Deduction of Exact Equations of Modern Astronomy
through Ancient texts of Siddhanta Jyotisha
-Vinay Jha, Panchanga-maker of Adi Shankara's Govardhana Matha(Puri), and
maker of one dozen panchangas and free astronomical and astrological softwares.
INTRODUCTION
Sage Vyasa has clearly said in Vishnudarmottara Purana (.......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 :
................... ....... .......... ........ ........ . ........ .......
Nirnaya Sindhu also states that Suryasiddhanta should be used for knowing invisible
results ("Adrishta" or Fortune) :
......-..-. ...... ........... ..... ..... ... ......... ......
........ ... ....
The mathematics of Suryasiddhanta is given in the Narada Purana too. In all other
Puranas too, Suryasiddhanta 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-laghava (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 (........-.......) is an essential part of ancient Siddhanta skandha of
Jyotisha. But Drika-Karma corrections are never used in finding True Longitudes of planets
(Graha-spashtikarana or ....-..........) in any ancient Siddhanta text. It is used only when
perceivable phenomena like eclipses, heliacal risings and settings (....... .......), etc are needed.
.
Two chief components of Drika-Karma correction are Aksha and Ayana Drika-Karma corrections
(....-........-....... and ...-........-.......) which are explained in ancient siddhantas, chief of which
is Suryasiddhanta. But these two Drika-Karma corrections give only that position of a planet
which is needed for predictive astrology, e.g. udayasta 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
Siddhantic texts. For this reason, many mediaeval scholars like Ganesha Daivajna of Grahalaghava
or Divakara Daivajna of Makaranda-vivarana declared that Suryasiddhanta has become
obsolete and some changes are needed in its formulations or methods. They advocated removal
of mandaphalardha (.............
) from four corrections made in Mean Longitude of a planet to get
True Longitude, forgetting that the fundamental theory of siddhanta texts will become distorted
if any one of four corrections is removed. Unfortunately, no siddhanta text or its commentator
ever explained the fundamental theory involved in those four corrections of siddhanta texts,
namely sheeghra-phalardha, manda-phalardha, manda-phala and sheeghra-phal (.........,.
............,..........., .......). Rev Eveneger Burgess, the translator and commentator of
Suryasiddhanta, candidly accepted that he could not understand the rationale behind these four
corrections even after spending eight years among Indian experts to learn Suryasiddhanta.
Other commentator are worse, they neither explained nor admitted their inability to explain. All
ancient siddhantas and Puranas 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 mandaphalardha, they
did not bother to go into the rationale behind either mandaphalardha or the other three
corrections. If mandaphalardha was rejected, what is the mathematical reason of sheeghraphalardha
? 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-phalardha and sheeghra-phalardha ? Modern astronomy knows no
such things as manda-phalardha and sheeghra-phalardha. 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 siddhanta texts, is not something mysterious about siddhanta texts ? Either
all siddhanta texts are wrong or all mediaeval and modern "experts" are ignorants in the field of
siddhanta skandha of Jyotisha. A false excuse is invented by some "experts" : these ancient
siddhanta texts were accurate in ancient times but have become outdated now. This false logic
was first invented by the author of Graha-laghava, 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 SuryaSiddhanta) 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 343:33:59 001:39:24304:06:20 320:29:20 238:48:12 310:08:09 050:58:12
Saur 344:09:44 002:18:18306:00:04 317:26:27 236:14:05 307:10:43 058:18:51
482 Drik 344:18:44 318:25:11347:52:07 319:15:50 025:16:49 027:27:47 209:22:01
Saur 344:47:48 319:25:52350:42:50 324:10:33 021:03:18 025:40:02 214:40:16
582 Drik 345:03:34 253:57:54029:03:14 335:51:57 188:46:46 325:47:33 337:17:06
Saur 345:25:49 258:28:12031:42:36 343:39:19 185:05:00 322:54:50 342:03:42
682 Drik 345:48:00 215:27:37073:50:27 358:38:34 342:03:44 028:07:06 128:39:19
Saur 346:03:50 214:34:27076:53:20 000:13:16 338:05:47 031:01:54 138:56:21
782 Drik 346:33:23 152:21:34157:55:10 357:25:17 136:30:39 342:28:19 272:56:05
Saur 346:41:49 154:02:50165:14:47 350:55:52 132:22:37 340:03:29 276:49:23
882 Drik 347:18:01 109:07:50260:33:02 322:29:25 298:43:55 323:44:48 044:58:58
Saur 347:19:46 107:58:29261:48:04 320:02:06 295:40:57 335:09:06 051:04:16
982 Drik 348:02:48 052:09:32311:52:48 324:01:45 085:44:25 359:21:07 205:23:02
Saur 347:57:41 052:17:24312:05:43 328:07:58 081:53:55 357:30:27 209:48:18
1082 Drik 348:48:22 000:17:10355:34:55 341:21:32 253:17:16 302:24:10 335:41:00
Saur 348:35:35 000:24:57356:47:17 347:45:54 251:39:09 301:33:34 337:05:04
Tropical longitudes
have been chosen for this
comparison so that the
controversies related to
ayanamshas do not
intervene. The differences
are clearly due to Mandaphalardha
and Sheeghraphalardha,
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
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
and Saura systems use Mandaphala
as well as Sheeghraphala. Even if
Mandaphalardha is discarded, as
Ganesha Daivajna proposed, this
non-linear anomaly does not
vanish, because differences due to
sheeghraphalardha are much more
than those due to mandaphalardha.
This highly irregular non-linearity
proves that no changes in
siddhantic values of mandaphalaparidhi
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
Suryasiddhanta 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 ayanamsha), 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 Suryasiddhanta was not
created on the basis of observation of physical planets. This result conforms with the
statements in Suryasiddhanta and all other available siddhantas and texts like Narada Purana
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 siddhantas,
what is the rationale and what is the use of such siddhantas ? The utility aspect is very simple to
answer : predictive astrology, although this utility of siddhantas 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 Suryasiddhanta 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
Suryasiddhantic astrology without any bias. During past few decades, I have found only a
handful of Drik-supporters ostensibly ready to test Suryasiddhantic 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, Suryasiddhantic astrology is used by a few among internet
astrologers. But even today, overwhelming majority of traditional panchangas are made with
some mediaeval tables which have been either directly created by means of Suryasiddhanta
(such as Makaranda Tables) or were indirectly based on some earlier source derived from
Suryasiddhanta (such as South Indian Vakya texts). For those who are not ready to test the
validity of Suryasiddhanta just because its planetary positions do not tally with physical planets,
is not any method available to prove the validity of Suryasiddhanta? The following sections
outline some of the answers to this question.
DECLINATION : Deduction of Modern Equation from Suryasiddhanta
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 Suryasiddhanta. If both modern
astronomy and Suryasiddhanta describe the same Sun, then Suryasiddhanta is certainly a
wrong text. But if the integral Suryasiddhantic 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 Vyasa 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 Suryasiddhantic 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 siddhantic 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
siddhantic equation mentioned above can be comfortably used to create modern table of solar
declination,provided we replace siddhantic 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 siddhantic 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 siddhantic equation of declination was
absolutely correct,
excepting the effect of
nutation which was
never used in any
siddhanta. Has any
historian of science ever
credited Suryasiddhanta
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"
Suryasiddhanta which is
supposedly lost, while
so-called "modern"
Suryasiddhanta is of a
much later unspecified
date. But it has been
shown in this paper that
the so-called modern
Suryasiddhanta 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 Suryasiddhanta
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 :
Suryasiddhantic 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 Suryasiddhantic 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 CosM/2
where 'M/2' is maximum possible value of siddhantic manda-phalardha, 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
Suryasiddhanta. 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 siddhantic values are changeless which scientists may like to explain as long-term
average. This siddhantic value is equal to NASA's value for 2000 AD, which confirms another
major finding that with proper ayanamsha the period of minimum difference between sidereal
siddhantic solar longitude with sidereal Drik 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 -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 Suryasiddhanta. In Suryasiddhantic
system, planets are not physical bodies, hence have no masses and gravitation. Therefore,
there is no effect of barycentre. Second effect is of Meru. Suryasiddhantic 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 Suryasiddhantic terms.
Suryasiddhanta 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 siddhantic 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-siddhantic. Siddhantic
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
siddhantic 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 siddhantic equations of Sunrise.
