-
Modern Equations On Ancient Principles
Deduction of Exact Equations of Modern Astronomy through Ancient
texts of Siddhnta Jyotia
Vinay Jha
Disclaimer from uploader:
I feel that this paper presented herein as authored by Vinay Jha
has a lot of merits and, only for aesthetic reasons, the
presentation (layout) has been altered as well as corrections were
made while some (unnecessarily) wordings have been struck out
wherein it was deemed necessary in order to maintain the simplicity
of this great research for the sake of ease in digesting such a
sagaciously-written scientific writeup.
Contents INTRODUCTION
...............................................................................................................................................................
2
Comparison of Tropical Planetary Longitudes for Ujjain on March
3
....................................................................
4
Difference in Tropical Planetary Longitudes : Dk vs Saura, in
Arc-Sec
.................................................................
5
DECLINATION: Deduction of Modern Equation from Srya-Siddhnta
....................................................................
7
LATITUDE OF MOON
.......................................................................................................................................................
9
Exact Differential Equation Of Physical Moon
..............................................................................................................
10
Evidence Of Lost Portions Of Srya-Siddhnta
.............................................................................................................
12
Deduction of Modern Astronomical Constants from Srya Siddhnta
.....................................................................
20
Theorem of Dk-Pakya Sidereal and Tropical Years and of
Precessional Period ..............................................
21
Vedic (ie, Srya-Siddhntika) Theorem of Lunar month
........................................................................................
23
Lunar Binomial Theorem :
..........................................................................................................................................
24
Srya Siddhntika Theory of the Rotation of Material Universe
................................................................................
25
Ancient Cosmogony and Geography
..............................................................................................................................
27
The Cycles of Lord Brahm
.........................................................................................................................................
28
-
INTRODUCTION
Viu Dharmottara Pura of Vedavysa
yantra vedhdi njta yad bja gaakaistata grahadi parketa na
tithydi kadcana
Sage Vysa has clearly said in Viudharmottara Pura ( ) that in
examining perceivable
events like eclipses etc ., where an actual observation is
needed , the position of the planets should be
further corrected using Dk -Karma corrections (i.e., adding the
Ayan a to get the Tropical longitude) so
that they can be used in determining the actual event , but
these Dk -corrections should never be made use
of in computation of Tithis and others.
Nir aya Sindhu
- -
ada phala sidhyartha yathrka gaita kuru gaita yadi drtha tad dy
udbhava tassad
Nir aya-Sindhu also states that Srya -Siddhnta should be used
for knowing invisible results ("Ad a
Phala" i.e., things like Destiny or Fortune).
The mathematics of Srya -Siddhnta is given in the Nrada Pur a
too. In all other Puras too, Srya -
Siddhnta has been made us e of for the purpose of computation
and its ideas have been presented at
many place. But since the time of Graha -lghava (cir.1440 AD) ,
materialists have begun to dominate the
scene gradually. They consider physical planets to be exactly
same as the astrol ogical planets.
dk-karma correction ( - ) is an essential part of ancient
Siddhnta skandha of Jyoti a. But dk-karma saskra are never used in
finding True Longitudes of planets ( graha-spa-karaa | - ) in any
ancient Siddhnta text It is used only when perceivable phenomena
like eclipses , heliacal risings
& settings ( skrdi udaysta | ) etc ., are needed. Two chief
components of dk-karma correction are
-
1. ka & yana dk-karma saskra (corrections ) ( - - ) and 2.
ayana-dk-karma saskra ( - - )
both of which , are explained in ancient siddhntas , chief of
which is Srya -Siddhnta.
But these 2 dk-karma corrections give only that position of a
planet which i s needed for phalita astrology, e.g. udaysta of
Jupiter & Venus is needed for determining Muhrta s of
auspicious events like Vivha|marriage , Upanaya| sacred thread
ceremony , etc. Positions of physical planets as perceived by
our
naked -eyes is not given by the equations given in any
Siddhntika texts.
It is for this reason , many medieval scholars like Ga ea
Daivaja of Graha -lghava or Divkara
Daivaja of Makaranda -Vivaraa have all declared that the Srya
-Siddhnta treatise has now b ecome
obsolete and some changes are needed in its formulations or
methods. They advocated removal of manda-phalrdha | from the 4
corrections made in Mean Longitude of a planet to get the True
Longitude , while ignoring completely that, if such a thing were to
be indulged, the very fundamental theory of
siddhnt ika texts likewise will become distorted. Unfortunately
, no any siddhnt ik a text or its commentator
n ever explained the basis of the fundamental t heory involved
in those 4 corrections of siddhnta texts ,
namely
1. ghra -phalrdha | ,
2. manda -phalrdha | ,
3. manda -phala | and,
4. ghra -p hala |
Rev . Eveneger Burgess , the translator & commentator of
Srya -Siddhnta , candidly accepted that he could
never understand the rationale behind these 4 corrections in
spite of having spent 8 years among Indian
experts to learn the Srya -Siddhnta. Other commentator s of this
text were even worse , they neither
explained nor had the humility to admit their inability to
explain the WHY s behind these calculations . All
ancient S iddhntas and Puras which deal with graha-spa-karaa are
unanimous in the applicability and order of aforementioned 4
corrections , but none of them explain the mathematical reason ing
and
related geometry.
Although 2 medieval so-called Indian experts , namely Ga ea
Daivaja and Divkara Daivaja ,
rejected the applicability of manda-phalrdha, they did not
bother to go into the rationale behind either manda-phalrdha or
even the remaining 3 corrections.
-
If manda-phalrdha was rejected , what is the mathematical reason
of ghra-phalrdha then ? manda & ghra phala are accepted in
modern astronomy too , as equation of centre and the reduction of
heliocentric to geocentric position , respective ly. But what about
their halves manda & ghra phalrdha?
Modern astronomy knows NO SUCH THINGS as manda & ghra
phalrdha. Nobody understands them , but surprisingly enough they
are taught by Jyoti a departments of Sanskrit univer sities.
Here , a question arises if no commentator has ever succeeded in
unravelling the mathematical logic
behind the most essential aspects of siddhnta texts , dont you
think there is something m ysterious about
siddhnta te xts ? Either all siddhnta texts are wrong or , all
medieval and modern experts are ignorants in the field of siddhnta
skandha of Jyoti a.
A false excuse is invented by some experts claiming that these
ancient siddhnta texts were then -accurate in ancient times but as
of now have become outdated. This false logic was first invented
by
the author of Graha-lghava, Ga ea Daivaja and is flaunted by
majority of modernisers of astrology. Here is the irrefutable proof
of falsity of such stat ements in tabular form , which shows there
was no period
in known history during which difference between
1. Dk and, i.e., perceived, or physical planets
2. Saura, i.e., of Srya-Siddhnta
tended towards any minimum value.
The First table (below) gives the planetary longitudes from both
methods , and the second table following
this gives differences , at regular intervals of 100 years.
