782389032276435"∗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 "Pañcāṅga Darpaṇa". Latest equations do not differ significantly.
(11) NirāyaṇaMeanMoon=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 Siddhāntika 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-PurānicSiddhāntika 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 Sūrya-Siddhānta has never been written down.
Evidence Of Lost Portions Of SūryaSiddhānta Modern Value of Precession in Bhāskarācārya's Work based on Sūrya-Siddhānta In the chapter “Direction, Place and Time” (Sūrya-Siddhānta, Ch.3), E. Burgess writes— (bracketed words are mine):
The (Sūrya Siddhāntika) 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 sixhundredth 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”. This is the interpretation of existing version of Sūrya Siddhānta (triṃśatkṛtyo yuge bhānāṃ cakre
prākparilambate… | ंश कृ यो युगे भानां च े ा प रल बते…, 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 (bhānāṃ cakre | भानां च े .., ie pendulum like motion of nakṣatra 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 (Sūrya-Siddhānta, 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 merely as fall back according to own logic of Burgess. If the circle of asterisms lags roundabout any fixed point (whether Revatī or Citrā), it is a to and fro motion as all traditional commentators accepted. Modern concept of precession is something different from the original concept of Ayanāṁśa. 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 Śiromaṇi 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 Sūrya Siddhānta and Muñjāla (elsewhere Muñjāla and Manjula), saying —
Sūrya-Siddhānta 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 Sūrya Siddhānta and Muñjāla were correct in Bhāskara's opinion. Colebrooke, Burgess, Wilkinson, etc., have misquoted Siddhānta Śiromaṇi 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 correct, although he could not get the real meaning. The startling fact is that Siddhānta Śiromaṇi 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 Sūrya-Siddhānta, while Muñjāla's value of ayana's motion is +199669, and both (Sūrya-Siddhānta and Muñjāla ) 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 Śiromaṇi'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 Śiromaṇi 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 Sūrya-Siddhānta, nor Muñjāla, but mentioned the both must be used, which is clear from verse-19, where he clearly asks to add Muñjāla's ayana-chalam to Sūrya-Siddhāntika sampāt-calanam (this sampāt-calanam 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-calanam of Sūrya-Siddhānta from ayana-calanam of Muñjāla, 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-calanam of Sūrya-Siddhānta quoted by Bhāskara-ii was an erroneous thing which must be forgotten, while ayanacalanam of Muñjāla 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-calanam of Sūrya-Siddhānta is a distinct phenomenon from ayanacalanam of Muñjāla according to Siddhānta Śiromaṇi, but readers are not informed of the real meaning of Siddhānta Śiromaṇi and false quotation from Siddhānta Śiromaṇi 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 sāhibs of India. Those who do not consult the original texts cited above will not believe me.
Siddhānta Tattva Viveka by Kamalākara Bhaṭṭa is a medieval text, which clearly states that Saura-Pakṣa is distinct from Dṛk-Pakṣa. Saura-Pakṣa (astronomy of Bhuva-Loka) is Sūrya-Siddhānta as it exists. Dṛk-Pakṣa (astronomy of Bhū-Loka or physical/material/sensory world) is that version of SūryaSiddhānta which was not preserved because it was useless in astrology.
Siddhānta Śiromaṇi uses many concepts of Dṛk-Pakṣīya astronomy, as the instance cited above proves. Saura-Pakṣīya Sūrya-Siddhānta does not contain any refence to 30000 cylces per Kalpa mentioned by Bhāskara-II. He was quoting from Dṛk-Pakṣīya Sūrya-Siddhānta which as a text had been lost ; Bhāskara-II said in his own Vāsanābhāshya commentary of Siddhānta-Śiromaṇi that Sūrya-Siddhānta is “āgama”. Modern commentators confuse both variants of Sūrya-Siddhānta. Siddhānta-Tattva-Viveka is prescribed in post-graduate (Ganitācārya) syllabus of Sanskrit universities, but no modern commentator has ever tried to translate it or comment on it. According to Bhāskara-ii, negative sampāt-calanam of Dṛk-Pakṣīya Sūrya-Siddhānta should be added to positive ayana-calanam of Muñjāla to get final Dṛk-Pakṣīya precession, which is very close to modern value. Ayana-calanam of Muñjāla is also Dṛk-Pakṣīya, because Saura-Pakṣīya entities are not used in Dṛk-Pakṣīya astronomy, and vice versa.