(This was published in a Hindi book by me in 2005 AD.)
Maximum mandaphala of Moon is 5°02'48" in Suryasiddhanta, but 6°17'19.7" or
22639.7" in modern astronomy (cf. NC Lahiri's Panchanga Darpana). Take the difference of sine
of mandaphalardha 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
Suryasiddhanta 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 Akasha), and therefore these equations need
revisions after few years. The above equation deduced siddhantically 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 siddhantic explanation of the most troublesome equation of modern physical
astronomy, the equation of Mean Moon (converted into Nirayana following NC Lahiri's method) :
The siddhantic equation for deducing any term in the above equation is this :
Ys is siddhantic 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 siddhantic mandochcha (apogee) in one Kalpa
(one Kalpa is of 4320 million years),
K is deduced siddhantically in following manner :
K= [{(Ys-Yd) / Ys} -(1/42000)]-1
x (Ys / t)
= 464.65408706471303027753666827
Then the wanted term in the siddhantic equation of Drik Nirayana Mean Moon is
Mn = [360°/ (n-1)! ] x [ tx [{ 1+ (1/ 387 ) } / K ] n]
Following is my siddhantic Drik formula of Nirayana Mean Moon created from above
equation, published in Hindi in 2005, built from purely Suryasiddhantic terms using Taylor's and
Lagrange's formulas of modern differential calculus :
Nirayana Mean Moon = 261°:10':1.24" + (17325593.803064287678" *T )
+100 *6.0337456626113312731046134872458" *t2
+10-3 *6.5095055710038624734367" *t3
+10-6 *4.681852716188407032" *t4
+10-9 *2.525508037859365516483207" *t5
+10-12 6
*1.0898575817626111529246014535145" *t
+10-15 7
*0.39193089427273663825034568365639" *t
+10-18 8
*0.12080988126146805887553801248113" *t
+10-21 9
*0.03258393040897135345673870555868" *t
+10-24 10
*0.0078118151691312247782389032276435" *t+......
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
"Panchanga Darpana". Latest equations do not differ significantly.
Nirayana Mean Moon=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 siddhantic
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-Puranic-Siddhantic 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 SuryaSiddhanta has never been written down.
EVIDENCE OF LOST PORTIONS OF SURYASIDDHANTA
Modern Value of Precession in Bhaskaracharya's Work based on Suryasiddhanta
In the chapter "Direction, Place and Time" (Suryasiddhanta, Ch.iii), E Burgess writes ;
Quote: (bracketed words are mine) : The (Surya Siddhantic) 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,
Mahayuga 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 Siddhanta ( ........... ... ..... .
.......
...............…, 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 (..... ......., 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 (Suryasiddhanta, 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 Chitra), it is a to and fro motion as all traditional commentators
accepted. Modern concept of precession is something different from the original concept of
ayanamsha. 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 Bhaskara-II, because he relied upon a wrong translation of Bhaskara by
Colebrooke (As. Res., xii 209 ; Essays, ii,374, etc) and did not try to examine Siddhanta
Shiromani which was wrongly translated by Lancelot Wilkinson due to Colebrooke's influence.
Bhaskara-II did not give his own opinion at all, and merely quoted Surya Siddhanta and Mujjal
(elsewhere Munjala and Manjula), saying Suryasiddhanta gives -30000 revolutions of sampat or
equinoctial point per Kalpa while ayana has a motion of +199669 revolutions per Kalpa (of 4320
million years). Bhaskara's own opinion was that these should be followed, which means both
Surya Siddhanta and Mujjala were correct in Bhaskara's opinion. Colebrooke, Burgess,
Wilkinson, etc have misquoted Siddhanta 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 Sharma is correct, although he
could not get the real meaning.
The startling fact is that Siddhanta 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 Suryasiddhanta,
while Mujjala's value of ayana's motion is +199669, and both (Suryasiddhanta 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 Siddhanta 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 Siddhanta
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. Bhaskara-II neither excluded Suryasiddhanta, nor Mujjala, but
mentioned the both must be used, which is clear from verse-19, where he clearly asks to add
Mujjala's ayana-chalam to Suryasiddhantic sampat-chalanam (this sampat-chalanam is
anomalistic precession with a period of 144000 years per cycle, not far from modern value).
Another startling fact is that Bhaskara-ii differentiates sampat-chalanam of Suryasiddhanta from
ayana-chalanam of Mujjala, and says both must be added before computing phenomena like
declension, ascensional differences, etc. But modern commentators like Colebrooke misinterpret
Bhaskara-II deliberately, and imply that sampat-chalanam of Suryasiddhanta quoted by
Bhaskara-ii was an erroneous thing which must be forgotten, while ayana-chalanam of Mujjala
was a crude approximation of modern precession. But this interpretation is falsified by
Bhaskara's original verses (and his own commentary Vasanabhashya) as shown above. The root
of this problem lies in the fact that sampat-chalanam of Suryasiddhanta is a distinct
phenomenon from ayana-chalanam of Mujjala according to Siddhanta Shiromani, but readers
are not informed of the real meaning of Siddhanta Shiromani and false quotation from
Siddhanta 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 sahibs of India. Those who do not consult the original texts cited above will not
believe me.
Siddhanta-tattva-viveka by Kamlakara Bhatt is a medieval text, which clearly states that
Saurpaksha is distinct from Drikpaksha. Saurpaksha (astronomy of bhuvaloka) is
Suryasiddhanta as it exists. Drikpaksha (astronomy of Bhooloka or physical/material/sensory
world) is that version of Suryasiddhanta which was not preserved because it was useless in
astrology. Siddhanta Shiromani uses many concepts of Drikpakshiya astronomy, as the instance
cited above proves. Saurpakshiya Suryasiddhanta does not contain any refence to 30000 cylces
per Kalpa mentioned by Bhaskara-II. He was quoting from Drikpakshiya Suryasiddhanta which
as a text had been lost ; Bhaskara-II said in his own Vasanabhashya commentary of Siddhantashiromani
that Suryasiddhanta is "agama". Modern commentators confuse both variants of
Suryasiddhanta. Siddhantatattvaviveka is prescribed in post-graduate (Ganitacharya) syllabus
of Sanskrit universities, but no modern commentator has ever tried to translate it or comment
on it.
According to Bhaskara-ii , negative sampat-chalanam of Drikpakshiya Suryasiddhanta should be
added to positive ayana-chalanam of Mujjala to get final Drikpakshiya precession, which is very
close to modern value. Ayana-chalanam of Mujjala 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 Suryasiddhanta 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.
Mujjala's ayana-chalanam, as mentioned in Siddhanta Shiromani, gives a period of (4320 million
/ 199669 = ) 21636 years per cycle. Siddhanta 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) Suryasiddhantic sampatchalanam. If
this 21636 year cycle is not precession, what is it ??
Readers should read a Wikipedian article Milankovitch cycles
( http://en.wikipedia.org/wiki/Milankovic_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 Mujjala 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 Siddhanta
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.
Siddhanta Shiromani also says that Mujjala's ayana-chalanam (21,636 years per cycle) is
opposite to sampata-chalanam. Bhaskara-ii clearly defines sampata-chalanam as "the point of
intersection of equatorial plane and ecliptic" (which is the very definition of equinox). Hence,
what Siddhanta Shiromani says is exactly what Wikipedia informs us, the only difference is that
Siddhanta Shiromani is misinterpreted and declared to be obscurantist, and the great cycles
mentioned in Siddhanta Shiromani is "discovered" by 20th century scientists. But we must
remember Bhaskara-ii did not discover these things, he acknowledged Suryasiddhanta and
Munjala.
Bhaskara-ii knew Drikpakshiya Suryasiddhanta, which has not survived because it was not
useful in astrology. In his formula of precession, Bhaskara-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 Puranic verse which
proves knowledge of equinoctial precession in Puranic times :
................. .... ...............................................................
It means : "Uttanpada'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 Puranic-epic stories. Hence, the bhachakra also
librates with respect to this fixed point Meru.
According to Bhaskara-II, orbital precession is derived by substracting anomalistic precession
(sampat-chalanam) from the first component of Milankovitch cycles (Munjala's ayanachalanam).
Bhaskara-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 Bhaskara-ii.