Comparison of Tropical Planetary Longitudes for Ujjain on March
3
AD Sun Moon Mars Mercury Jupiter Venus Saturn
382 Dk 343:33:59 001:39:24 304:06:20 320:29:20 238:48:12
310:08:09 050:58:12
Saura 344:09:44 002:18:18 306:00:04 317:26:27 236:14:05
307:10:43 058:18:51
482 Dk 344:18:44 318:25:11 347:52:07 319:15:50 025:16:49
027:27:47 209:22:01
-
Saura 344:47:48 319:25:52 350:42:50 324:10:33 021:03:18
025:40:02 214:40:16
582 Dk 345:03:34 253:57:54 029:03:14 335:51:57 188:46:46
325:47:33 337:17:06
Saura 345:25:49 258:28:12 031:42:36 343:39:19 185:05:00
322:54:50 342:03:42
682 Dk 345:48:00 215:27:37 073:50:27 358:38:34 342:03:44
028:07:06 128:39:19
Saura 346:03:50 214:34:27 076:53:20 000:13:16 338:05:47
031:01:54 138:56:21
782 Dk 346:33:23 152:21:34 157:55:10 357:25:17 136:30:39
342:28:19 272:56:05
Saura 346:41:49 154:02:50 165:14:47 350:55:52 132:22:37
340:03:29 276:49:23
882 Dk 347:18:01 109:07:50 260:33:02 322:29:25 298:43:55
323:44:48 044:58:58
Saura 347:19:46 107:58:29 261:48:04 320:02:06 295:40:57
335:09:06 051:04:16
982 Dk 348:02:48 052:09:32 311:52:48 324:01:45 085:44:25
359:21:07 205:23:02
Saura 347:57:41 052:17:24 312:05:43 328:07:58 081:53:55
357:30:27 209:48:18
1082 Dk 348:48:22 000:17:10 355:34:55 341:21:32 253:17:16
302:24:10 335:41:00
Saura 348:35:35 000:24:57 356:47:17 347:45:54 251:39:09
301:33:34 337:05:04
Tropical (Syana) longitudes have been chosen for this comparison
so that the controversies related to
Ayan a s do not intervene. The differences are clearly due to
manda & ghra phalrdha, because the difference in mean value s
of longitude will result in a linear increa se in difference with
time which is not the
case , while the differences in manda-phalrdha plus
ghra-phalrdha will also show another line of linear increase in
difference with time , because both dk & saura systems use
manda as well as ghra phala. Even if manda-phalrdha is discarded ,
as Ga ea Daivaja once proposed , still, this non -linear anomaly
does not vanish , because differences due to ghra-phalrdha are much
more than those due to manda-phalrdha.
Difference in Tropical Planetary Longitudes : Dk vs Saura, in
Arc-Sec
AD Sun Moon Mars Mercury Jupiter Venus Saturn
382 -2145 - 2334 - 6824 +10973 + 9247 +10646 -26439
482 -1744 - 3641 -10243 -17683 +15211 + 6465 -19095
-
582 -1335 -16218 - 9562 -28042 +13306 +10363 -17196
682 - 950 + 3190 -10973 - 5682 -21723 -10488 -37022
782 - 506 - 6076 -26377 +23365 +14882 + 8690 -13998
882 - 105 + 4161 - 4502 + 8839 +10978 -41058 -21918
982 + 307 - 472 - 775 -14773 +13830 + 6640 -15916
1082 + 767 - 467 - 4342 -23062 + 5887 + 3036 - 5044
This highly irregular non -linearity proves that no changes in
Siddhntika values of manda-phala-paridhi or ghra-phala -paridhi can
reduce this anomaly , because those changes will be linear while
actual difference is highly no n -linear , ranging from over +6 to
less than -11 , which is an unacceptably high
anomaly because ryabha a or Varhamihira and all other scholars
could not be so great fools to have
failed to notice such errors.
Had Srya -Siddhnta been created around 400 AD or on any other
date through sensory observations , this
anomaly should be minimum around that date. The fact is that
there is no such period in history. Sun's
anomaly is minimum around 900 AD , but the anomaly of Venus is
maximum then and other plane ts also
have very high divergences.
Actually , it is around 2000 AD when sidereal differences in
longitudes of D k and Saura planets become
minimum ( regardless of the Ayan a value), although these
differences still remain huge. All these
findings cannot be presented here. There are handy softwares
freely available online through which anyone
can check these conclusions.
Therefore , it is clear that Srya-Siddhnta was not created on
the basis of observation of physical planets. This result conforms
with t he statements in Srya -Siddhnta and all other available
siddhntas and texts like Nrada Pura mentioned above , which say D k
positions should not be used in
Phalita Jyoti a.
Now , the problem gets intensified instead of being solved. If
physical planetary positions and the
astronomy of modern scientists cannot explain the equations of
our ancient siddhntas , what is the rationale
and wha t is the use of such siddhntas ?
The utility aspect is very simple to answer predictive astrology
, although t his utility of siddhntas
is unpalatable to modern secularists who cannot tolerate the
very mention of " astrology". But whether astrology is a true or a
false science , it is a fact that all known societies had great
faith in and reverence for
-
astrology in ancient ages and astrology was the mother of modern
astronomy too. Scientists deliberately
omit to mention that not only ancient astronomers like Ptolemy
but even the forerunners of modern
astronomy like Copernicus and Kepler were practising astrologers
an d the motivating force behind their
interest in astronomy was to find better means for predictive
astrology.
The problem with materialists is that they cannot agree to test
the validity or falsity of Srya -Siddhnta on
the criterion of predictive astrology. Not only anti
-astrologers , but even supporters and users of Vedic
Astrology using D k astronomy are not ready to test Srya
-Siddhntika astrology without any bias. During
past few decades , I have found only a handful of D k
-supporters ostensibly ready to test Srya -Siddhntika
astrology , but they push their own habits and biases and
therefore could not test it in its own frame of
reference. This is a common problem with all materialists. On
the other hand , most of the spiritualists have
no intere st in Jyoti a.
Therefore , Srya -Siddhntika astrology is used by a few among
internet astrologers. But even
today, overwhelming majority of traditional Pac ga s are made
with some medieval tables which have
been either directly created by means of Srya -Siddhnta (such as
Makaranda Tables) or were indirectly
based on some earlier source derived from Srya -Siddhnta (such
as South Indian Vkya texts). For those
who are not ready to test the validity of Srya -Siddhnta just
because its planetary positions do not tally
with physical planets , isnt there any method available to prove
the validity of Srya -Siddhnta? The
following sections outline some of the answers to this
question.
DECLINATION: Deduction of Modern Equation from Srya-Siddhnta
The apparent srya vth the ecliptic which is the path of the Sun
is slanted on the projection of Equatorial Plane by a variable
amount which is about 23.4393 at present according to modern
astrono my
but this value is exactly equal to 24 according to Srya
-Siddhnta. If both modern astronomy and Srya -
Siddhnta describe the same Sun , then Srya -Siddhnta is
certainly a wrong text. But if the integral Srya -
Siddhntika values give the results obtain ed through modern
astronomy with a very high degree of precision
through simple D k -karma correction , what should we deduce ?
As cited above , Sage Vysa sai d that
perceived positions of planets should be obtained by means of
finding proper bja-corrections. Let us take
the case of Declination of Sun for any given date , for which
the Srya -Siddhntika equation is thus :
Sin D = Sin L x Sin P
where ,
-
D is Declination for a given time , L is Tropical Longitude of
Sun for that given time , and P is the maximum possible value of
Declination.
Modern value of maximum declination is less than the Siddhntika
value by 2018.6" arc -seconds. If we
neglect the effect of nutation whose maximum value ~17 is
negligible in respect to this huge difference ,
then the Siddhntika equation mentioned above can be comfortably
used to create modern table of solar
declination , provided we replace Siddhntika value of P (maximum
declination) with modern value.
Thus , we can create the modern scientific table of solar
declination , as given in N . C . Lahiri 's book
Advance Ephemeris, shown in the picture below. Using a
scientific calculator , anyone can check the Siddhntika equation
cited above with reference to Lahiri's table below. Out of 180
entries in the table at
in tervals of 1 , a difference of one arc -minute will be
noticed at a handful of places , which is due to effect
of nutation which is always less than 17.23 (arc -seconds ) but
sometimes results in 1 (arc -minute )
difference when value are rounded off in arc -minutes as given
in Lahiri's Table. It proves that the
Siddhntika equation of declination was absolutely correct ,
excepting the effect of nutation which was never
used in any siddhnta.
Has any historian of s cience ever credited Srya -Siddhnta with
invention of the correct equation of solar
declination which is used by even modern scientists ? No.
All of them insist that Ptolemy preceded the date of composition
of Old Srya -Siddhnta which is
supposedly lo st, while so -called modern Srya -Siddhnta is of a
much later unspecified date. But it has been shown in this paper
that the so -called modern Srya -Siddhnta cannot be ascribed to any
date of
known history without accepting very high amounts of errors in
all planets , which will result in declaring all
ancient Indians as idiots who made such errors.
Now , the real question is this if the author of Surya -siddhnta
was capable of finding such a fine
formula for computing declination , why the value of maxi mum
declination could not be measured within
tolerable limits of inaccuracy ?