I had put some of the most important extant theorems of Dṛk-Pakṣīya Sūrya-Siddhānta 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.
Muñjāla's ayana-calanam, as mentioned in Siddhānta Śiromaṇi, gives a period of (4320 million / 199669 = ) 21636 years per cycle. Siddhānta Śiromaṇi says that it is ayana-calanam according to Muñjāla & his followers but it was not accepted as precession by Bhāskara, precession is obtained after substracting (Saura-Pakṣīya) SūryaSiddhāntika sampātcalanam. 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, 22000 is mentioned instead of 21000
a
yana-calanam of Muñjāla 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
śiromaṇi, the afore-mentioned 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 Śiromaṇi also says that Muñjāla's ayana-calanam (21, 636 years per cycle) is opposite to sampāta-calanam. Bhāskara-ii clearly defines sampāta-calanam as,
the point of intersection of equatorial plane and ecliptic (which is the very definition of equinox). Hence, what Siddhānta Śiromaṇi says is exactly what Wikipedia informs us, the only difference is that Siddhānta Śiromaṇi is misinterpreted and declared to be obscurantist, and the great cycles mentioned in Siddhānta Śiromaṇi is “discovered” by 20th century scientists. But we must remember Bhāskara-ii did not discover these things, he acknowledged Sūrya-Siddhānta and Muñjāla. Bhāskara-ii knew Dṛk-Pakṣīya Sūrya-Siddhānta, 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. Bhāskara-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 :
उ ानपादपु ोऽसौ मेढीभूतो ुवो दिव । स िह मन् ामयते िन यं च ा द यौ हैः सह ॥ uttānapādaputro'sau meḍhībhūto dhruvo divi । sa hi bhraman bhrāmayate nityaṃ candrādityau grahaiḥ saha ॥ Translation
Uttanapāda'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 Purānic epics. Hence, the bhacakra also librates with respect to this fixed point Meru. According to Bhāskara-II, orbital precession is derived by substracting anomalistic precession (sampāt-calanam) from the first component of Milankovitch cycles (Muñjāla's ayana-calanam). 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 2 things about confusing terminology must be borne in mind— 1. this sampāt-calanam — he finally gets by combining the two quantities mentioned above. According to Bhāskara-II, Sūrya-Siddhāntika sampāt-calanam is 30, 000 per Kalpa. He does not give a name for the term which is finally obtained by combining this sampāt-calanam with Muñjāla's ayana-calanam, but the definition he provides for Sūrya-Siddhāntika sampāt-calanam is exactly the definition of the final quantity whose name he does not provide. Hence, there were many types of sampāt-calanams !! This is not a case of confusion of terms. It is a result of Saura-Pakṣīya term with Dṛk-Pakṣīya 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 Muñjāla's precession. It is quite distinct from Saura-Pakṣīya Sūrya-Siddhāntikan ayana-calanam (trepidation) as mentioned in existing text.
Burgess could not digest this theory of libration (oscillation or trepidation, ie, Ayanāṁśa - motion) and tried to distort the meaning of terms to fit modern view of orbital precession with this Saura-Pakṣīya precession. Bhāskara-ii knew and respected Sūrya-Siddhānta which he cited and used in his computations as shown above, and gave exact value of Dṛk-Pakṣīya precession. Therefore, it is foolish to impose Dṛk-Pakṣīya precession (50.9" per year according to Bhāskara-II, 50.3" really) upon Saura-Pakṣīya ayanamsha (54” per year, oscillating within a range of ± 27°). (There are further corrections on Dṛk-Pakṣīya 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 Śiromaṇi for those who want first hand proof, followed with discussion on its obscure passages : Vāsanā’s Bhāṣya (commentary) by Bhāskara-ii on his own work Siddhānta Śiromaṇi has never been translated or explained. Bhāskara-ii knew Siddhānta Śiromaṇi will be misunderstood, hence he wrote its commentary Vāsanā-Bhāṣya himself. This commentary also needs a commentary. In it, Bhāskara clearly writes that,
sa evāyam refers to krāntipāta, not to ayana-calanam. If verses 17-19 are taken together, we have six lines, and sa evāyam occurs in third line, which says that the ayanacalanam as defined by Muñjāla & others [his school of thoughts] is same as Krānti-Pāta defined in first line. This meaning from Vāsanā-Bhāṣya is further reinforced in same passage in Vāsanā-Bhāṣya which says that,
tatra mandoccha pātānām gatirasti the second line (minus 30000 revolutions per Kalpa) must refer not to Krānti-Pāta but to “motion of apogee” Thus, Bhāskara has made it clear that the definition of Krānti-Pāta 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 Muñjāla and his followers (Muñjālādi means Muñjāla and others beginning from Muñjāla, Ādi means beginning; hence the sense of Muñjālādi is not “Muñjāla and others” but, Muñjāla and his followers).