But two things about confusing terminology must be borne in mind : this sampat-chalanam he
finally gets by combining the two quantities mentioned above. According to Bhaskara-II,
Suryasiddhantic sampat-chalanam is 30000 per Kalpa. He does not give a name for the term
which is finally obtained by combining this sampat-chalanam with Munjala's ayana-chalanam,
but the definition he provides for Suryasiddhantic sampat-chalanam is exactly the definition of
the final quantity whose name he does not provide. Hence, there were many types of sampatchalanams
!! 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 Munjala's precession. It is quite
distinct from Saurpakshiya Suryasiddhantic ayana-chalanam (trepidation) as mentioned in
existing text. Burgess could not digest this theory of libration (oscillation or trepidation, ie,
ayanaamsha -motion) and tried to distort the meaning of terms to fit modern view of orbital
precession with this Saurpakshiya precession. Bhaskara-ii knew and respected Suryasiddhanta
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 Bhaskara-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 Siddhanta 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 Siddhanta Shiromani has never
been translated or explained. Bhaskar-ii knew Siddhanta 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 Siddhanta 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 Siddhanta
(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 SuryaSiddhanta" 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-udayaAshcharadala-
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 SuryaSiddhanta does not give a motion of -30000 per Kalpa of any entity, while
Bhaskara claims SuryaSiddhanta says so. But Bhjaskar says SuryaSiddhanta is "Agama" and
therefore must be accepted as final proof ("pramANa"). Hence, some version of SuryaSiddhanta
available to him mentioned -30000 per kalpa as the motion of SOLAR APOGEE. But
SuryaSiddhanta gives a value of only 387 revolutions for solar apogee, and Siddhantashiromani
gives a figure of 480 per Kalpa (verse 5 in bhagaNAdhyAya). Bhaskar's value is +93 more than
that given in SuryaSiddhanta. Late NC Lahiri wrote in Advance Ephemeris (page 90) that some
corrections were needed in SuryaSiddhantic 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 SuryaSiddhantic mandochcha value. But Bhaskar never said
SuryaSiddhanta was incorrect. Hence, there were two versions of SuryaSiddhanta : 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
SuryaSiddhanta. Bhaskar says SuryaSiddhanta'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 SuryaSiddhanta 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 SuryaSiddhanta 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 SuryaSiddhanta.
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 Siddhanta
Kamlakara Bhatt(author of Siddhant-tattva-viveka,as yet untranslated),an ardent supporter of Surya
Siddhanta and an opponent of Bhaskara II,had strongly advocated in 16th century that Surya Siddhantic
planets are to be distinguished from the 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 Siddhanta. Drik-paksha meant the world perceived by means of sense organs,
and therefore it denoted the foeld of modern astronomy, while Saurpaksha denoted the gods of Next
World bearing same name as the material planets but being non-material. Ketaki system of almanac used
these concepts in actual practice. But the Surya Siddhantic viewpoint of Drikpaksha was never elaborated
by anyone.Unfortunately, after the disappearance of the Surya Siddhantic commentary of Aryabhata the
Elder, even the Saurpakshiya mathematics became obscure, and all the commentators kept on repeating
hackneyed phrases whose practical significance was clear to none. Ranganath,Kamlakar Bhat,Sudhakar
Dwivedi, Kapileshwar Shashtri, etc wrote voluminous commentories on Surya Siddhanta, elucidating
everything except the practical ways of using the formulas and the Merucentric geometrics.
Let us examine some orally transmitted occult theorems of Surya Siddhantic school which show that
Drikpaksha can be deduced from Saurpaksha mathematically, without the aid of any observatory.
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 (= e),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 e and 'pi' by p . Then,
=365.25640000130486608685495644391days
This is the limiting value of scientific sidereal year by means of Vedic (i.e.,Surya Siddhantic) equation.
The Vedic (i.e.,Surya Siddhantic) theorem of scientific Tropical Year Yt (=365.24219878125) will be
demonstrated later, let us first get the value of mean sidereal year with the help of following equation :
=365.25636122581667241689259003252668days
Now we can get the Period of Precession PP :
= 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 :
= 29.53058780664716371374days.
Metonic Year Ym is equal to :
=365.246743924320182775185653635days
Precessional Period due to Moon's effect (PPM1) :
= 37978.09022183997109169737years
Precessional Period due to Sun's effect (PPS1), intermediate term :
= 80356.674413324332490977057144470years
Precessional Period due to Sun's effect from alternative equation (PPS2) , intermediate term :
= 80356.674413324332490977057250561years
The difference between PPS1 and PPS2 is due to computer's errors and is equal to a negligible quatity :
Difference=1.320251252*10-27years
Intermediate terms are :
A1 = PPS1 / PPM1 = 2.1158692799964388041303958720096.
A2 = PPS2 / PPM1 = 2.1158692799964388041303958748028.
Precessional Period due to Sun's effect (PPS) , final value :
PPS = PPS1 + A1 = 80358.790282604328929781187540342
PPS = PPS2 + A2 = 80358.790282604328929781187646436
There is difference in two values of solar precessional period shown above (PPS) in 27th digit only. Hence,
the computations are highly reliable.
There are three equations for obtaining scientific Tropical Year (in days) :
= 365.24219878124999999999999999999638527125
= 365.24219878124999999999999999999638595267
= 365.2421987812499999999999999999999999972349
Drikpakshiya Tropical Year is the most precise constant known to modern astronomy, whose empirical
value is 365.24219878125 ± 0.00000000058 days.
The error of ± 0.00000000058 days is due to errors in modern instruments. The three values we obtained
above through Vedic equations have errors in 34th digit which is due to 34-digit precisiuon of Windows
Calculator used to obtain above results. The net result is startling : value of 'pi' is the basic term used to
deduce exact value of most important astronomical constants, if you know the exact value of 'pi' then you
can deduce the exact value of astronomical constants. Modern physicists know many such equations,
which are called "coincidences" by atheists, and as proofs of Intelligent Design of Universe by believers in
God.
SuryaSiddhantic Theorem of Lunar month
M1 = 365.256400001304866086855 / (42/p) = 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/ )* {(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
A=A1*A2*(42 / p)=0.45270842758190827172
Here is the Lunar Binomial Equation :
(A*M2)+M-Ys=0
Roots of this binomial are :
M1 = [-1 + Sqr(1-(4A*Ys)] / 2A = -29.5305886713712313156 days.
M2 = [-1 -Sqr(1-(4A*Ys)] / 2A = +27.3216613815891770963 days.
M2 -Mss = 0.063953054266910187950698752 seconds.
This apparent 'error' is equivalent to the error of 104.643228673117 years in 4.1748 billion years ( = 14
manavantara of 71 mahayugas each, each Drikpakshiya mahayuga being of 4.2 million years).This is the
value of Drikpakshiya correction in Kalpa-Mandochcha, for which Bhaskaracharya deduced the value 93 in
Siddhantashiromani and stated Kalpa-Mandochcha to be equal to 480 (= Saurpakshiya Kalpa Mandochcha
387 + 93 Drikpakshiya correction). Its elucidation will be shown below.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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 lunar month used by tropicalist scientists !
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Surya Siddhantic Theory of the Rotation of Material Universe
According to modern physical science, material universe cannot be said to be rotating even if it rotates,
because all space-time-continuum is intrinsically related to matter as part of a unified whole, and there
can be no space or time outside the realm of matter. Since there is no space or time outside material
universe, rotation of this material universe cannot be measured because there is no external space-time.
Let us call the space of time of this material universe as material-space and material-time. There are 14
universes (Bhuvanas) in the Multiverse (= Creation or Srishti), and we live in the middle universe. Since
all forms of matter have shown to be associated with SPIN, from galactic to sub-atomic levels, it is natural
that the material universe should also rotate. But it can be measured only with reference to the non-
material universe or Bhuvaloka, which is the world of Saurapakshiya Suryasiddhanta. Suryasiddhanta
states our universe to be finite, and according to Godel's theorem a finite system cannot be fully
explained on account of its internal properties and phenomena only. There must be something outside
this finite universe which should explain the workings of this universe and its raison-de-etre.
