Astrology Software

The Alpha Numeric System of Mathematica Indica

2011-11-03T20:46:00.001-07:00

Known as Paral Sankhya, the Alpha Numeric System was developed by Vararuchi. It is also known as Katapayadi, as 1 represents the letters Ka, Ta, Pa and Ya, whose corresponding digit is 1.

Number Letters

1 ka ta pa ya
2 kha tta pha ra
3 hu da bha la
4 gha da ba va
5 nga na ma sha
6 cha tha sha
7 chha dha sa
8 ja dha ha
9 jha ddha
0 nja na ksha

The Value of Kaa ki ku ke and ko was 1

31 was represented by Kala

Kala is ka + la = 31 ( The digits are counted from the right )

and 351 by Kamala
Kamala = ka + ma + la = 351

Elemental Numbers in Mathematica Indica

2011-11-01T20:58:00.000-07:00

Sanskrit poets used Elemental Numbers in their poems. As eyes are 2, two represents eyes. As the Vedas are four, four represents the Vedas. Netra Netra ( eyes , eyes ) means 22 and Veda Veda means 44.

Here we give the correspondence between numbers and the Elements

1 - Earth, Moon
2. Eyes, hands, feet, ears
3. Worlds, trinitarian unity, three yogas, three vedas.
4. Vedas
5. Sense organs.
6 Rithus or the six seasons.
7. Rishies
8 Directions, eightfold prosperity
9 Digits, numbers
0 Ether

10 - Ego and its ten heads.
11 - Rudras
12 Months, Zodiacal Signs
13 Universe
14 Vidyas, Manus
15 Lunations, thidhis
16 King
17 Athushti
18 Treatises astronomical, mythological
19 Athi Dhruthi
20 Nails
21 Uthkruthi
22 Akrithi
23 Vikruthi
24 Gayathri
25 Principles
27 Constellations
33 Deities

The digits for the letters are written, counting from right to left

For example,

Bhanandagni

Bham = Stars = 27
Nandan = 9
Agni = 3

Bhanandagni = 3927

Of Scholarship

2011-10-30T03:01:00.001-07:00

Scholarship is great and is like an expanding flower

Pandityam nava pallavam vikasitham pushpam prayogajnatha

In order to have scholarism graced, one should strive hard to gain it. It is said that the hard work done by the scholar is known only to the scholar ! How can others know it ?

The scholar and the world, the endless strife
The discord in the harmonies of Life
The love of Learning, the sequestered nooks
And the sweet serenity of Books
The marketplace, eager love for gain
Whose aim is vanity, whose end is pain !

Vidwaneva Vijanathi
Vidwajjana parishramam
Na hi vandhya vijanathi
Gurveem prasava vedanam !

How can others know the work hard
Which the scholars have indulged in ?
Like a barren woman who cannot know
The pain of delivering !

Names of big Indian numbers ( contd )

2011-10-28T20:20:00.000-07:00

There are greater numbers, than the ones mentioned below.

Maha Padma = 10^15
Kshoni = 10^16
Parardha = 10^17
Sankha = 10^18
Maha Sankha = 10^19
Kshithi = 10^20
Maha Kshiti = 10^21
Kshobha = 10^22
Maha Kshobha = 10^23

Neethi Lamba = 10^27
Sarva Bala = 10^45
Thallakshana = 10^83

Indian names for big numbers

2011-10-27T20:26:00.001-07:00

Ganitha Kerala, the Kerala School of Astronomy and Maths, has given a lot of names for big numbers.

Like the Western

Myriad = 10^4
Million = 10^6

Indian names are

Shata = 10^2
Sahasra = 10^3
Ayutha = 10^4
Laksha = 10^5
Dasa Laksha = 10^6 ( Million )
Koti = 10^7
Dasa Koti = 10^8
Vrinda = 10^9
Kharva = 10^10
Nikharva = 10^11
Mahapadma = 10^12
Mahakharva = 10^13
Padma = 10^14

In the Western, we have

Million = 1000^2
Billion = 1000^3
Trillion = 1000^4

or

Nillion = 1000^(n+1)

where n is the number. Tri meaning 3 and trillion = 1000^(3+1)!