tat pakṣe — relates to ayana-calanam. If one Kalpa of 4320 million years is divided with 199669 given by Muñjāla, 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 Muñjāla (read the footnote of Siddhānta Śiromaṇi's photograph given above which gives the verses from Muñjāla 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 (Vāsanā-Bhāṣya of verse 17-18 says —
yadā punarmahatā kālena mahadantaram bhaviṣyati tadā mahāmatimanto brahmaguptādinām samānadharmāṇa evotpatsyante But this crude figure on one minute per year will give 200, 000 revolutions per Kalpa and not the figure 199669 said by Muñjāla. Rationale for 199669 is unexplained. Now, let me summarize the whole issue Verse 17 defines Krānti-Pāta, and then gives a figure,
:
minus 30000 revolutions per Kalpa as said in Sūrya-Siddhānta which Bhāskara elaborates in Vāsanā-Bhāṣya to be the motion of solar apogee. The next verse mentions +199669 revolutions of ayanacalanam as said by Muñjāla & others [his school of thoughts], and clarifies that the Krānti-Pāta defined in preceding verse in same as ayanacalanam of Muñjāla. But Bhāskara does not accept Muñjāla's notion of Krānti-Pāta and says that real motion of KrāntiPāta should be deduced by combining -30000 with +199669. This is clear in the third verse (19th):
tat-samjātam pātam kṣiptvā kheṭe-apamaḥ sādhyaḥ । krāntivaṣāt-caram-udayāś-caradala-lagnāgame tataḥ kṣepyaḥ ॥ apamaḥ — means Krānti-Pāta = the declination of a planet. (Monier Williams). kheṭa — means “planet”. Hence, Bhāskara says —
Uttanapāda's pāta 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. Pāta means the intersecting point of two circles. Hence, here the [intended] meaning is thus —
The pāta 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-mānas, caradala, lagna, etc., should be computed from this final declination. What Bhāskara says is in current-practice by all pañcāṅga-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 from the rising time of same rasi in ecliptic. Bhāskara says pāta born out of tat should be used for deducing declination. By definition, a pāta is a resultant of two entities. Hence, the two entities mentioned in preceding verses must be combimed to give the Krānti-Pāta of Bhāskara. Existing Sūrya-Siddhānta does not give a motion of -30000 per Kalpa of any entity, while Bhāskara claims Sūrya-Siddhānta says so. But Bhjaskar says Sūrya-Siddhānta is āgama and therefore must be
accepted as final proof (pramāṇa). Hence, some version of Sūrya-Siddhānta available to him mentioned 30000 per kalpa as the motion of SOLAR APOGEE. But Sūrya-Siddhānta gives a value of only 387 revolutions for solar apogee, and SiddhāntaŚiromaṇi gives a figure of 480 per Kalpa (verse 5 in bhagaṇādhyāya). Bhāskara's value is +93 more than that given in Sūrya-Siddhānta. Late NC Lahiri wrote in Advance Ephemeris (page 90) that some corrections were needed in Sūrya-Siddhāntika 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 Bhāskara's bīja correction in Sūrya-Siddhāntika mandoccha value. But Bhāskara never said Sūrya-Siddhānta was incorrect. Hence, there were two versions of Sūrya-Siddhānta: 1. one was Dṛk-Pakṣīya, ie related to the phenomanal world revealed directly to the senses, and, 2. the other was Saura-Pakṣīya manifest only astrologically. Astrologers did not preserve the Dṛk-Pakṣīya Sūrya-Siddhānta. Bhāskara says Sūrya-Siddhānta'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. Bhāskara also says Sūrya-Siddhānta is itself a PROOF and needs no other proof for its correctness because it is āgama. But the figure of -30000 per kapla is never used in Sūrya-Siddhānta used and preserved by astrologers, and Bhāskara's own value of 480 per Kalpa is also near to this version. Hence, he knew about two versions of Sūrya-Siddhānta. Bhāskara'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 Sūrya Siddhānta Kamalākāra Bhaṭṭa (author of Siddhānt-tattva-viveka, as yet untranslated) — an ardent supporter of Sūrya Siddhānta and an opponent of Bhāskara II — had strongly advocated in 16th century that Sūrya Siddhāntika planets are to be distinguished from the material planets. In the beginning of 20th century, terms like Dṛk-Pakṣa and Saura-Pakṣa came into vogue in India, to distinguish planets and phenomena of Sensory World from that of Sūrya Siddhānta. 1. Dṛk-Pakṣa meant the world perceived by means of sense organs, and therefore it denoted the fold of modern astronomy, while, 2. Saura-Pakṣa 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 Sūrya Siddhāntika viewpoint of Dṛk-Pakṣa was never elaborated by anyone.