Now we show the Vedic theorem of Rotation of the Material Universe. Surya Siddantic Kalpa is equal to
4.32 billion years. The Creator (Brahma) took 47400 divine yuears to create the Creation, which is equal
to 47400 * 360 human years. Hence the total Age of Creation = 4.32 billion -(47400 * 360) =
4302936000 years.
4302936000 / 24000 = 179289 is the extra years due to Saurpakshiya precession. Hence total number of
Saurpakshiya tropical years in one creation is equal to 4302936000 + 179289 = 4303115289 years.
Divide this number with (Saurvarsh / Chandravarsh) = (Saurpakshiya Sidereal Year / Twelve
Saurpakshiya synodical months) = 365.258756481481481 / (12*29.53058794607) = 1.0307356481481.
The result is 4174800101.976788423. In it, 4174800000 is the duration of Drikpakshiya Creation ( =
4200000*71*14), and 101.976788423 is the exact value of Drikpakshiya correction in Kalpa
Mandochcha, for which we had got a crude value 104.643228673117 above, and Bhaskaracharya had got
93. A quantity of 101.976788423 years in 4.1748 billion years is equal to 0.107065 hours in 500 years.
Nirmal Chandr Lahiri was the secretary of Panchanga Reform Committee of Government of India. He
analysed the differencebetween Drikpakshiya and Saurpakshiya tithi (elongation of moon), and found a
difference of 0.11 hours in 500 years,which he assumed to be due to error in Surya Siddhantic values(NC
Lahiri,1968,p.90). But Surya Siddhantic values do not belong to this physical Universe. This apparent
error of 0.107065 hours in 500 years is a result of extra 102 rotations of the Drikpakshiya solar orbit
during one Creation : Saurpakshiya value is 387 while Drikpakshiya value is 489 (Bhaskaracharya-II gave
480 only in Siddhantashiromani). This Drikpakshiya rotation of solar ellipse is in addition to the normal
Drikpakshiya rotation per 136000 years which is the cause behind anomalistic year.
---------——
In the same book NC Lahiri gives data of Surya Siddhantic beej corrections applied to lunar anomaly in
comparison to modern scientific values, which shows that beej correction needed in lunar anomaly in
order to get Siddhantic tithi from scientific tithi increases at a rate of one revolution in 42000 years(NC
Lahiri,1968,p.90). Difference between modern scientific tropical Sun and Siddhantic Sun also show 360°
change during 42000 years. Sun and moon do not move in same orbits. Hence we must conclude that the
physical Universe itself is revolving at the rate of one revolution per 42000 years round some point very
near to Earth's centre,which suggests that the centre of Universe is not far from Earth's centre. Before
dealing with this centre (Meru or Mt Kenya in Africa),let us first elucidate the 42000 year cycle of the Sun.
Siddhantic sidereal year (365.258756481481)and Drikpakshiya tropical year(365.24219878125) differ at
the rate of one revolution or one year in 22059.75174 years. But in reality both divurge from each other
at the rate of one revolution in 42000 years. For instance,Kaliyuga commenced at Ujjain midnight 17-18
Feb,3102 BCE,when Siddhantic nirayan(=sidereal in Indian system) Mean Sun was at zero longitude.
5106 years later Siddhantic zero Sun was to be found on 16 Apr,2005 at 5:03:15 AM (Ujjain). If mean
Sun differs by 44.2106 days in 5106 years(taking into account 13 days of Gregorian reform), it should
differ by one year in 42182.8 years. Due to non-linearity of elliptical paths,we get here 42182.8, the
exact figure is an integer 42000. It raises a question : if mathematically Siddhantic year and scientific
year should show a difference of one revolution in 22059 years, why do they differ by one revolution in
42000 years in reality ? Where does 19941.24826 years come from ? We have here compared sidereal
Siddhantic year with tropical scientific year, hence this extra difference of 19941 years must be related to
precession. Siddhantic period of precession is 24000 years and scientific period is 25789.4883233 years.
Both form cycles of 100000 ± 12000 years with respect to 19941 in harmonic series. Thus, we are now
getting close to constants of Milankowitz,just by means of analysing Surya Siddhantic constants !
The Vedic value for Drikpakshiya period of precession is 25789.4883233 years. But it needs slight
modifications due to long term cycles.We had got 101.976788423 years per Drikpakshiya Creation for the
exact value of Drikpakshiya correction in Kalpa-Mandochcha, which is equal to
101.976788423/4174800000 per year. Add this correction to 1/257898.488, we get 1/25773.252377 in
the harmonic series. Again add 1/(4200000*71) to it and get 1/25771.025002. (4200000*71) is the
duration of one Drikpakshiya Manvantara. A period of 25771.025 years is equal to 50.28903584 seconds
of arc per sidereal year, or 50.288160017 seconds per Julian Year. Presently, 50.28796195 seconds per
Julian Year is the accepted value.
Ancient Cosmogony and Geography
Surya Siddhantic system is neither heliocentric nor geocentric. It clearly states in Bhoogoladhyaya that Mt
Meru resides at the centre (equator) of globe in the region of Zamboodweep. In Africa, Mt Kenya is
situated upon equator in a region where many modern place names are reminiscent of Surya Siddhanta :
Meru town near Mt Kenya, another Mt Meru slightly southwards, a place named kinyan-giri which means
Mt Kinyan or Mt Kenya in sanskrit, river Zamboonadi > *zamboodi > *zambedi > *zambezi, Muzambique,
Zambia, Zimb-abwe, Gabon (< *Zamboon), Congo (< *Gongo < *zambo),etc. Homo genus of
mankind is known to have evolved in that region around 4 million years ago. Indian Puranic ttreadition
also mention that modern races of mankind evolved near Meru in 3891194 BCE when the present
Mahayuga commenced. Surya Siddhantic formulae of making true planets from mean ones require the
use of distance from Earth's centre to a point in space 28.913 kilometres above the top of Mt Meru (Mt
Kenya), which was believed to be centre of all universes by Puranic authors.
Surya Siddhantic universe is much smaller in comparison to material universe, and Sun's distance from
Earth is only 861.7 times of Earth's equatorial radius. Material Sun's distance is 23455 times of Earth's
equatorial radius ! Ptolemy used a figure 1210, which is not much removed from Surya Siddhantic figure.
Ptolemic system is well known, but Surya Siddhantic system is rather obscure, known to a few initiated
brahmanas only. Due to lack of knowledge of orally transmitted and unpublished portions of original
Surya Siddhanta, European commentators believe that Surya Siddhantic system was influenced by
Ptolemy's Almagest. But those who know the secrets of Surya Siddhanta say that its framework is too
complex and organically self-contrained to have been influenced by any other system. For instance, Surya
Siddhantic daily motions of all planets are exactly equal to a constant, but this rule is not followed in
Almagest. Surya Siddhantic system is based upon a cosmic centre at Meru, which is absent in Almagest.
Surya Siddhantic solar epicycle is equal to 14 yojanas per degree, which is equal to 5040 yojanas for 360
degrees. Its diameter is 1604.3 yojanas, which is 4.3 yojanas more than Earth's equatorial diameter. 4.3
yojanas equals 5.199 kilometres ( height of Mt Meru or Mt Kenya)plus 28.913669 kilometres. Solar
epicycle equals to 14 yojanas, which gets reduced to 13:40 at perigee of this elliptical epicycle, which
when divided by 2 gives 2:10':31" degrees, which is the maximum value of equation of centre
(mandaphala = difference between mean and true Sun) for Sun. Surya Siddhantic theory, therefore
relates yojana to degrees in an intrinsic manner, which makes it clear that it was not borrowed from
Almagest. Earth's diameter is an integer 1600 yojana. Moon's diameter is also an integer 436 yojanas.
These rations are perfectly scientific. Such integral values seem to be mysterious when they are
confirmed with modern science. This value of yojana was not only prehistoric, manifest in the story of
Jarasandha's 99 yojanas from Girivraja to Mathura proving that siddhantic yojana was prevalent in prehistoric
era of Girivraja's kings, as mentioned in Mahabharata, but was also intrinsically related to many
native concepts of Surya Siddhanta, discussed in other sections of this article.
Only the most simple and easiest aspects of Suryasiddhantic mathematics has been presented
here. The details are highly intricate and difficult. Kaliyuga is not fit for Suryasiddhanta and
therefore calls it obsolete. The extant text of Suryasiddhantic provides sufficient clues for
unravelling its unwritten marvels.
through Ancient texts of Siddhanta Jyotisha
-Vinay Jha, Panchanga-maker of Adi Shankara's Govardhana Matha(Puri), and
maker of one dozen panchangas and free astronomical and astrological softwares.