Historians of science have a handy answer : Indians stole the
equation from Greeks , but could not
measure planetary positions accurately. They can never accept
the reality which is much more astounding
than anyone can ever imagine Srya -Siddhntika equation of
Declination can give exact modern values
of solar declination down to the lim it of less than one arc
-second. Two bja corrections are needed. The
major correction is simple : multiply the Srya -Siddhntika
declination P with the cosine of its exactly half -
value :
-
Sin D' = Sin D x Cos P/2
It gives a maximum value of 23.443745 which is only 16 arc
-seconds more than modern value obtained
by NASA scientists. Its geometric implication is that D k
ecliptic is exactly 12 slanted to Saura ecliptic ,
which means D k Sun is a completely different entity than the
Saura Sun. Now comes th e second bja-
correction
Sin D" = Sin D' x Cos M/2
where 'M/2' is maximum possible value of Siddhntika manda
-phalrdha , which Ga ea Daivajya and his
followers tried foolishly to expel from traditional astronomy
without understanding its significance. Max imum
manda-phala is equal to 2 10 32 according to Srya -Siddhnta.
Thus we get a final value of 23 26 22.27 , nearly equal to 23 26
22.27 which is the value given by latest DE -series ephemerides
from
NASA's JPL , the difference is merely of 0.8654 (arc -second ).
Here it must be noted that NASA's values
change with time , while Siddhntika values are changeless which
scientists may like to explain as long -
term average. This Siddhntika value is equal to NASA's value for
2000 AD , which confirms another major
finding that with proper Ayan a the period of minimum difference
between sidereal Siddhntika solar
longitude with sidereal D k longitude was 2000 AD , as mentioned
in previous section. Here only
summarized results of many important themes are show n.
LATITUDE OF MOON
The page from Lahiri's Advance Ephemeris given above gives table
for lunar latitude. Its formula is simple:
Sin Lm" = Sin (Moon - Rhu) x Sin Lm
Here , Lm is the latitude of Moon to be known , Lm is the
maximum possible Latitude of Moon , while Moon
& Rhu are their longitudes , tropical or sidereal. The only
problem is Lm, whose value in modern astronomy is higher than in
Srya -Siddhnta.
In Srya -Siddhntika system , planets are not physical bodies ,
hence have no masses and gravitation.
Therefore , there is no effect of barycentre. Second effect is
of Meru. Srya -Siddhntika astronomy is Meru -
Centric and not geocentric ( Ptolemaic astronomy was also not
geocentric; geocentricity is a wrong propaganda of medieval
Church). If we take these tw o effects into account , it is easy to
compute Lunar latitude of modern astronomy from Srya -Siddhntika
terms. Srya -Siddhnta has maximum lunar latitude
equal to 4.5 . Multiply its sine with the distance of Earth's
centre to the tip of Mt. Meru ( Mt. Ken ya) at
equator , which is 6383.362 KM s. We get 500.8328 KM s which is
equal to 0.001302891538 multiplied with
Moon's average distance from Earth. Substract it from Sine of
4.5 which is Siddhntika maximum latitude
-
of Moon , and get the arc -sine of the result. Thus we get the
reduced latitude due to effect of Meru -Centric ity
versus geocentricity. Now , add 'Moon / Earth' mass ratio
(nearly 1/81) to the sine of this reduced latitude in
order to get the effect of barycentre , and get arc -sine of the
resultant , which is the maximum D k latitude of
Moon , equal to slightly more than 5 08 . Accuracy needs correct
Earth:Moon ratio. A very small correction
is further needed due to effect of finer motions around Mt. Meru
, but its expl anation is lengthy and tedious.
This is a crude method , taking help from mass ratio , which is
un -Siddhntika . Siddhntika corrections in
Saura latitude to get D k lunar latitide is easy , but requires
such terms whose explanation is highly
complicated. Even the crude method given above is enough to show
that Siddhntika terms are neither
wrong nor outdated , but need D k corrections to make Saura
entities visi ble. The complicated geometrix
around a few yojanas around the tip of Mt. Meru ( Mt. . Kenya )
is required to get the D k corrections to get
Dk Sunrise from Siddhntika equations of Sunrise . (This was
published in a Hindi book by me in 2005 AD.)
Maximum Manda -Phala of Moon is 5 02 48 in Srya -Siddhnta , but
6 17 19.7 or 22639.7 in modern
astronomy (cf. NC Lahiri's Pacga Darpaa). Take the difference of
sine of manda-phalrdha of both , which is same as difference of
saura & dk eccentricies. Multiply it with distance of Moon and
add the Meru correction of 500.8328 KM s deduced above , the
resultant will be barycentre with 83 KM anoma ly
whose reason lies again in the intricate mathematics around the
tip of Mt. Meru. If this small anomaly is
neglected , dk manda-phala of Moon can be thus deduced from
Saura Moon's terms. Adding effects of barycentre to Meru's effect ,
we get dk manda-phala of Moon. Hitherto , some simple terms were
being discussed , but now let us get something out of Srya
-Siddhnta which is beyond the reach of modern
science.
Exact Differential Equation Of Physical Moon
Setting up an empirically correct planetary differential
equation is most difficult part of modern astronomy.
Statistically arranged empirical data are analyzed through
various statistical tools and Fourier Transforms
to find out proper differential equations , but after few years
the constants term s and co -efficients in these
equations change due to reasons not known to modern astronomers
(real reason in rotations and
revolutions of physical entities and the whole physical Universe
in the permanently fixed k a), and
therefore these equations need revisions after few years. The
above equation deduced Siddhntika ally
conforms with Lahiri's and later equations admirably , and
perfectly satisfies the procedures of differential
calculus perfectly for 2000 AD when dk & saura universes
coincided (it happens at intervals of 42000 years). Here is the
Siddhntika explanation of the most troublesome equation of modern
physical
astronomy , the equation of Mean Moon (converted into Nirya a
following NC Lahiri's method):
-
The Siddhnt ika equation for deducing any term in the above
equation is this
Ys is Siddhntika Niryaa year equal to 365.258756481481481 Svana
days, Yd is Dk tropical year equal to 365.24219878125 days , n is
the number of term in the following differential equation of Nirya
a Mean Moon , t is Julian centuries of 36525 days , T = Julian
years of 365.25 days , 261 10 1.24 is Mean Moon on Zero date of
1900 AD (Greenwich Noon 31 Dec , 1899)
387 is the total number of revolutions of Siddhntika mandoccha
(apogee) in one Kalpa (1 Kalpa = 4320
million years)
K is deduced Siddhnti c ally in following manner :
K = [{(Ys-Yd) / Ys} - (1/42000)]-1 x (Ys / t) =
464.65408706471303027753666827
Then the wanted term in the Siddhntika equation of D k Nirya a
Mean Moon is
Mn = [360 / (n - 1)! ] x [ t x [{ 1 + ( 1 / 387 ) } / K ] n
]
Following is my Siddhntika Dk formula of Niryaa Mean Moon
created from above equation , published in Hindi in 2005 , built
from purely Srya -Siddhntika terms using Taylor's and
Lagrange's
formulas of modern differential calculus :
(1)
NiryaaMeanMoon=261:10:1.24"+(17325593.803064287678"T)
(2)
+1006.0337456626113312731046134872458"t2
(3)
+1036.5095055710038624734367"t3
(4)
+1064.681852716188407032"t4
(5)
+1092.525508037859365516483207"t5
-
(6)
+10121.0898575817626111529246014535145"t6
(7)
+10150.39193089427273663825034568365639"t7
(8)
+10180.12080988126146805887553801248113"t8
(9)
+10210.03258393040897135345673870555868"t9
(10)
+10240.0078118151691312247782389032276435"t10+......
The equation above can be extended upto infinite number of terms
, although there is no use of higher
terms because of impossibility of empirically verifying the
higher terms.
Now , here is NC Lahiri's formula of Mean Moon published by him
in Bengali book " Pac ga Darpa a".
Latest equations do not differ significantly.