Unfortunately, after the disappearance of the Sūrya
Siddhāntika commentary of Āryabhaṭṭa, the Elder, even the Saura-Pakṣīya mathematics became obscure, and all the commentators kept on repeating hackneyed phrases whose practical significance was clear to none. Ranganath, Kamalākara Bhaṭṭa, Sudhākara Dvivedī, Kapileśvara Śāstri etc., wrote voluminous commentaries on Sūrya Siddhānta, elucidating everything except the practical ways of using the formulas and the Meru-Centric geometrics. Let us examine some orally transmitted occult theorems of Sūrya Siddhāntika school which show that DṛkPakṣa can be deduced from Saura-Pakṣa mathematically, without the aid of any observatory.
Theorem of Dṛk-Pakṣīya Sidereal and Tropical Years and of Precessional Period Saura-Pakṣīya eccentricity of Sun's elliptic orbit round the centre of Cosmos (Mt. Meru) is exactly equal to 1/60 (= ε), although Saura-Pakṣīya 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,
(12) Ys′=[1π2∗ε2+12(1+ε2)]=[3600π2+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) will 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=365.256361225816672 41689259003252668 days Now we can get the Period of Precession PP :
(14) PP=Yt(Ys−Yt)=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(YsMss−1)=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), intermediate term :
(18) PPS1=11PP−1PPM1=80356.674413324332490977057144470 years Precessional Period due to Sun's effect from alternative equation (PPS2) , intermediate term :
(19) PPS2=1Ys(1Yt−1Ym)=80356.674413324332490977057250561 years The difference between PPS1 and PPS2 is due to computer's errors and is equal to a negligible quatity :
(20) Difference=1.320251252∗10 − 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 27th 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 Dṛk-Pakṣīya 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, Sūrya-Siddhāntika) 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°. 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 Dṛk-Pakṣīya 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 (Sūrya-Siddhāntika) theorems. First of all, let us see :
Lunar Binomial Theorem : A1 = 12/(K4-1) = 1 / 29.5311794213296538 A2 = Ys / 365.256400001304866086855
(24) A=A1∗A2∗(42π)=0.45270842758190827172 Here is the Lunar Binomial Equation :
(25) (A∗M2)+M−Ys=0 Roots of this binomial are : M1 = [-1 + Sqr(1-(4A*Ys)] / 2A = -29.5305886713712313156 days. M2 = [-1 - Sqr(1-(4A*Ys)] / 2A = +27.3216613815891770963 days. M2 - Mss = 0.063953054266910187950698752 seconds. This apparent 'error' is equivalent to the error of 104.643228673117 years in 4.1748 billion years ( = 14 manavantara of 71 Mahā yugas each, where each Dṛk-Pakṣīya Mahāyuga = 4.2 million years).
This is the value of Dṛk-Pakṣīya correction in Kalpa-Mandoccha, for which Bhāskarācārya deduced the value 93 in SiddhantaŚiromaṇi and stated Kalpa-Mandoccha to be equal to 480 (= Saura-Pakṣīya Kalpa Mandoccha 387 + 93 Dṛk-Pakṣīya correction). Its elucidation will be shown later.
Sūrya Siddhānta states Saura-Pakṣīya period of precession to be of 24000 years exactly, while modern value is near the Dṛk-Pakṣīya 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 !