Of Mathematica Vedica

2011-10-17T23:10:00.000-07:00

By one more than the one before

Ekadhikena Purvecha is Sanskrit for " One more than the previous one". This
sutra can be used for multiplying or dividing algorithms.

You can use this formula to compute the squares of numbers.

For example.

35×35 = ((3×3)+3),25 = 12,25 and 125×125 = ((12×12)+12),25 = 156,25

By the sūtra, multiply "by one more than the previous one."

35×35 = ((3×4),25 = 12,25 and 125×125 = ((12×13),25 = 156,25

India will overtake Japan by 2012

2011-09-20T20:51:00.001-07:00

India may overtake Japan by 2012 and become the third largest economy by 2012. According to Pricewatherhouse Coopers, India's GDP PPP will overtake Japan by 2012. Such a forecast seems to be probable, as Jupiter will be in the House of Gains for India next year. Jove in the 11th will bring handsome gains.

China will become the world's largest economy by 2020. Within one year, Indian GDP PPP will become $4.32 trillion, overtaking Japan's economy, estimated at $1000^4 ( 4.32 tr to be exact ).

“While the exact date is open to doubt, it seems highly likely that, by 2030, China will clearly be the largest economy in the world on PPP,” John Hawksworth, head of macroeconomics at PwC, wrote in the report.

The Decoupling theory, that India and China will not be affected by the global meltdown, still holds true. China will overtake Japan as the second largest economy this year, as Japan is facing a severe crisis !.

Yesterday the Sensex grew by 353 points and closed about 17 K. Despite the secondary reactions, the Stock Market seems to be on a growth track.

The Churning of the Milk Ocean at Bangkok Airport

2011-09-18T04:25:00.001-07:00

We were amazed to see Palazhi Madhanam, the Churning of the Ocean, depicted at
Thai Suvarnabhoomi Airport.

The Churning of the Ocean is allegorical, symbolising the great fight in the human bosom between Virtue and Vice. The forces of Virtue, the celestials, the devas fight the forces of Vice, the demons, the asuras. In this fight Immortality is the end result and Immortality is nothing but Self Actualisation !

P N Oak's theory that the base Civilization was Vedic from which everything began seems to be proved right !

Dr Kenneth Chandler averrs that the Vedic Civilizations is 10,000 years old.

He writes in his thesis " The Origins of Vedic Civilization" ....

How Ancient is Vedic Civilization?

Astronomical References in the Rig Veda and Other Evidence

Evidence from other sources known since the late nineteenth century also tends to
confirm the great antiquity of the Vedic tradition. Certain Vedic texts, for example,
refer to astronomical events that took place in ancient astronomical time. By calculating
the astronomical dates of these events, we thus gain another source of evidence that can
be used to place the Rig Veda in a calculable time-frame.

A German scholar and an Indian scholar simultaneously discovered in 1889 that the
Vedic Brahmana texts describe the Pleiades coinciding with the spring equinox. Older
texts describe the spring equinox as falling in the constellation Orion. From a
calculation of the precision of the equinoxes, it has been shown that the spring equinox lay in Orion in about 4,500 BC.

The German scholar, H. Jacobi, came to the conclusion that the Brahmanas are from a
period around or older than 4,500 BC. Jacobi concludes that “the Rig Vedic period of
culture lies anterior to the third pre-Christian millennium.”22 B. Tilak, using similar astronomical calculations, estimates the time of the Rig Veda at 6,000 BC.23
More recently, Frawley has cited references in the Rig Veda to the winter solstice
beginning in Aries. On this basis, he estimates that the antiquity of these verses of the Veda must go back at least to at least 6,500 BC.24 The dates Frawley gives for Vedic civilization are:

Period 1. 6500-3100 BC, Pre-Harappan, early Rig Vedic
Period 2. 3100-1900 BC, Mature Harappan 3100-1900, period of the Four Vedas
Period 3. 1900-1000 BC, Late Harappan, late Vedic and Brahmana period

Professor Dinesh Agrawal of Penn State University reviewed the evidence from a
variety of sources and estimated the dates as follows:

• Rig Vedic Age - 7000-4000 BC
• End of Rig Vedic Age - 3750 BC
• End of Ramayana-Mahabharat Period - 3000 BC
• Development of Saraswati-Indus Civilization - 3000-2200 BC
• Decline of Indus and Saraswati Civilization - 2200-1900 BC
• Period of chaos and migration - 2000-1500 BC
• Period of evolution of syncretic Hindu culture - 1400-250 BC

The Taittiriya Samhita (6.5.3) places the constellation Pleiades at the winter solstice, which correlates with astronomical events that took place in 8,500 BC at the earliest.