(11)
NiryaaMeanMoon=261:10:1.24"+(17325593.8031"T)+(6.03"t2)+(0.0067"t3)
It is clear that the modern scientific formula is a crude form
of the exact Siddhntika equation. Even after
supercomputers and other sensitive instruments used by NASA
scientists , they have not been able to
discover any equation approaching this Vedic equatio n. Vedic
here means based on Vedic -Purnic -
Siddhntika traditions and being eternal , changeless ,
perfect.
Materialist cannot digest such things and start abusing ,
instead of studying the mathematics and trying to
prove it wrong on the basis of pure mathema tics or pure
science. They are guided by their materialist
prejudices. But following section is a concrete proof of the
fact that the entire Srya -Siddhnta has never
been written down.
Evidence Of Lost Portions Of Srya-Siddhnta
Modern Value of Precession in Bhskarcrya 's Work based on Srya
-Siddhnta
In the chapter Direction, Place and Time (Srya -Siddh nta , Ch.
3 ), E . Burgess writes
(bracketed words are mine) :
-
The (Srya Siddhntika) theory which the passage (verses 9-12), in
its present form, is
actually intended to put forth is as follows : the vernal
equinox librates westward and
eastward from the fixed point, war Piscium, assumed as the
commencement of the
sidereal sphere the limits of the libratory movement being 27 in
either direction
from that point, and the time of a complete revolution of
libration being the six-
hundredth part of the period called the Great Age (ie, Mahyuga
as defined by Burgess
in chapter i, 15-17, where he gave it a span of 4320000 years),
or 7200 years; so that
the annual rate of motion of the equinox is 54.
This is the interpretation of existing version of Srya Siddhnta
(triatktyo yuge bhn cakre prkparilambate | , SS , iii.9) in own
words of E. Burgess
[as it is actually intended to put forth] by all traditional
commentators.
This is exactly what I illustrated with example in the
illustrated example of computation of ayanamsha.
The moot point is this : Burgess knew the traditional
interpretation ( bhn cakre | .., ie pendulum
like motion of nak atra orbit itself) , but gave his own meaning
based upon modern concept of precession
of equinoxes , and tried to create doubts about the authenticity
of these verses ( Ch.3. 9 -12) by putting forth
deliberately false arguments.
Let us examine Burgess. In verse -9 (Srya -Siddhnta , Ch. 3.9 ),
he translates pari-lambate as falls back , although he says lambate
means lag, hang back, fall behind and pari means about, round
about.
Therefore , pari-lambate should have been translated as fall
back roundabout and not me rely as fall back according to own logic
of Burgess. If the circle of asterisms lags roundabout any fixed
point (whether Revat
or C itr), it is a to and fro motion as all traditional
commentators accepted. Modern concept of precession
is something different from the original concept of Ayan a .
Theon in West had mentioned this oscillating
motion , Arab astronomers also accepted it , and almos t all
Europeans accepted it upto Renaissance , after
which Hipparchus was rediscovered and modern concept of
precession became a well established fact in
astronomy. But this concept of equinoctial precession (as well
as anomalistic precession) was also know n
to ancient Indians and Greeks.
Burg ess wrongly quotes Bhskara -II, because he relied upon a
wrong translation of Bhskara by
Colebrooke (As. Res. , xii 209 ; Essays , ii, 374 , etc) and did
not try to examine Siddhnta iromai which
was wrongly translated by Lancelot Wilkinson due to Colebrooke's
influence.
Bhskara -II did not give his own opinion at all , and merely
quoted Srya Siddhnta and Muj la (elsewhere
Muj la and Manjula) , saying
-
Srya-Siddhnta gives -30000 revolutions of sampt or equinoctial
point per Kalpa while ayana has a motion of +199669 revolutions per
Kalpa (of 4320 million years).
Bhskara's own opinion was that these should be followed , which
means both Srya Siddhnta and Muj la
were correct in Bhskara's opinion. Colebrooke , Burge ss,
Wilkinson , etc ., have misquoted Siddhnta
iromai and created an impression that ancient Indians were inept
in astronomical observations , as
Whitney shamelessly declared in his prologue to Burgess , but
the Hindi translation by Satyadeva Sharma
is corr ect , although he could not get the real meaning.
The startling fact is that Siddhnta iromai clearly says that the
point of intersection of equatorial plane and ecliptic (which is
the very definition of equinox) has a negative motion of 30000
revolutions per Kalpa according to Srya -Siddhnta , while Muj la's
value of ayana's motion is +199669 , and both
(Srya -Siddhnta and Muj la ) must be added to get the final
motion (of the equinox ). Hence , we get
+169669 revolutions per Kalpa , which give s (4320000000 /
169669 =) 25461 years per revolution or 50.9"
per year , which is very near to modern value of about 50.3" per
year for precession of equinoxes.
Fuller discussion of Siddhnta iromai's text is given below. We
must not forget that Hipparchus had given
a period of 36000 years for precession , which was not corrected
by Europeans till the onset of modern age.
It is unfortunate that Siddhnta iromai is still being
misinterpreted by foreigners , and if a true rendering
is offered by Ind ian scholars , they are abused , esp by those
who do not care to consult the originals and
declare the forign missionaries to reliable. Bhskara -II neither
excluded Srya -Siddhnta , nor Muj la, but
mentioned the both must be used , which is clear from verse -19
, where he clearly asks to add Muj la's
ayana -chalam to Srya -Siddhntika sampt -calanam (this sampt
-calanam is anomalistic precession with
a period of 144000 years per cycle , not far from modern value).
Another startling fact is that Bhskara -ii
differentiates sampt -calanam of Srya -Siddhnta from ayana
-calanam of Muj la, and says both must be
added before computing phenomena like declension , ascensional
differences , etc. But modern
commentators like Colebrooke misinterpret Bhskara -II
deliberately, and imply that sampt -calanam of
Srya -Siddhnta quoted by Bhskara -ii was an erroneous thing
which must be forgotten , while ayana -
calanam of Muj la was a crude approximation of modern
precession. But this interpretation is falsified by
Bhskara's origina l verses (and his own commentary Vsanbhshya)
as shown above. The root of this
problem lies in the fact that sampt -calanam of Srya -Siddhnta
is a distinct phenomenon from ayana -
calanam of Muj la according to Siddhnta iromai, but readers are
not inf ormed of the real meaning of
Siddhnta iromai and false quotation from Siddhnta iromai was
quoted by Colebrooke and Burgess
(12th verse , Ch.3 ). This is a sign of intellectual
incompetence and dishonesty of Western "experts" who are
blindly followed by brown shibs of India. Those who do not
consult the original texts cited above will not
believe me.
-
Siddhnta Tattva Viveka by Kamalkara Bha a is a medieval text,
which clearly states that Saura -Pak a is distinct from Dk -Pak a.
Saura -Pak a (astronomy of Bhuva -Loka ) is Srya -Siddhnta as
it
exists. Dk -Pak a (astronomy of Bh -Loka or
physical/material/sensory world) is that version of Srya -
Siddhnta which was not preserved because it was useless in
astrology.
Siddhnta iromai uses many c oncepts of Dk -Pak ya astronomy , as
the instance cited above proves. Saura -Pak ya Srya -Siddhnta does
not contain any refence to 30000 cylces per Kalpa mentioned
by Bhskara -II. He was quoting from Dk -Pak ya Srya -Siddhnta
which as a text had been lo st ;
Bhskara -II said in his own Vsanbhshya commentary of Siddhnta
-iromai that Srya -Siddhnta is
gama . Modern commentators confuse both variants of Srya
-Siddhnta. Siddhnta -Tattva -Viveka is
prescribed in post -graduate (Ganit crya ) syllabus of Sanskrit
universities , but no modern commentator
has ever tried to translate it or comment on it.
According to Bhskara -ii, negative sampt -calanam of Dk -Pak ya
Srya -Siddhnta should be
added to positive ayana -calanam of Muj la to get final Dk -Pak
ya precession , which is very close to
modern value. Ayana -calanam of Muj la is also Dk -Pak ya,
because Saura -Pak ya entities are not used
in Dk -Pak ya astronomy , and vice versa.