INTRODUCTION
Sage Vyasa has clearly said in Vishnudarmottara Purana (.......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 :
................... ....... .......... ........ ........ . ........ .......
Nirnaya Sindhu also states that Suryasiddhanta should be used for knowing invisible
results ("Adrishta" or Fortune) :
......-..-. ...... ........... ..... ..... ... ......... ......
........ ... ....
The mathematics of Suryasiddhanta is given in the Narada Purana too. In all other
Puranas too, Suryasiddhanta 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-laghava (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 (........-.......) is an essential part of ancient Siddhanta skandha of
Jyotisha. But Drika-Karma corrections are never used in finding True Longitudes of planets
(Graha-spashtikarana or ....-..........) in any ancient Siddhanta text. It is used only when
perceivable phenomena like eclipses, heliacal risings and settings (....... .......), etc are needed.
.
Two chief components of Drika-Karma correction are Aksha and Ayana Drika-Karma corrections
(....-........-....... and ...-........-.......) which are explained in ancient siddhantas, chief of which
is Suryasiddhanta. But these two Drika-Karma corrections give only that position of a planet
which is needed for predictive astrology, e.g. udayasta 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
Siddhantic texts. For this reason, many mediaeval scholars like Ganesha Daivajna of Grahalaghava
or Divakara Daivajna of Makaranda-vivarana declared that Suryasiddhanta has become
obsolete and some changes are needed in its formulations or methods. They advocated removal
of mandaphalardha (.............
) from four corrections made in Mean Longitude of a planet to get
True Longitude, forgetting that the fundamental theory of siddhanta texts will become distorted
if any one of four corrections is removed. Unfortunately, no siddhanta text or its commentator
ever explained the fundamental theory involved in those four corrections of siddhanta texts,
namely sheeghra-phalardha, manda-phalardha, manda-phala and sheeghra-phal (.........,.
............,..........., .......). Rev Eveneger Burgess, the translator and commentator of
Suryasiddhanta, candidly accepted that he could not understand the rationale behind these four
corrections even after spending eight years among Indian experts to learn Suryasiddhanta.
Other commentator are worse, they neither explained nor admitted their inability to explain. All
ancient siddhantas and Puranas 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 mandaphalardha, they
did not bother to go into the rationale behind either mandaphalardha or the other three
corrections. If mandaphalardha was rejected, what is the mathematical reason of sheeghraphalardha
? 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-phalardha and sheeghra-phalardha ? Modern astronomy knows no
such things as manda-phalardha and sheeghra-phalardha. 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 siddhanta texts, is not something mysterious about siddhanta texts ? Either
all siddhanta texts are wrong or all mediaeval and modern "experts" are ignorants in the field of
siddhanta skandha of Jyotisha. A false excuse is invented by some "experts" : these ancient
siddhanta texts were accurate in ancient times but have become outdated now. This false logic
was first invented by the author of Graha-laghava, 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 SuryaSiddhanta) 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 343:33:59 001:39:24304:06:20 320:29:20 238:48:12 310:08:09 050:58:12
Saur 344:09:44 002:18:18306:00:04 317:26:27 236:14:05 307:10:43 058:18:51
482 Drik 344:18:44 318:25:11347:52:07 319:15:50 025:16:49 027:27:47 209:22:01
Saur 344:47:48 319:25:52350:42:50 324:10:33 021:03:18 025:40:02 214:40:16
582 Drik 345:03:34 253:57:54029:03:14 335:51:57 188:46:46 325:47:33 337:17:06
Saur 345:25:49 258:28:12031:42:36 343:39:19 185:05:00 322:54:50 342:03:42
682 Drik 345:48:00 215:27:37073:50:27 358:38:34 342:03:44 028:07:06 128:39:19
Saur 346:03:50 214:34:27076:53:20 000:13:16 338:05:47 031:01:54 138:56:21
782 Drik 346:33:23 152:21:34157:55:10 357:25:17 136:30:39 342:28:19 272:56:05
Saur 346:41:49 154:02:50165:14:47 350:55:52 132:22:37 340:03:29 276:49:23
882 Drik 347:18:01 109:07:50260:33:02 322:29:25 298:43:55 323:44:48 044:58:58
Saur 347:19:46 107:58:29261:48:04 320:02:06 295:40:57 335:09:06 051:04:16
982 Drik 348:02:48 052:09:32311:52:48 324:01:45 085:44:25 359:21:07 205:23:02
Saur 347:57:41 052:17:24312:05:43 328:07:58 081:53:55 357:30:27 209:48:18
1082 Drik 348:48:22 000:17:10355:34:55 341:21:32 253:17:16 302:24:10 335:41:00
Saur 348:35:35 000:24:57356:47:17 347:45:54 251:39:09 301:33:34 337:05:04
Tropical longitudes
have been chosen for this
comparison so that the
controversies related to
ayanamshas do not
intervene. The differences
are clearly due to Mandaphalardha
and Sheeghraphalardha,
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
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
and Saura systems use Mandaphala
as well as Sheeghraphala. Even if
Mandaphalardha is discarded, as
Ganesha Daivajna proposed, this
non-linear anomaly does not
vanish, because differences due to
sheeghraphalardha are much more
than those due to mandaphalardha.
This highly irregular non-linearity
proves that no changes in
siddhantic values of mandaphalaparidhi
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
Suryasiddhanta 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 ayanamsha), 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 Suryasiddhanta was not
created on the basis of observation of physical planets. This result conforms with the
statements in Suryasiddhanta and all other available siddhantas and texts like Narada Purana
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 siddhantas,
what is the rationale and what is the use of such siddhantas ? The utility aspect is very simple to
answer : predictive astrology, although this utility of siddhantas 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 Suryasiddhanta 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
Suryasiddhantic astrology without any bias. During past few decades, I have found only a
handful of Drik-supporters ostensibly ready to test Suryasiddhantic 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, Suryasiddhantic astrology is used by a few among internet
astrologers. But even today, overwhelming majority of traditional panchangas are made with
some mediaeval tables which have been either directly created by means of Suryasiddhanta
(such as Makaranda Tables) or were indirectly based on some earlier source derived from
Suryasiddhanta (such as South Indian Vakya texts). For those who are not ready to test the
validity of Suryasiddhanta just because its planetary positions do not tally with physical planets,
is not any method available to prove the validity of Suryasiddhanta? The following sections
outline some of the answers to this question.
DECLINATION : Deduction of Modern Equation from Suryasiddhanta
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 Suryasiddhanta. If both modern
astronomy and Suryasiddhanta describe the same Sun, then Suryasiddhanta is certainly a
wrong text. But if the integral Suryasiddhantic 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 Vyasa 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 Suryasiddhantic 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 siddhantic 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
siddhantic equation mentioned above can be comfortably used to create modern table of solar
declination,provided we replace siddhantic 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 siddhantic 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 siddhantic equation of declination was
absolutely correct,
excepting the effect of
nutation which was
never used in any
siddhanta. Has any
historian of science ever
credited Suryasiddhanta
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"
Suryasiddhanta which is
supposedly lost, while
so-called "modern"
Suryasiddhanta is of a
much later unspecified
date. But it has been
shown in this paper that
the so-called modern
Suryasiddhanta 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 Suryasiddhanta
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 :
Suryasiddhantic 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 Suryasiddhantic 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 CosM/2
where 'M/2' is maximum possible value of siddhantic manda-phalardha, 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
Suryasiddhanta. 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 siddhantic values are changeless which scientists may like to explain as long-term
average. This siddhantic value is equal to NASA's value for 2000 AD, which confirms another
major finding that with proper ayanamsha the period of minimum difference between sidereal
siddhantic solar longitude with sidereal Drik 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 -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 Suryasiddhanta. In Suryasiddhantic
system, planets are not physical bodies, hence have no masses and gravitation. Therefore,
there is no effect of barycentre. Second effect is of Meru. Suryasiddhantic 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 Suryasiddhantic terms.
Suryasiddhanta 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 siddhantic 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-siddhantic. Siddhantic
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
siddhantic 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 siddhantic equations of Sunrise.