The Taittiriya Brahmana (3.1.2) refers to the Purvabhadrapada nakshatra as rising due
east—an event that occurred no later than 10,000 BC, according to Dr. B.G.Siddharth
of India’s Birla Science Institute. Since the Rig Veda is more ancient than the
Brahmanas, this would put the Rig Veda before 10,000 BC.

Ramayana Garden in Thailand

2011-09-17T22:11:00.001-07:00

This is the photo of the Ramayana Garden in Thailand.

The first poem and the greatest was Ramayana, opined Aurobindo. When the poet Valmiki saw two birds mating and a native killing one of the two said " Ma Nishada ", meaning " Dont do that, for it is Sin, it is Evil, it is against the Law of Conscience"!

Ma nishada pratishtantva nigama shashvathi sama
Yat krouncha midhunath eva avadhim kamamohitam

Ramayana is an allegorical and epic poem. As the Aryan Invasion Theorists argue, it is the not onslaught of the " Aryans" against the " Dravidians". The Aryan Invasion Theory has been proved wrong by scholars like Dr Konrad Elst, Dr Dennis Chandler, Aurobindo and Vivekananda.

Man's dual aspect is highlighted in this poem. The Ego is the imperfect term in Man and Self or the Divine in the perfect term. The Ego is the lower imperfect term of our being; Self is the higher, perfect term.

The Ego is symbolised as Ravana, the ten headed demon king. His ten heads represent Mind, Intelligence, Processing Mind, Ego, Lust, Greed, Anger, Avarice, Jealousy, Gluttony and Sloth.The Self is symbolised by Rama, who goes in search of Peace, Seetha, his beloved consort. The great struggle for supremacy between good and evil, light and darkness, prosperity and adversity, happening in the human bosom, is the Ramayana, where the forces of the Ego clash with the forces of the Self.

Ramayana is part of Buddhist lore and the Ramayana Garden is a testimony to this fact. This strengthens P N Oak's theory that the mother civilization of all was Vedic.

Saturn in Thailand

2011-09-15T21:06:00.000-07:00

Shani, the deity of Justice, Destiny and Retribution, has His presence in Thailand. In ancient Siam, one can see his statue.

Saturn, the melancholy planet, was rising at the birth of Dante. He is prominent in the horoscopes of Goethe and other poets and philosophers like Sankara. Without His Grace, liberation is not possible.

The most ancient Civilization was the Vedic and Dr Kenneth Chandler puts the origin at 4900 BC. According to him, the Aryan Invasion Theory is not correct.

Will Durant opined that India " is the mother of us all, through Sanskrit, the mother of Europe's languages".

Dr Kenneth Chandler writes

"The original theory proposed by the early historical linguistics who considered these issues was that Vedic Sanskrit conserved the original sound system of the “proto-Indo-European” language most closely, and that Iranian and European languages underwent a systematic sound shift, creating break-away or daughter languages spoken by the people who populated India and Europe. According to this theory, Vedic Sanskrit was put at near the trunk of the proto-Indo-European language tree, if not the trunk itself.

This theory has been challenged and hotly debated in recent years, most especially by
computer linguists.

Since the 1990s, it is now common for computer linguists to hold
that Sanskrit is not so near the root of the Indo-European language tree, but a
subsequent branch. A currently dominant theory is that the original Indo-European
language stemmed from an Indo-European proto-language that has since been lost.
The first languages to break off from the proto-Indo-European root, according to the
dominant contemporary linguistic theories, was Anatolian (the language of what is now
central Turkey), followed by Celtic (a language found in nearby Thrace in northeastern Greece, and also Ireland suggesting that there was a commerce or colonization between Ireland and early Thrace), then Greek, and then Armenian. According to these theories, the Indian and Iranian language groups are still later branches off the proto-Indo-European “root.”