Muj la's ayana-calanam , as mentioned in Siddhnta iromai,
gives
a period of (4320 million / 199669 = ) 21636 years per cycle.
Siddhnta
iromai says that it is ayana-calanam according to Muj la &
his followers but it was not accepted as precession by Bhskara
,
precession is obtained after substracting ( Saura -Pak ya) Srya
-
Siddhntika sampt calanam . If this 21636 year cycle is not
precession ,
what is it??
Readers should read Milankovitch cycles (wiki ) which
informs:
Earth's axis completes one full cycle of precession
approximately every 26, 000 years (25771.5 precisely at present,
25789.5 years is long term mean). At the same time, the elliptical
orbit rotates, more slowly, leading to a 21, 000-year cycle between
the seasons and the orbit This orbital precession is in the
opposite sense to the gyroscopic motion of the axis of rotation(cf.
anomalistic precession as distinct from equinoctial precession),
shortening the period of the precession of the equinoxes with
respect to the perihelion from 26, 000 to 21, 000 years.
Note: at some sites of NOAA of USA , 2200 0 is mentioned instead
of
21000
I had put some of the most important extant theorems of Dk-Pakya
Srya-Siddhnta at a website. I had put parts of it at one of most
popular websites, where a German Indologist deleted it and abused
me profusely; later I found those deleted materials at an
Australian website, without any name of author!! But I am here
divulging one important secret of ancient science of India which
has been neglected by wrongheaded commentators.
-
yana-calanam of Muj la is not orbital precession , it is the
most important of all components of Milankovitch cycles as this
Wikipedian definition shown. If we take cue from siddhnta iromai,
the afore-mentioned Wikipedi an clause can be rewri tten thus :
This orbital precession of equinoxes is in the opposite sense to
the gyroscopic motion
of the axis of rotation, shortening the period of the precession
of the equinoxes with
respect to the perihelion from 25771 to 21, 636 years.
Siddhnta iromai also says that Muj la's ayana-calanam (21 , 636
years per cycle) is opposite to sampta -calanam . Bhskara -ii
clearly defines sampta -calanam as,
the point of intersection of equatorial plane and ecliptic
(which is the very definition of equinox).
Hence , what Siddhnta iromai says is exactly what Wikipedia
informs us , the only difference is that
Siddhnta iromai is misinterpreted and declared to be
obscurantist , and the great cycles mentioned in
Siddhnta iromai is discovered by 20th centur y scientists. But
we must remember Bhskara -ii did not discover these things , he
acknowledged Srya -Siddhnta and Muj la. Bhskara -ii knew Dk -Pak
ya
Srya -Siddhnta , which has not survived because it was not
useful in astrology. In his formula of
precession , Bhskara -II used a figure 30000 cycles per Kalpa.
Bhskara -II got an approximate value of
50.9 per year , which was the most precise value before modern
astronomy developed in the West. Here I
quote a Purnic verse which proves knowledge of equ inoctial
precession in Purnic times :
uttnapdaputro'sau me hbhto dhruvo divi
sa hi bhraman bhrmayate nitya candrdityau grahai saha
Translation
Uttanapda's son Dhruva is the fixed point in the Heavens, round
which all planets including Sun and Moon, but Dhruva himself also
moves round.
Round what ? Ans.: Mt. Meru , which is the only fixed point in
Cosmos according to Purnic epic s. Hence ,
the bhacakra also librates with respect to this fixed point
Meru. According to Bhskara -II, orbital precession
is derived by substracting anomalistic precession (sampt
-calanam ) from the first component of
Milankovitch cycles ( Muj la's ayana-calanam). Bhskara -II
acknowledged earlier authors. Hence , we
a
-
must conclude that modern values and concepts of orbital
precession , anomalistic precession , Milankovitch
cycles , etc were known to ancient I ndians well before Bhskara
-ii.
But 2 things about confusing te rminology mu st be borne in
mind
1. this sampt-calanam he finally gets by combining the two
quantities mentioned above. According to Bhskara -II, Srya
-Siddhntika sampt -calanam is 30 , 000 per Kalpa. He does not give
a name for
the term which is finally obtained by combining this
sampt-calanam with Muj la's ayana-calanam , but the definition he
provides for Srya -Siddhntika sampt-calanam is exactly the
definition of the final quantity whose name he does not provide.
Hence , there were many types of sampt -calanam s !!
This is not a case of confusion of terms. It is a result of
Saura -Pak ya term with Dk -Pak ya terms
bearing same names but having different magnitudes and sometimes
even having difference in basic
properties !
2. Second confusion is due to use of the term ayana -calanam for
Muj la's precession. It is quite distinct
from Saura -Pak ya Srya -Siddhntika n ayana-calanam (trepidati
on) as mentioned in existing text.
Burgess could not digest this theory of libration (oscillation
or trepidation , ie, Ayan a - motion) and tried
to distort the meaning of terms to fit modern view of orbital
precession with this Saura -Pak ya precession .
Bhskara -ii knew and respected Srya -Siddhnta which he cited and
used in his computations as shown
above , and gave exact value of Dk -Pak ya precession. Therefore
, it is foolish to impose Dk -Pak ya
precession (50.9" per year according to Bhskara -II, 50.3"
really) upon Saura -Pak ya ayanamsha (54 per
year, oscillating within a range of 27 ). (There are further
corrections on Dk -Pak ya precession which
give a final value of one revolution in 25771.4 years , exactly
equal to the value deduced by NA SA - JPL ,
but these corrections requires some long theorems to prove).
I do not want to say that all ancient texts are true and should
be blindly followed. But it is equally
wrong to deride them as outdated and obscurantist just because
they could not be understood by
moderns.We have yet to discover the real Wonder that Is India.
Unless and until ancient texts are proven
false, it is suicidal to reject them. Here is the photographed
copy of relevant page from Siddhnta iromai
for those who want first han d proof , followed with discussion
on its obscure passages :
Vsan s Bh ya (commentary ) by Bhskara -ii on his own work
Siddhnta iromai has never been
translated or explained. Bhskara -ii knew Siddhnta iromai will
be misunderstood , hence he wrote its
commentary Vsan -Bh ya himself. This commentary also needs a
commentary. In i t, Bhskara clearly
writes that ,
-
sa evyam
refers to kr ntip ta, not to ayana -calanam .
If verses 17 -19 are taken to gether , we have six lines , and
sa evyam occurs in third line , which says that the ayanacalanam as
defined by Muj la & others [his school of thoughts] is same as
Krnti-Pta defined in first line.
This meaning from Vsan -Bh ya is further reinforced in same
passage in Vsan -Bh ya which say s
that,
tatra mandoccha ptnm gatirasti
the second line (minus 30000 revolutions per Kalpa) must refer
not to K rnti -Pta but t o motion of apogee
Thus , Bhskara has made it clear that the definition of Krnti
-Pta as given in first line applies not to -30000
revolutions per Kalpa ( the latter being motion of mandoccha )
but applies to +199669 revolutions per Kalpa
(="ayam") which is same as the ayana-calanam (= "sa") as said by
Muj la and his followers ( Muj ldi means Muj la and others
beginning from Muj la, di means beginning; hence the sense of Muj
ldi is not Mujla and others but , Mujla and his followers).
tat pake relates to ayana-calanam.
If one Kalpa of 4320 million years is divided with 199669 given
by Muj la, we get one revolution
in 21635.8 years , which is equal to annual motion of 59.9
seconds of arc which was rounded to one minute
of arc by Muj la (read the footnote of Siddhnta iromai's
photograph given above which gives the
verses from Muj la about precession). Karana texts use crude
numbers in order to facilitate panchanga
making , and after long time when errors accumulate new Karana
texts are made from same Siddhnta
(Vsan -B hya of verse 17 -18 says
yad punarmahat klena mahadantaram bhaviyati
tad mahmatimanto brahmaguptdinm samnadharma evotpatsyante
But this crude figure on one minute per year will give 200 , 000
revolutions per Kalpa and not the
figure 199669 said by Muj la. Rationale for 199669 is
unexplained. Now , let me summarize the whole
issue :
Verse 17 defines Krnti -Pta, and then gives a figure ,
-
minus 30000 revolutions per Kalpa as said in Srya-Siddhnta
which Bhskara elaborates in Vsan -Bh ya to be the motion of
solar apogee.