(This was published in a Hindi book by me in 2005 AD.)
Maximum mandaphala of Moon is 5°02'48" in Suryasiddhanta, but 6°17'19.7" or
22639.7" in modern astronomy (cf. NC Lahiri's Panchanga Darpana). Take the difference of sine
of mandaphalardha 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
Suryasiddhanta 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 Akasha), and therefore these equations need
revisions after few years. The above equation deduced siddhantically 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 siddhantic explanation of the most troublesome equation of modern physical
astronomy, the equation of Mean Moon (converted into Nirayana following NC Lahiri's method) :
The siddhantic equation for deducing any term in the above equation is this :
Ys is siddhantic 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 siddhantic mandochcha (apogee) in one Kalpa
(one Kalpa is of 4320 million years),
K is deduced siddhantically in following manner :
K= [{(Ys-Yd) / Ys} -(1/42000)]-1
x (Ys / t)
= 464.65408706471303027753666827
Then the wanted term in the siddhantic equation of Drik Nirayana Mean Moon is
Mn = [360°/ (n-1)! ] x [ tx [{ 1+ (1/ 387 ) } / K ] n]
Following is my siddhantic Drik formula of Nirayana Mean Moon created from above
equation, published in Hindi in 2005, built from purely Suryasiddhantic terms using Taylor's and
Lagrange's formulas of modern differential calculus :
Nirayana Mean Moon = 261°:10':1.24" + (17325593.803064287678" *T )
+100 *6.0337456626113312731046134872458" *t2
+10-3 *6.5095055710038624734367" *t3
+10-6 *4.681852716188407032" *t4
+10-9 *2.525508037859365516483207" *t5
+10-12 6
*1.0898575817626111529246014535145" *t
+10-15 7
*0.39193089427273663825034568365639" *t
+10-18 8
*0.12080988126146805887553801248113" *t
+10-21 9
*0.03258393040897135345673870555868" *t
+10-24 10
*0.0078118151691312247782389032276435" *t+......
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
"Panchanga Darpana". Latest equations do not differ significantly.
Nirayana Mean Moon=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 siddhantic
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-Puranic-Siddhantic 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 SuryaSiddhanta has never been written down.
EVIDENCE OF LOST PORTIONS OF SURYASIDDHANTA
Modern Value of Precession in Bhaskaracharya's Work based on Suryasiddhanta
In the chapter "Direction, Place and Time" (Suryasiddhanta, Ch.iii), E Burgess writes ;
Quote: (bracketed words are mine) : The (Surya Siddhantic) 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,
Mahayuga 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 Siddhanta ( ........... ... ..... .
.......
...............…, 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 (..... ......., 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 (Suryasiddhanta, 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 Chitra), it is a to and fro motion as all traditional commentators
accepted. Modern concept of precession is something different from the original concept of
ayanamsha. 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 Bhaskara-II, because he relied upon a wrong translation of Bhaskara by
Colebrooke (As. Res., xii 209 ; Essays, ii,374, etc) and did not try to examine Siddhanta
Shiromani which was wrongly translated by Lancelot Wilkinson due to Colebrooke's influence.
Bhaskara-II did not give his own opinion at all, and merely quoted Surya Siddhanta and Mujjal
(elsewhere Munjala and Manjula), saying Suryasiddhanta gives -30000 revolutions of sampat or
equinoctial point per Kalpa while ayana has a motion of +199669 revolutions per Kalpa (of 4320
million years). Bhaskara's own opinion was that these should be followed, which means both
Surya Siddhanta and Mujjala were correct in Bhaskara's opinion. Colebrooke, Burgess,
Wilkinson, etc have misquoted Siddhanta 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 Sharma is correct, although he
could not get the real meaning.
The startling fact is that Siddhanta 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 Suryasiddhanta,
while Mujjala's value of ayana's motion is +199669, and both (Suryasiddhanta 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 Siddhanta 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 Siddhanta
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. Bhaskara-II neither excluded Suryasiddhanta, nor Mujjala, but
mentioned the both must be used, which is clear from verse-19, where he clearly asks to add
Mujjala's ayana-chalam to Suryasiddhantic sampat-chalanam (this sampat-chalanam is
anomalistic precession with a period of 144000 years per cycle, not far from modern value).
Another startling fact is that Bhaskara-ii differentiates sampat-chalanam of Suryasiddhanta from
ayana-chalanam of Mujjala, and says both must be added before computing phenomena like
declension, ascensional differences, etc. But modern commentators like Colebrooke misinterpret
Bhaskara-II deliberately, and imply that sampat-chalanam of Suryasiddhanta quoted by
Bhaskara-ii was an erroneous thing which must be forgotten, while ayana-chalanam of Mujjala
was a crude approximation of modern precession. But this interpretation is falsified by
Bhaskara's original verses (and his own commentary Vasanabhashya) as shown above. The root
of this problem lies in the fact that sampat-chalanam of Suryasiddhanta is a distinct
phenomenon from ayana-chalanam of Mujjala according to Siddhanta Shiromani, but readers
are not informed of the real meaning of Siddhanta Shiromani and false quotation from
Siddhanta 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 sahibs of India. Those who do not consult the original texts cited above will not
believe me.
Siddhanta-tattva-viveka by Kamlakara Bhatt is a medieval text, which clearly states that
Saurpaksha is distinct from Drikpaksha. Saurpaksha (astronomy of bhuvaloka) is
Suryasiddhanta as it exists. Drikpaksha (astronomy of Bhooloka or physical/material/sensory
world) is that version of Suryasiddhanta which was not preserved because it was useless in
astrology. Siddhanta Shiromani uses many concepts of Drikpakshiya astronomy, as the instance
cited above proves. Saurpakshiya Suryasiddhanta does not contain any refence to 30000 cylces
per Kalpa mentioned by Bhaskara-II. He was quoting from Drikpakshiya Suryasiddhanta which
as a text had been lost ; Bhaskara-II said in his own Vasanabhashya commentary of Siddhantashiromani
that Suryasiddhanta is "agama". Modern commentators confuse both variants of
Suryasiddhanta. Siddhantatattvaviveka is prescribed in post-graduate (Ganitacharya) syllabus
of Sanskrit universities, but no modern commentator has ever tried to translate it or comment
on it.
According to Bhaskara-ii , negative sampat-chalanam of Drikpakshiya Suryasiddhanta should be
added to positive ayana-chalanam of Mujjala to get final Drikpakshiya precession, which is very
close to modern value. Ayana-chalanam of Mujjala 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 Suryasiddhanta 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.
Mujjala's ayana-chalanam, as mentioned in Siddhanta Shiromani, gives a period of (4320 million
/ 199669 = ) 21636 years per cycle. Siddhanta 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) Suryasiddhantic sampatchalanam. If
this 21636 year cycle is not precession, what is it ??
Readers should read a Wikipedian article Milankovitch cycles
( http://en.wikipedia.org/wiki/Milankovic_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 Mujjala 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 Siddhanta
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.
Siddhanta Shiromani also says that Mujjala's ayana-chalanam (21,636 years per cycle) is
opposite to sampata-chalanam. Bhaskara-ii clearly defines sampata-chalanam as "the point of
intersection of equatorial plane and ecliptic" (which is the very definition of equinox). Hence,
what Siddhanta Shiromani says is exactly what Wikipedia informs us, the only difference is that
Siddhanta Shiromani is misinterpreted and declared to be obscurantist, and the great cycles
mentioned in Siddhanta Shiromani is "discovered" by 20th century scientists. But we must
remember Bhaskara-ii did not discover these things, he acknowledged Suryasiddhanta and
Munjala.
Bhaskara-ii knew Drikpakshiya Suryasiddhanta, which has not survived because it was not
useful in astrology. In his formula of precession, Bhaskara-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 Puranic verse which
proves knowledge of equinoctial precession in Puranic times :
................. .... ...............................................................
It means : "Uttanpada'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 Puranic-epic stories. Hence, the bhachakra also
librates with respect to this fixed point Meru.
According to Bhaskara-II, orbital precession is derived by substracting anomalistic precession
(sampat-chalanam) from the first component of Milankovitch cycles (Munjala's ayanachalanam).
Bhaskara-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 Bhaskara-ii.