The linguistic evidence appears to imply migrations of people from the Black Sea area
into India, and yet there is no anthropological evidence to support either a migration into northern India, or an invasion. Evidence from skeletal remains, as we saw, as well as pottery and other artifacts, show no cultural replacement at any time in north Indian Thomas V. Gamkrelidze and V. V. Ivanov, “Family Tree of the Indo-European Languages,” Scientific American, March, 1990, p. 110 and following.

Dr. Don Ringe and Dr. Ann Taylor, two linguists at the University of Pennsylvania, with the help of computer scientist Dr. Tandy Warnow, developed a computer algorithm to sift through the Indo- European languages and look for grammatical and phonetic similarities between them. Their work, published in 1996, has thrown up four possible family trees. “We have come up with a favorite,” says Dr. Warnow. The tree shows that the first breakaway language was Anatolian, an ancient group of languages once spoken in Turkey. Celtic was quick to follow, spawning Irish, Gaelic, Welsh and Breton. Armenian and Greek then developed from proto-Into-European. Strangely enough, one of the later branches to emerge, according to the runs of the computer programs, was Sanskrit.

It is interesting that the Celts settled in Thrace in northern Greece, just a short distance from Anatolia. Thrace was the birthplace of the Orphic mysteries which swept into Greece in the sixth century BC. Celtic is one of the earliest languages, along with Anatolian and Greek, to break off from the Indo European proto-language. The technique for self-knowledge described by Socrates were said to have come from Thrace. The Anatolians of central Turkey occupied the area near where the pre-Socratic tradition sprang up in the sixth century BC. This suggests that a technique was passed from India into the Celtic language.

Of Intercalary months, Adhi Masas

2011-09-01T21:24:00.001-07:00

The solar month is 30.438030202068 days

A lunar month = 29.5305881 days

It need not be added that a lunation or synodic month means the interval between two consecutive full moons or new moons. Conjunction ( New Moon ) is 0 degrees and Opposition ( Full Moon ) is 180 degrees

Hence a solar year does not have a whole number of lunar months ( about 12.37 lunations ) So a thirteenth embolismic or intercalary month is inserted.

It was observed that 19 solar years or 19*12 = 228 solar months = 235 lunations and hence 7 Adhi Masas were found in every 19 years. An intercalary or 13th month had to be inserted in a 19 year cycle and 19/7 was the ratio. .

They are called Adhi Masas in Indian Astronomy and they were computed using the Theory of continued fractions. The Theory of contiued Fractions is attributed to Euler. This 19 year old cycle is called the Metonic Cycle, named after the Greek astronomer, Meton.

But then the Indian mathematicians correctly computed the Adhi Masas, centuries before Meton or Euler ! The Indian National Calender is lunisolar, whose dates both indicate the solar year and the moon phases and the next date when the New Moon or Full Moon will occur. The length of the synodic month is given as 29.5305879 days in the Surya Siddhanta, which is correct to six decimals. Surya Siddhanta stated that there are 15933396 Adhi Masas in 51840000 solar months !

Of Vedic Maths

2011-08-30T20:43:00.000-07:00

Consisting of 16 basic aphorisms or Sutras, Vedic Mathematics is a system of Maths which prevailed in ancient India. Composed by Bharati Krishna Thirtha, these 16 sutras help one to do faster maths.

The first aphorism is this

"Whatever the extent of its deficiency, lessen it still further to that very extent; and also set up the square (of that deficiency)"

When computing the square of 9, as the nearest power of 10 is 9, let us take 10 as our base. As 9 is 1 less than 10, we can decrease it by the deficiency = 9-1 =8. This is the leftmost digit
On the right hand put deficiency^2, which is 1^2.

Hence the square of nine is 81.

For numbers above 10, instead of looking at the deficit we look at the surplus.

For example:

11^2 = (11+1)*10+1^2 = 121

12^2 = (12+2)*10+2^2 = 144

14^2 = ( 14+4)*10+4^2 = 196

25^2 = ((25+5)*2)*10+5^2 = 625

35^2= ((35+5)*3)*10+5^2 = 1225

Indian Maths, on Argive heights divinely sang !

2011-08-27T21:42:00.001-07:00

In India, mathematics is related to Philosophy. We can find mathematical
concepts like Zero ( Shoonyavada ), One ( Advaitavada ) and Infinity
(Poornavada ) in Philosophia Indica.