The next verse mentions +199669 revolutions of ayana calanam as
said by Muj la & others [his school of
thoughts] , and clarifies that the Krnti -Pta defined in
preceding verse in same as ayana calanam of
Muj la. But Bhskara does not accept Muj la's notion of Krnti
-Pta and says that real motion of Krnti -
Pta should be deduced by combining -30000 with +199669. T his is
clear in the third verse (19th) :
tat-samjtam ptam kiptv khee-apama sdhya
krntivat-caram-uday-caradala-lagngame tata kepya
apama means Krnti -Pta = the declination of a planet . (Monier
Williams).
khea means planet .
Hence , Bhskara says Uttanapda's pta born out of that / those
should be used to deduce declination of a planet.
tat normally is singular , but in samaasa it is used for dual
and plural too. Pta means the intersecting point of two circles.
Hence , here the [intended] meaning is thus
The pta born out of intersection of circles / ellipses of
mandoccha and ayana-calanam should be used for computing
declination of planets, and phenomena like chara, udaya-mnas,
caradala, lagna, etc., should be computed from this final
declination.
What Bhskara says is in current -practice by all pac ga -makers
in India. Cara is a term used for intermediate quantities needed in
computation of Sunrise , Lagna (ascendant) & others and , is
defined as
the difference of rising time a rasi in equatorial plane f rom
the rising time of same rasi in ecliptic.
Bhskara says pta born out of tat should be used for deducing
declination.
By definition , a pta is a resultant of two entities. Hence ,
the two entities mentioned in preceding verses
must be combimed to give the Krnti -Pta of Bhskara .
Existing Srya -Siddhnta does not give a motion of -30000 per
Kalpa of any entity , while Bhskara
claims Srya -Siddhnta says so. But Bhjaskar says Srya -S iddhnta
is gama and therefore must be
-
accepted as final proof ( prama). Hence , some version of Srya
-Siddhnta available to him mentioned -30000 per kalpa as the motion
of SOLAR APOGEE.
But Srya -Siddhnta gives a value of only 387 revolutions for
sola r apogee , and Siddhnta iromai
gives a figure of 480 per Kalpa (verse 5 in bhagadhyya). Bhskara
's value is +93 more than that given in Srya -Siddhnta. Late NC
Lahiri wrote in Advance Ephemeris (page 90) that some corrections
were
needed in Srya -Siddhntika figures for making it scientifically
correct , and the value of one such term
given by him was equal to nearly 109 revolutions per Kalpa , not
too far from Bhskara 's bja correction in
Srya -Siddhntika mandoccha value. But Bhskara never said Srya
-Siddhnta was incorrect. Hence ,
there were two versions of Srya -Siddhnta :
1. one was D k -Pak ya, ie related to the phenomanal world revea
led directly to the senses , and ,
2. the other was Saura -Pak ya manifest only astrologically.
Astrologers did not preserve the Dk -Pak ya Srya -Siddhnta.
Bhskara says Srya -Siddhnta's solar
apogee has a motion of -30000 revolutions per Kalpa , or a
period of 144000 years , which is not too far
away from modern value of physical astronomy. Bhskara also says
Srya -Siddhnta is itself a PROOF
and needs no other proof for its correctness because it is gama.
But the figure of -30000 per kapla is never used in Srya -Siddhnta
used and preserved by astrologers , and Bhskara 's own value of 480
per Kalpa
is also near to this version. Hence , he knew about two versions
of Srya -Siddhnta. Bhskara 's statement
about gravitational force and its proportionality to distance
was also related to sensory (i.e. , material) world.
Deduction of Modern Astronomical Constants from Srya
Siddhnta
Kamalkra Bha a (author of Siddhnt -tattva-viveka , as yet
untranslated) an ardent supporter of Srya
Siddhnta and an opponent of Bhskara II had strongly advocated in
16 th century that Srya Siddhntika
planets are to be distinguished from the material planets.
In the beginning of 20 th century , terms like Dk -Pak a and
Saura -Pak a came into vogue in India ,
to distinguish planets and phenomena of Sensory World from that
of Srya Siddhnta .
1. Dk-Paka meant the world perceived by means of sense organs ,
and therefore it denoted the fo ld of modern astronomy , while
,
2. Saura -Pak a denoted the gods of Next World bearing same name
as the material planets but being
non -material.
-
Ketaki system of almanac used t hese concepts in actual
practice. But the Srya Siddhntika viewpoint of
Dk -Pak a was never elaborated by anyone. Unfortunately , after
the disappearance of the Srya
S iddhntika commentary of ryabha a, the Elder , even the Saura
-Pak ya mathematics bec ame obscure ,
and all the commentators kept on repeating hackneyed phrases
whose practical significance was clear to
none. Ranganath , Kam alkar a Bha a, Sudh kar a Dvived, Kapile v
ara stri etc ., wrote voluminous
comment aries on Srya Siddhnta , elucidating everything except
the practical ways of using the formulas
and the Meru -Centric geometrics.
Let us examine some orally transmitted occult theorems of Srya
Siddhntika school which show that Dk -
Pak a can be deduced from Saura -Pak a mathematica lly, without
the aid of any observatory.
Theorem of Dk-Pakya Sidereal and Tropical Years and of
Precessional Period
Saura -Pak ya eccentricity of Sun's elliptic orbit round the
centre of Cosmos ( Mt. Meru) is exactly equal to
1/60 (= ) , although Saura -Pak ya equation of centre requires
an equant , which will be elaborated in the
section 'The True Places of Surya Siddhantic Planets'. Let us
denote 1/60 by and 'pi' by . Then ,
(12)
Ys=[122+12(1+2)]=[36002+0.5+17200]=365.25640000130486608685495644391
days
This is the limiting value of scientific sidereal year by means
of Vedic (i.e. , Surya Siddhantic) equation.
The Vedic (i.e. , Surya Siddhantic) theorem of scientific
Tropical Year Yt (=365.24219878125) wil l be
demonstrated later , let us first get the value of mean sidereal
year with the help of following equation :
(13)
Ys=(Ys+1)(1+1Yt)=366.2564000013048660868551+1365.24219878125=365.25636122581667241689259003252668
days
Now we can get the Period of Preces sion PP :
(14)
PP=Yt(YsYt)=25789.488323276570161593347095778 years
This mean value needs two complex correction which are too
intricate to be shown here. Let us deduce
the value of scientific Tropical Year first.We will not explain
all the intermediate terms here, which can be
easily recognised by students of modern astronomy.
Let sidereal lunar month be equal to :
-
Mss = 27. 321660641391789747802454274321 days , which will be
proven later. Then , synodic month
Ms will be :
(15)
Ms=Ys(YsMss1)=29.53058780664716371374 days.
Metonic Year Ym is equal to :
(16)
Ym=235Ms19=365.246743924320182775185653635 days
Precessional Period due to Moon's effect (PPM1) :
(17)
PPM1=1(YsYm))=37978.09022183997109169737 years
Precessional Period due to Sun's effect (PPS1) , inter mediate
term :
(18)
PPS1=11PP1PPM1=80356.674413324332490977057144470 years
Precessional Period due to Sun's effect from alternative
equation (PPS2) , intermediate term :
(19)
PPS2=1Ys(1Yt1Ym)=80356.674413324332490977057250561 years
The difference between PPS1 and PPS2 is due to computer's errors
and is equal to a negligible quatity :
(20)
Difference=1.32025125210 27 years
Intermediate terms are :
A1 = PPS1 / PPM1 = 2.1158692799964388041303958720096. A2 = PPS2
/ PPM1 = 2.1158692799964388041303958748028.