But two things about confusing terminology must be borne in mind : this sampat-chalanam he
finally gets by combining the two quantities mentioned above. According to Bhaskara-II,
Suryasiddhantic sampat-chalanam is 30000 per Kalpa. He does not give a name for the term
which is finally obtained by combining this sampat-chalanam with Munjala's ayana-chalanam,
but the definition he provides for Suryasiddhantic sampat-chalanam is exactly the definition of
the final quantity whose name he does not provide. Hence, there were many types of sampatchalanams
!! 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 Munjala's precession. It is quite
distinct from Saurpakshiya Suryasiddhantic ayana-chalanam (trepidation) as mentioned in
existing text. Burgess could not digest this theory of libration (oscillation or trepidation, ie,
ayanaamsha -motion) and tried to distort the meaning of terms to fit modern view of orbital
precession with this Saurpakshiya precession. Bhaskara-ii knew and respected Suryasiddhanta
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 Bhaskara-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 Siddhanta 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 Siddhanta Shiromani has never
been translated or explained. Bhaskar-ii knew Siddhanta 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 Siddhanta 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 Siddhanta
(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 SuryaSiddhanta" 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-udayaAshcharadala-
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 SuryaSiddhanta does not give a motion of -30000 per Kalpa of any entity, while
Bhaskara claims SuryaSiddhanta says so. But Bhjaskar says SuryaSiddhanta is "Agama" and
therefore must be accepted as final proof ("pramANa"). Hence, some version of SuryaSiddhanta
available to him mentioned -30000 per kalpa as the motion of SOLAR APOGEE. But
SuryaSiddhanta gives a value of only 387 revolutions for solar apogee, and Siddhantashiromani
gives a figure of 480 per Kalpa (verse 5 in bhagaNAdhyAya). Bhaskar's value is +93 more than
that given in SuryaSiddhanta. Late NC Lahiri wrote in Advance Ephemeris (page 90) that some
corrections were needed in SuryaSiddhantic 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 SuryaSiddhantic mandochcha value. But Bhaskar never said
SuryaSiddhanta was incorrect. Hence, there were two versions of SuryaSiddhanta : 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
SuryaSiddhanta. Bhaskar says SuryaSiddhanta'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 SuryaSiddhanta 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 SuryaSiddhanta 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 SuryaSiddhanta.
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 Siddhanta
Kamlakara Bhatt(author of Siddhant-tattva-viveka,as yet untranslated),an ardent supporter of Surya
Siddhanta and an opponent of Bhaskara II,had strongly advocated in 16th century that Surya Siddhantic
planets are to be distinguished from the 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 Siddhanta. Drik-paksha meant the world perceived by means of sense organs,
and therefore it denoted the foeld of modern astronomy, while Saurpaksha denoted the gods of Next
World bearing same name as the material planets but being non-material. Ketaki system of almanac used
these concepts in actual practice. But the Surya Siddhantic viewpoint of Drikpaksha was never elaborated
by anyone.Unfortunately, after the disappearance of the Surya Siddhantic commentary of Aryabhata the
Elder, even the Saurpakshiya mathematics became obscure, and all the commentators kept on repeating
hackneyed phrases whose practical significance was clear to none. Ranganath,Kamlakar Bhat,Sudhakar
Dwivedi, Kapileshwar Shashtri, etc wrote voluminous commentories on Surya Siddhanta, elucidating
everything except the practical ways of using the formulas and the Merucentric geometrics.
Let us examine some orally transmitted occult theorems of Surya Siddhantic school which show that
Drikpaksha can be deduced from Saurpaksha mathematically, without the aid of any observatory.
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 (= e),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 e and 'pi' by p . Then,
=365.25640000130486608685495644391days
This is the limiting value of scientific sidereal year by means of Vedic (i.e.,Surya Siddhantic) equation.
The Vedic (i.e.,Surya Siddhantic) theorem of scientific Tropical Year Yt (=365.24219878125) will be
demonstrated later, let us first get the value of mean sidereal year with the help of following equation :
=365.25636122581667241689259003252668days
Now we can get the Period of Precession PP :
= 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 :
= 29.53058780664716371374days.
Metonic Year Ym is equal to :
=365.246743924320182775185653635days
Precessional Period due to Moon's effect (PPM1) :
= 37978.09022183997109169737years
Precessional Period due to Sun's effect (PPS1), intermediate term :
= 80356.674413324332490977057144470years
Precessional Period due to Sun's effect from alternative equation (PPS2) , intermediate term :
= 80356.674413324332490977057250561years
The difference between PPS1 and PPS2 is due to computer's errors and is equal to a negligible quatity :
Difference=1.320251252*10-27years
Intermediate terms are :
A1 = PPS1 / PPM1 = 2.1158692799964388041303958720096.
A2 = PPS2 / PPM1 = 2.1158692799964388041303958748028.
Precessional Period due to Sun's effect (PPS) , final value :
PPS = PPS1 + A1 = 80358.790282604328929781187540342
PPS = PPS2 + A2 = 80358.790282604328929781187646436
There is difference in two values of solar precessional period shown above (PPS) in 27th digit only. Hence,
the computations are highly reliable.
There are three equations for obtaining scientific Tropical Year (in days) :
= 365.24219878124999999999999999999638527125
= 365.24219878124999999999999999999638595267
= 365.2421987812499999999999999999999999972349
Drikpakshiya Tropical Year is the most precise constant known to modern astronomy, whose empirical
value is 365.24219878125 ± 0.00000000058 days.
The error of ± 0.00000000058 days is due to errors in modern instruments. The three values we obtained
above through Vedic equations have errors in 34th digit which is due to 34-digit precisiuon of Windows
Calculator used to obtain above results. The net result is startling : value of 'pi' is the basic term used to
deduce exact value of most important astronomical constants, if you know the exact value of 'pi' then you
can deduce the exact value of astronomical constants. Modern physicists know many such equations,
which are called "coincidences" by atheists, and as proofs of Intelligent Design of Universe by believers in
God.
SuryaSiddhantic Theorem of Lunar month
M1 = 365.256400001304866086855 / (42/p) = 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/ )* {(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
A=A1*A2*(42 / p)=0.45270842758190827172
Here is the Lunar Binomial Equation :
(A*M2)+M-Ys=0
Roots of this binomial are :
M1 = [-1 + Sqr(1-(4A*Ys)] / 2A = -29.5305886713712313156 days.
M2 = [-1 -Sqr(1-(4A*Ys)] / 2A = +27.3216613815891770963 days.
M2 -Mss = 0.063953054266910187950698752 seconds.
This apparent 'error' is equivalent to the error of 104.643228673117 years in 4.1748 billion years ( = 14
manavantara of 71 mahayugas each, each Drikpakshiya mahayuga being of 4.2 million years).This is the
value of Drikpakshiya correction in Kalpa-Mandochcha, for which Bhaskaracharya deduced the value 93 in
Siddhantashiromani and stated Kalpa-Mandochcha to be equal to 480 (= Saurpakshiya Kalpa Mandochcha
387 + 93 Drikpakshiya correction). Its elucidation will be shown below.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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 lunar month used by tropicalist scientists !
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Surya Siddhantic Theory of the Rotation of Material Universe
According to modern physical science, material universe cannot be said to be rotating even if it rotates,
because all space-time-continuum is intrinsically related to matter as part of a unified whole, and there
can be no space or time outside the realm of matter. Since there is no space or time outside material
universe, rotation of this material universe cannot be measured because there is no external space-time.
Let us call the space of time of this material universe as material-space and material-time. There are 14
universes (Bhuvanas) in the Multiverse (= Creation or Srishti), and we live in the middle universe. Since
all forms of matter have shown to be associated with SPIN, from galactic to sub-atomic levels, it is natural
that the material universe should also rotate. But it can be measured only with reference to the non-
material universe or Bhuvaloka, which is the world of Saurapakshiya Suryasiddhanta. Suryasiddhanta
states our universe to be finite, and according to Godel's theorem a finite system cannot be fully
explained on account of its internal properties and phenomena only. There must be something outside
this finite universe which should explain the workings of this universe and its raison-de-etre.
Now we show the Vedic theorem of Rotation of the Material Universe. Surya Siddantic Kalpa is equal to
4.32 billion years. The Creator (Brahma) took 47400 divine yuears to create the Creation, which is equal
to 47400 * 360 human years. Hence the total Age of Creation = 4.32 billion -(47400 * 360) =
4302936000 years.