Sūrya Siddhāntika 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 Sṛṣṭi), 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 Bhuva-Loka, which is the world of Saura-Pakṣīya Sūrya-Siddhānta. Sūrya-Siddhānta 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-d’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 Saura-Pakṣīya precession. Hence total number of Saura-Pakṣīya tropical years in one creation is equal to 4302936000 + 179289 = 4303115289 years. Divide this number with (Saura-Varśa / Candra-Varśa) = (Saura-Pakṣīya Sidereal Year / 12 Saura-
Pakṣīya synodical months) = 365.258756481481481 / (12*29.53058794607) = 1.0307356481481. The result is 4174800101.976788423. In it, 4174800000 is the duration of Dṛk-Pakṣīya Creation ( = 4200000*71*14), and 101.976788423 is the exact value of Dṛk-Pakṣīya correction in Kalpa-Mandoccha, for which we had got a crude value 104.643228673117 above, and Bhāskarācārya 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 Pañcāṅga Reform Committee of Government of India. He analysed the differencebetween Dṛk-Pakṣīya and Saura-Pakṣīya tithi (elongation of moon), and found a difference of 0.11 hours in 500 years, which he assumed to be due to error in Sūrya Siddhāntika values (NC Lahiri, 1968, p.90). But Sūrya Siddhāntika 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 Dṛk-Pakṣīya solar orbit during one Creation : Saura-Pakṣīya value is 387 while Dṛk-Pakṣīya value is 489 (Bhāskarācārya-II gave 480 only in SiddhāntaŚiromaṇi). This Dṛk-Pakṣīya rotation of solar ellipse is in addition to the normal Dṛk-Pakṣīya rotation per 136000 years which is the cause behind anomalistic year. In the same book NC Lahiri gives data of Sūrya Siddhāntika 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 Siddhāntika 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 Siddhāntika 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. Siddhāntika sidereal year (365.258756481481)and Dṛk-Pakṣīya 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 Siddhāntika nirayan(=sidereal in Indian system) Mean Sun was at zero longitude. 5106 years later Siddhāntika 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 Siddhāntika 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 Siddhāntika year with tropical scientific year, hence this extra difference of 19941 years must be related to precession. Siddhāntika 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 Sūrya Siddhāntika 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 Dṛk year. Substract one 4, 200, 000 Dṛk 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. ,
,
ṛ
=
36738727.96511627907 25789.48832327657
=
1424.56211246181876
25789.4883232765702 with the derived-value amounting to 1424.56211246181876 which stands for (let’s call it that way) per dṛk year value per
2. Now, dividing the value of 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 value [abeit slightly differs but having seeming resemblance to the derived one] is 25771.4021 years.
Ancient Cosmogony and Geography Sūrya Siddhāntika 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 Sūrya 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. Sūrya Siddhāntika 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. Sūrya Siddhāntika 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 Sūrya Siddhāntika figure. Ptolemic system is well known, but Sūrya Siddhāntika system is rather obscure, known to a few initiated brahmanas only. Due to lack of knowledge of orally transmitted and unpublished portions of original Sūrya Siddhānta, European commentators believe that Sūrya Siddhāntika system was influenced by Ptolemy's Almagest. But those who know the secrets of Sūrya Siddhānta say that its framework is too complex and organically self-contrained to have been influenced by any other system. For instance, Sūrya Siddhāntika daily motions of all planets are exactly equal to a constant, but this rule is not followed in Almagest. Sūrya Siddhāntika system is based upon a cosmic centre at Meru, which is absent in Almagest. Sūrya Siddhāntika 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 2π gives 2° 10’ 31” — which is the maximum value of equation of centre (manda-phala = difference between mean & true Sun) for Sun. Sūrya Siddhāntika 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 Mathurā 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 Sūrya 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 (= 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, but in siddhantic astronomy, everything is constant. Siddhāntika Astronomy is fundamental from which physical (= material = sensorily perceived = Māyā) 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 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 Sūrya-Siddhāntika mathematics has been presented here. The details are highly intricate and difficult. Kaliyuga is not fit for SūryaSiddhānta and therefore calls it obsolete. The extant text of Sūrya-Siddhāntika provides sufficient clues for unravelling its unwritten marvels. -Vinay Jha