Precessional Period due to Sun's effect (PPS) , final value
:
PPS = PPS1 + A1 = 80358.790282604328929781187540342 PPS = PPS2 +
A2 = 80358.790282604328929781187646436
-
There is difference in two values of solar precessional period
shown above (PPS) in 27 th digit only.
Hence , the computations are highly reliable.
There are three equations for obtaining scientific Tropical Year
(in days) :
(21)
Yt.1=Ym1+1(PPS1+A1)=365.24219878124999999999999999999638527125
(22)
Yt.2=YmPPS=365.24219878124999999999999999999638595267
(23)
Yt.3=Ym1+1(PPS2+A2)=365.2421987812499999999999999999999999972349
Dk -Pak ya Tropical Year is the most precise constant known to
modern astronomy , whose empirical value
is 365.24219878125 0.00000000058 days.
The error of 0.00000000058 days is due to errors in modern
instruments. The three values we obtained
above through Vedic equations have errors in 34 th digit which
is due to 34 -digit precisiuon of Windows
Calculator used to obtain above results. The net result is
startling : value of 'pi' i s the basic term used to
deduce exact value of most important astronomical constants , if
you know the exact value of 'pi' then you
can deduce the exact value of astronomical constants. Modern
physicists know many such equations ,
whic h are called coincidences by atheists , and as proofs of
Intelligent Design of Universe by believers in God.
Vedic (ie, Srya-Siddhntika) Theorem of Lunar month
M1 = 365.256400001304866086855 / (42/) =
27.321114831446531255657
K1 = M1 / ( Mss - M1 ) = 50056.095658915529
K2 = 4 2000(Ys -Yt) = 594.8226718002415
Now raise (Ys/360) to the power (1/K2):
Z1 = (Ys/360)^(1/K2) = 1.014601^(1/594.82267) =
1.000024369635568 .
K3 = 1 -[(180/)* {(Sin(Z1+1) -Sin(Z1)}]
-
= 1 -[57.296*{(Sin(2.000024369635568)
-Sin(1.000024369635568)}]
= 0.0003553741530559558546620855628939
K4 = K3 * 1000000 = 355.3741530559558546620855628939
K5 = 1+(1/K1)
Now we get the value of Dk-Pakya synodical or lunar month : Ms =
[(K4 / K5) -1}/12 = 29.53058780664716371373841555 days.
Sidereal lunar month will b e :
Mss = Ys / [(Ys/Ms)+1] = 27.321660641391789747802454274321
Now we show some more intricate Vedic ( Srya -Siddhntika )
theorems. First of all, let us see :
Lunar Binomial Theorem :
A1 = 12/(K4 -1) = 1 / 29.5311794213296538
A2 = Ys / 365.256400001304866086855
(24)
A=A1A2(42)=0.45270842758190827172
Here is the Lunar Binomial Equation :
(25)
(AM2)+MYs=0
Roots of this binomial are :
M1 = [ -1 + Sqr(1 -(4A*Ys)] / 2A = -29.5305886713712313156
days.
M2 = [ -1 - Sqr(1 -(4A*Ys)] / 2A = +27.32 16613815891770963
days.
M2 - Mss = 0.063953054266910187950698752 seconds.
This apparent 'error' is equivalent to the error of
104.643228673117 years in 4.1748 billion years ( = 14
manavantara of 71 Mah yugas each , where each Dk -Pak ya Mah
yuga = 4.2 mil lion years).
-
This is the value of Dk -Pak ya correction in Kalpa -Mandoccha ,
for which Bhskarcrya deduced the
value 93 in Siddhanta iromai and stated Kalpa -Mandoccha to be
equal to 480 (= Saura -Pak ya Kalpa
Mandoccha 387 + 93 Dk -Pak ya correction). Its elucidation will
be shown later.
Srya Siddhnta states Saura -Pak ya period of precession to be of
24000 years exactly , while modern
value is near the Dk -Pak ya value of PP deduced above ( =
25789.4883233 years). Let us see its logic.
1/K' = (1/24000) - (1/25789.4883233) = 1/ 345879.71975438125 Mt.
= Mss - (Mss/K') = 27.32158164959469683453 days. This constant Mt.
is the modern value of tropical sidereal lunar month !
Srya Siddhntika Theory of the Rotation of Material Universe
According to modern physical science , material universe cannot
be said to be rotating even if it rotates ,
because all space -time-continuum is intrinsically related to
matter as part of a unified whole , and there can
be no space or time outside the realm of matter. Since there is
no space or time outside material universe ,
rotation of this material universe cannot be measured because
there is no external space -time.
Let us call the space of time of this material universe as
material -space and material -time. There are 14
universes (Bhuvanas) in the Multiverse (= Creation or S i), and
we live in the middle universe. Since all
forms of matter have shown to be associated with SPIN , from
galactic to sub -atomic levels, it is natural that
the material universe sho uld also rotate. But it can be
measured only with reference to the non -material
universe or Bhuva -Loka , which is the world of Saura -Pak ya
Srya -Siddhnta. Srya -Siddhnta states our
universe to be finite , and according to Godel's theorem a
finite system cannot be fully explained on account
of its internal properties and phenomena only. There must be
something outside this finite universe which
should explain the workings of this universe and its raison
-detre.
Now we show the Vedic Theorem of Rotation of the Material
Universe.
Surya Siddantic Kalpa is equal to 4.32 billion years. The
Creator (Brahma) took 47400 divine yuears to
create the Creation , which is equal to 47400 * 360 human years.
Hence the total Age of Creation = 4.32
billion - (47400 * 360) = 4302936000 years.
4302936000 / 24000 = 179289 is the extra years due to Saura -Pak
ya precession. Hence total
number of Saura -Pak ya tropical years in one creation is equal
to 4302936000 + 179289 = 4303115289
years. Divide this number with ( Saura -Vara / Candra -Vara ) =
( Saura -Pak ya Sidereal Year / 12 Saura -
-
Pak ya synodical months) = 365.258756481481481 /
(12*29.53058794607) = 1.0307356481481. The
result is 4174800101.976788423. In it , 4174800000 is the
duration of Dk -Pak ya Creation ( =
4200000*71*14 ), and 101.976788423 is the exact value of Dk -Pak
ya correction in Kalpa -Mandoccha , for
which we had got a crude value 104.643228673117 above , and
Bhskarcrya had got 93. A quantity of
101.976788423 years in 4.1748 billion years is equal to 0.107065
hours in 500 years. Nirmala Candra Lahiri was the secretary of Pac
ga Reform Committee of Government of India. He analysed the
differencebetween Dk -Pak ya and Saura -Pak ya tithi (elongation of
moon) , and found a difference of
0.11 hours in 500 years , which he assumed to be due to error in
Srya Siddhntika values (NC Lahiri , 1968 ,
p.90 ).
But Srya Siddhntika values do not belong to this physical
Universe. This apparent error of
0.107065 hours in 500 years is a result of extra 102 rotations
of the Dk -Pak ya solar orbit during one
Creation : Saura -Pak ya value is 387 while Dk -Pak ya value is
489 ( Bhskarc rya-II gave 480 only in
Siddhnta iromai). This Dk -Pak ya rotation of solar ellipse is
in addition to the normal Dk -Pak ya
rotation per 136000 years which is the cause behind anomalistic
year.
In the same book NC Lahiri gives data of Srya Siddhntika beej
corrections applied to lunar anomaly in
comparison to modern scientific values , which shows that beej
correction needed in lunar anomaly in order
to get Siddhntika tithi from scientific tithi increases at a
rate of one revolution in 42000 years(NC Lahiri ,
1968 , p.90). Difference between modern scientific tropical Sun
and Siddhntika Sun also show 360 change
during 42000 years. Sun and moon do not move in same orbits.
Hence we must conclude that the physical
Universe itself is revolving at the rate of one revolution per
42000 years round some point very near to
Earth's centre , which suggests that the centre of Universe is
not far from Earth's centre. Before dealing with
this centre (Meru or Mt. . Kenya in Africa) , let us first
elucidate the 42000 year cycle of the Sun.