The Sine Tables of Aryabhata and Madhava, which gives correct sine values or values of
24 R Sines, at intervals of 3 degrees 45 minutes and the trignometric tables of
Brahmagupta, which gives correct sine and tan values for every 5 degrees influenced
Christopher Clavius, who headed the Gregorian Calender Reforms of 1582. These
correct trignometric tables solved the problem of the three Ls, ( Longitude, Latitude and
Loxodromes ) for the Europeans, who were looking for solutions to their navigational
problem ! It is said that Matteo Ricci was sent to India for this purpose and the
Europeans triumphed with Indian knowledge !

The Western mathematicians have indeed lauded Indian Maths & Astronomy. Here are
some quotations from maths geniuses about the long forgotten Indian Maths !

In his famous dissertation titled "Remarks on the astronomy of Indians" in 1790,
the famous Scottish mathematician, John Playfair said

"The Constructions and these tables imply a great knowledge of
geometry,arithmetic and even of the theoretical part of astronomy.But what,
without doubt is to be accounted,the greatest refinement in this system, is
the hypothesis employed in calculating the equation of the centre for the
Sun,Moon and the planets that of a circular orbit having a double
eccentricity or having its centre in the middle between the earth and the
point about which the angular motion is uniform.If to this we add the great
extent of the geometrical knowledge required to combine this and the other
principles of their astronomy together and to deduce from them the just
conclusion;the possession of a calculus equivalent to trigonometry and
lastly their approximation to the quadrature of the circle, we shall be
astonished at the magnitude of that body of science which must have
enlightened the inhabitants of India in some remote age and which whatever
it may have communicated to the Western nations appears to have received
another from them...."

Albert Einstein commented "We owe a lot to the Indians, who taught us how to count,
without which no worthwhile scientific discovery could have been made."

The great Laplace, who wrote the glorious Mechanique Celeste, remarked

"The ingenious method of expressing every possible number
using a set of ten symbols (each symbol having a place value and an absolute
value) emerged in India. The idea seems so simple nowadays that its
significance and profound importance is no longer appreciated. Its
simplicity lies in the way it facilitated calculation and placed arithmetic
foremost amongst useful inventions. The importance of this invention is more
readily appreciated when one considers that it was beyond the two greatest
men of antiquity, Archimedes and Apollonius."

The Infinite Series of the Pi function of Madhava

2011-08-26T19:55:00.001-07:00

By means of the same argument, the circumference can be computed in another way too. That is as (follows): The first result should by the square root of the square of the diameter multiplied by twelve. From then on, the result should be divided by three (in) each successive (case). When these are divided in order by the odd numbers, beginning with 1, and when one has subtracted the (even) results from the sum of the odd, (that) should be the circumference. ( Yukti deepika commentary )

This quoted text specifies another formula for the computation of the circumference c of a circle having diameter d. This is as follows.

c = SQRT(12 d^2 - SQRT(12 d^2/3.3 + sqrt(12 d^2)/3^2.5 - sqrt(12d^2)/3^3.7 +.......

As c = Pi d , this equation can be rewritten as

Pi = Sqrt(12( 1 - 1/3.3 + 1/3^2.5 -1/3^3.7 +......

This is obtained by substituting z = Pi/ 6 in the power series expansion for arctan (z).

Pi/4 = 1 - 1/3 +1/5 -1/7+.....

This is Madhava's formula for Pi, and this was discovered in the West by Gregory and Liebniz.

Arctangent series of Madhava, Gregory and Liebniz

2011-08-25T21:20:00.001-07:00

The inverse tangent series of Madhava is given in verse 2.206 – 2.209 in Yukti-dipika commentary (Tantrasamgraha-vyakhya) by Sankara Variar . It is also given by Jyeshtadeva in Yuktibhasha and a translation of the verses is given below.

Now, by just the same argument, the determination of the arc of a desired sine can be (made). That is as follows: The first result is the product of the desired sine and the radius divided by the cosine of the arc. When one has made the square of the sine the multiplier and the square of the cosine the divisor, now a group of results is to be determined from the (previous) results beginning from the first. When these are divided in order by the odd numbers 1, 3, and so forth, and when one has subtracted the sum of the even(-numbered) results from the sum of the odd (ones), that should be the arc. Here the smaller of the sine and cosine is required to be considered as the desired (sine). Otherwise, there would be no termination of results even if repeatedly (computed).