4302936000 / 24000 = 179289 is the extra years due to Saurpakshiya precession. Hence total number of
Saurpakshiya tropical years in one creation is equal to 4302936000 + 179289 = 4303115289 years.
Divide this number with (Saurvarsh / Chandravarsh) = (Saurpakshiya Sidereal Year / Twelve
Saurpakshiya synodical months) = 365.258756481481481 / (12*29.53058794607) = 1.0307356481481.
The result is 4174800101.976788423. In it, 4174800000 is the duration of Drikpakshiya Creation ( =
4200000*71*14), and 101.976788423 is the exact value of Drikpakshiya correction in Kalpa
Mandochcha, for which we had got a crude value 104.643228673117 above, and Bhaskaracharya had got
93. A quantity of 101.976788423 years in 4.1748 billion years is equal to 0.107065 hours in 500 years.
Nirmal Chandr Lahiri was the secretary of Panchanga Reform Committee of Government of India. He
analysed the differencebetween Drikpakshiya and Saurpakshiya tithi (elongation of moon), and found a
difference of 0.11 hours in 500 years,which he assumed to be due to error in Surya Siddhantic values(NC
Lahiri,1968,p.90). But Surya Siddhantic values do not belong to this physical Universe. This apparent
error of 0.107065 hours in 500 years is a result of extra 102 rotations of the Drikpakshiya solar orbit
during one Creation : Saurpakshiya value is 387 while Drikpakshiya value is 489 (Bhaskaracharya-II gave
480 only in Siddhantashiromani). This Drikpakshiya rotation of solar ellipse is in addition to the normal
Drikpakshiya rotation per 136000 years which is the cause behind anomalistic year.
---------——
In the same book NC Lahiri gives data of Surya Siddhantic beej corrections applied to lunar anomaly in
comparison to modern scientific values, which shows that beej correction needed in lunar anomaly in
order to get Siddhantic tithi from scientific tithi increases at a rate of one revolution in 42000 years(NC
Lahiri,1968,p.90). Difference between modern scientific tropical Sun and Siddhantic Sun also show 360°
change during 42000 years. Sun and moon do not move in same orbits. Hence we must conclude that the
physical Universe itself is revolving at the rate of one revolution per 42000 years round some point very
near to Earth's centre,which suggests that the centre of Universe is not far from Earth's centre. Before
dealing with this centre (Meru or Mt Kenya in Africa),let us first elucidate the 42000 year cycle of the Sun.
Siddhantic sidereal year (365.258756481481)and Drikpakshiya tropical year(365.24219878125) differ at
the rate of one revolution or one year in 22059.75174 years. But in reality both divurge from each other
at the rate of one revolution in 42000 years. For instance,Kaliyuga commenced at Ujjain midnight 17-18
Feb,3102 BCE,when Siddhantic nirayan(=sidereal in Indian system) Mean Sun was at zero longitude.
5106 years later Siddhantic zero Sun was to be found on 16 Apr,2005 at 5:03:15 AM (Ujjain). If mean
Sun differs by 44.2106 days in 5106 years(taking into account 13 days of Gregorian reform), it should
differ by one year in 42182.8 years. Due to non-linearity of elliptical paths,we get here 42182.8, the
exact figure is an integer 42000. It raises a question : if mathematically Siddhantic year and scientific
year should show a difference of one revolution in 22059 years, why do they differ by one revolution in
42000 years in reality ? Where does 19941.24826 years come from ? We have here compared sidereal
Siddhantic year with tropical scientific year, hence this extra difference of 19941 years must be related to
precession. Siddhantic period of precession is 24000 years and scientific period is 25789.4883233 years.
Both form cycles of 100000 ± 12000 years with respect to 19941 in harmonic series. Thus, we are now
getting close to constants of Milankowitz,just by means of analysing Surya Siddhantic constants !
The Vedic value for Drikpakshiya period of precession is 25789.4883233 years. But it needs slight
modifications due to long term cycles.We had got 101.976788423 years per Drikpakshiya Creation for the
exact value of Drikpakshiya correction in Kalpa-Mandochcha, which is equal to
101.976788423/4174800000 per year. Add this correction to 1/257898.488, we get 1/25773.252377 in
the harmonic series. Again add 1/(4200000*71) to it and get 1/25771.025002. (4200000*71) is the
duration of one Drikpakshiya Manvantara. A period of 25771.025 years is equal to 50.28903584 seconds
of arc per sidereal year, or 50.288160017 seconds per Julian Year. Presently, 50.28796195 seconds per
Julian Year is the accepted value.
Ancient Cosmogony and Geography
Surya Siddhantic system is neither heliocentric nor geocentric. It clearly states in Bhoogoladhyaya that Mt
Meru resides at the centre (equator) of globe in the region of Zamboodweep. In Africa, Mt Kenya is
situated upon equator in a region where many modern place names are reminiscent of Surya Siddhanta :
Meru town near Mt Kenya, another Mt Meru slightly southwards, a place named kinyan-giri which means
Mt Kinyan or Mt Kenya in sanskrit, river Zamboonadi > *zamboodi > *zambedi > *zambezi, Muzambique,
Zambia, Zimb-abwe, Gabon (< *Zamboon), Congo (< *Gongo < *zambo),etc. Homo genus of
mankind is known to have evolved in that region around 4 million years ago. Indian Puranic ttreadition
also mention that modern races of mankind evolved near Meru in 3891194 BCE when the present
Mahayuga commenced. Surya Siddhantic formulae of making true planets from mean ones require the
use of distance from Earth's centre to a point in space 28.913 kilometres above the top of Mt Meru (Mt
Kenya), which was believed to be centre of all universes by Puranic authors.
Surya Siddhantic universe is much smaller in comparison to material universe, and Sun's distance from
Earth is only 861.7 times of Earth's equatorial radius. Material Sun's distance is 23455 times of Earth's
equatorial radius ! Ptolemy used a figure 1210, which is not much removed from Surya Siddhantic figure.
Ptolemic system is well known, but Surya Siddhantic system is rather obscure, known to a few initiated
brahmanas only. Due to lack of knowledge of orally transmitted and unpublished portions of original
Surya Siddhanta, European commentators believe that Surya Siddhantic system was influenced by
Ptolemy's Almagest. But those who know the secrets of Surya Siddhanta say that its framework is too
complex and organically self-contrained to have been influenced by any other system. For instance, Surya
Siddhantic daily motions of all planets are exactly equal to a constant, but this rule is not followed in
Almagest. Surya Siddhantic system is based upon a cosmic centre at Meru, which is absent in Almagest.
Surya Siddhantic solar epicycle is equal to 14 yojanas per degree, which is equal to 5040 yojanas for 360
degrees. Its diameter is 1604.3 yojanas, which is 4.3 yojanas more than Earth's equatorial diameter. 4.3
yojanas equals 5.199 kilometres ( height of Mt Meru or Mt Kenya)plus 28.913669 kilometres. Solar
epicycle equals to 14 yojanas, which gets reduced to 13:40 at perigee of this elliptical epicycle, which
when divided by 2 gives 2:10':31" degrees, which is the maximum value of equation of centre
(mandaphala = difference between mean and true Sun) for Sun. Surya Siddhantic theory, therefore
relates yojana to degrees in an intrinsic manner, which makes it clear that it was not borrowed from
Almagest. Earth's diameter is an integer 1600 yojana. Moon's diameter is also an integer 436 yojanas.
These rations are perfectly scientific. Such integral values seem to be mysterious when they are
confirmed with modern science. This value of yojana was not only prehistoric, manifest in the story of
Jarasandha's 99 yojanas from Girivraja to Mathura proving that siddhantic yojana was prevalent in prehistoric
era of Girivraja's kings, as mentioned in Mahabharata, but was also intrinsically related to many
native concepts of Surya Siddhanta, discussed in other sections of this article.
Only the most simple and easiest aspects of Suryasiddhantic mathematics has been presented
here. The details are highly intricate and difficult. Kaliyuga is not fit for Suryasiddhanta and
therefore calls it obsolete. The extant text of Suryasiddhantic provides sufficient clues for
unravelling its unwritten marvels.
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