Siddhntika sidereal year (365.258756481481)and Dk -Pak ya
tropical year(365.24219878125) differ at
the rate of one revolution or one year in 22059.75174 years. But
in reality both divurge from each other at
the rate of one r evolution in 42000 years. For instance ,
Kaliyuga commenced at Ujjain midnight 17 -18 Feb ,
3102 BCE , when Siddhntika nirayan(=sidereal in Indian system)
Mean Sun was at zero longitude. 5106
years later Siddhntika zero Sun was to be found on 16 Apr , 2005
at 5:03:15 AM (Ujjain). If mean Sun
differs by 44.2106 days in 5106 years(taking into account 13
days of Gregorian reform) , it should differ by
one year in 42182.8 years. Due to non -linearity of elliptical
paths , we get here 42182.8 , the exact figure is
an i nteger 42000. It raises a question : if mathematically
Siddhntika year and scientific year should show
a difference of one revolution in 22059 years , why do they
differ by one revolution in 42000 years in reality
? Where does 19941.24826 years come from ? We have here compared
sidereal Siddhntika year with
tropical scientific year , hence this extra difference of 19941
years must be related to precession.
Siddhntika period of precession is 24000 years and scientific
period is 25789.4883233 years. Both for m
-
cycles of 100000 12000 years with respect to 19941 in harmonic
series. Thus , we are now getting close
to constants of Milankowitz , just by means of analysing Srya
Siddhntika constants !
An excess of 101.9767884 years of anomaly in 4.1748 billion year
s as we got above means one year of
anomaly in each 40938727.965116279069767363571421 D k year.
Substract one 4 , 200 , 000 D k years
to get another periodic constant of
36738727.965116279069767363571421 years we will need in some
computations needed to get modern value of precessional period.
We found precessional period equal to
25789.48832327657 years.
1. Divide the number 36738727.96511627907 as obtained in the
previous paragraph with this precessional -period value, and one
will get 1424.56211246181876.
,,
=
36738727.96511627907
25789.48832327657 = 1424.56211246181876
2. Now , dividing the value of 25789.4883232765702 with the
derived-value amounting to
1424.56211246181876 which stands for (lets call it that way) per
dk year value per precessional-lapse .
. = 18.1034495426171053
3. and finally, to get the modern precessional value period as
used by scientists , you go about to
substract the previously -derived value from
25789.48832327657
. . = = 25771.3848737339530562881748
Modern valu e [abeit slightly differs but having seeming
resemblance to the derived one] is
25771.4021 years .
Ancient Cosmogony and Geography
Srya Siddhntika system is neither heliocentric nor geocentric.
It clearly states in Bhoogoladhyaya
that Mt. Meru resides at t he centre (equator) of globe in the
region of Zamboodweep. In Africa , Mt. . Kenya
is situated upon equator in a region where many modern place
names are reminiscent of Srya Siddhnta
: Meru town near Mt. . Kenya , another Mt. Meru slightly
southwards , a place named kinyan -giri which means
Mt. Kinyan or Mt. . Kenya in sanskrit , river Zamboonadi >
*zamboodi > *zambedi > *zambezi , Mu -zambique ,
Zambia , Zimb -abwe , Gabon (< *Zamboon) , Congo (< *Gongo
< *zambo) , etc. Homo genus of mankind is
known to have evol ved in that region around 4 million years
ago. Indian Purnic ttreadition also mention
-
that modern races of mankind evolved near Meru in 3891194 BCE
when the present Mahayuga
commenced. Srya Siddhntika formulae of making true planets from
mean ones requi re the use of
distance from Earth's centre to a point in space 28.913
kilometres above the top of Mt. Meru ( Mt. . Kenya) ,
which was believed to be centre of all universes by Purnic
authors. Srya Siddhntika universe is much
smaller in comparison to mater ial universe , and Sun's distance
from Earth is only 861.7 times of Earth's
equatorial radius. Material Sun's distance is 23455 times of
Earth's equatorial radius ! Ptolemy used a figure
1210 , which is not much removed from Srya Siddhntika figure.
Ptolemic system is well known , but Srya
Siddhntika system is rather obscure , known to a few initiated
brahmanas only. Due to lack of knowledge
of orally transmitted and unpublished portions of original Srya
Siddhnta , European commentators believe
that Srya S iddhntika system was influenced by Ptolemy's
Almagest.
But those who know the secrets of Srya Siddhnta say that its
framework is too complex and
organically self -contrained to have been influenced by any
other system. For instance , Srya Siddhntika
daily motions of all planets are exactly equal to a constant ,
but this rule is not followed in Almagest.
Srya Siddhntika system is based upon a cosmic centre at Meru ,
which is absent in Almagest.
Srya Siddhntika solar epicycle is equal to 14 yojanas per degree
, which is equal to 5040 yojanas for
360 . Its diameter is 1604.3 yojanas , which is 4.3 yojanas more
than Earth's equatorial diameter. 4.3
yojanas equals 5.199 kilometres ( height of Mt. Meru or Mt.
Kenya ) plus 28.913669 kilometres. Solar epicycle equals to 14
yojanas , which gets reduced to 13:40 at perigee of this elliptical
epicycle , which when
divided by 2 gives 2 10 31 which is the maximum value of
equation of centre ( manda-phala = difference between mean &
true Sun) for Sun.
Srya Siddhntika theory, therefore, relates yojana to degrees in
an intrinsic manner , which makes it clear that it was not borrowed
from Almagest. Earth's diameter is an integer 1600 yojana. Moon's
diameter
is also an integer 436 yojanas. These rations are perf ectly
scientific. Such integral values seem to be
mysterious when they are confirmed with modern science. This
value of yojana was not only prehistoric ,
manifest in the story of Jarasandha's 99 yojanas from Girivraja
to Mathur proving that siddhantic yoja na
was prevalent in pre -historic era of Girivraja's kings , as
mentioned in Mahabharata , but was also intrinsically
related to many native concepts of Srya Siddhnta , discussed in
other sections of this article.
The Cycles of Lord Brahm
Every Creation is repeated after 60.24 billion years , in which
half or 30.24 billion years comprise
the existence of Universe or Day of Lord Brahm and the other
half is Dark Band which is Night of Lord
Brahm. Modern instruments have started to get some faint views
of thes e distant bands , which are actually
due to illusion : telescopes reveal only the past states of our
Universe but scientists imagine these past
-
states to be co -existent. Each visible band is actually seven
concentric rings of seven universes , each
lasting f or 4.32 billion years (= value for one Kalpa). Present
universe is 1.95885115 x 7 = 13.7 billion light
years according to scientists.
The dimension of Time is viewed as Space by them , although
Einstein had proved that Time is the fourth
dimension of Space . If some star is 1 billion light years away
, it means we are viewing something which
existed one billion years ago , not the present state of that
thing , Its present state may be very near to us.
In physical astronomy , orbital elements are not constants , b
ut in siddhantic astronomy , everything is
constant. Siddhntika Astronomy is fundamental from which
physical (= material = sensorily perceived =
My) is created.
The revised version of Steady State Theory originally propounded
by Hoyle-Narlikar which now includes Big Bang Theory is the correct
theory, which is in tune with Vedic Astronomy : each universe is
created, appears to be expanding in a Big Bang manner due to
illusion created by the dimension of Time viewed as dimension of
Space, and then collapses, in order to give rise to next Big Banga,
hence the theory of Oscillating Universe is joined with Big Bang
theory to give a Steady State in the long run. Each existence or
Big Bang is Day of Lord Brahm, and Collapse into Cosmic Black Hole
is Night of Lord Brahm. There are 72000 such Oscillations in the
life of one Brahm ji, after which Brahm ji passes into the navel of
Lord Vishnu and next Brahm ji comes. This is Vedic-Purnic view.
Only the most simple and easiest aspects of Srya-Siddhntika
mathematics has been presented here. The details are highly
intricate and difficult. Kaliyuga is not fit for Srya-Siddhnta and
therefore calls it obsolete. The extant text of Srya-Siddhntika
provides sufficient clues for unravelling its unwritten
marvels.
-Vinay Jha