Rendering in modern notations

Let s be the arc of the desired sine, bhujajya, y. Let r be the radius and x be the cosine (kotijya).

The first result is y.r/x
From the divisor and multiplier y^2/x^2
From the group of results y.r/x.y^2/x^2, y.r/x. y^2/x^2.y^2/x^2
Divide in order by number 1,3 etc
1 y.r/1x, 1y.r/3x y^2/x^2, 1y.r/5x.y^2/x^2.Y^2/x^2

a = (Sum of odd numbered results) 1 y.r/1x + 1y.r/5x.y^2/x^2.y^2/x^2+......

b= ( Sum of even numbered results) 1y.r/3x.y^2/x^2 + 1 y.r/7x.y^2/x^2.y^2/x^.y^2/x^2+.....

The arc is now given by
s = a - b

Transformation to current notation

If x is the angle subtended by the arc s at the Center of the Circle, then s = rx and kotijya = r cos x and bhujajya = r sin x. And sparshajya = tan x

Simplifying we get

x = tan x - tan^3x/'3 + tan^5x/5 - tan^7x/7 + .....

Let tan x = z, we have

arctan ( z ) = z - z^3/3 + z^5/5 - z^7/7

We thank www.wikipedia.org for publishing this on their site.

The Madhava cosine series

2011-08-24T21:32:00.001-07:00

Madhava's cosine series is stated in verses 2.442 and 2.443 in Yukti-dipika commentary (Tantrasamgraha-vyakhya) by Sankara Variar. A translation of the verses follows.

Multiply the square of the arc by the unit (i.e. the radius) and take the result of repeating that (any number of times). Divide (each of the above numerators) by the square of the successive even numbers decreased by that number and multiplied by the square of the radius. But the first term is (now)(the one which is) divided by twice the radius. Place the successive results so obtained one below the other and subtract each from the one above. These together give the śara as collected together in the verse beginning with stena, stri, etc.

Let r denote the radius of the circle and s the arc-length.

The following numerators are formed first:

s.s^2,
s.s^2.s^2
s.s^2.s^2.s^2

These are then divided by quantities specified in the verse.

1)s.s^2/(2^2-2)r^2,
2)s. s^2/(2^2-2)r^2. s^2/4^2-4)r^2
3)s.s^2/(2^2-2)r^2.s^2/(4^2-4)r^2. s^2/(6^2-6)r^2

As per verse,

sara or versine = r.(1-2-3)

Let x be the angle subtended by the arc s at the center of the Circle. Then s = rx and sara or versine = r(1-cosx)

Simplifying we get the current notation

1-cosx = x^2/2! -x^4/4!+ x^6/6!......

which gives the infinite power series of the cosine function.

The Madhava Trignometric Series

2011-08-23T22:30:00.001-07:00

The Madhava Trignometric series is one one of a series in a collection of infinite series expressions discovered by Madhava of Sangramagrama ( 1350-1425 ACE ), the founder of the Kerala School of Astronomy and Mathematics. These are the infinite series expansions of the Sine, Cosine and the ArcTangent functions and Pi. The power series expansions of sine and cosine functions are called the Madhava sine series and the Madhava cosine series.

The power series expansion of the arctangent function is called the Madhava- Gregory series.

The power series are collectively called as Madhava Taylor series. The formula for Pi is called the Madhava Newton series.

One of his disciples, Sankara Variar had translated his verse in his Yuktideepika commentary on Tantrasamgraha-vyakhya, in verses 2.440 and 2.441

Multiply the arc by the square of the arc, and take the result of repeating that (any number of times). Divide (each of the above numerators) by the squares of the successive even numbers increased by that number and multiplied by the square of the radius. Place the arc and the successive results so obtained one below the other, and subtract each from the one above. These together give the jiva, as collected together in the verse beginning with "vidvan" etc.

Rendering in modern notations

Let r denote the radius of the circle and s the arc-length.

The following numerators are formed first:

s.s^2,
s.s^2.s^2
s.s^2.s^2.s^2

These are then divided by quantities specified in the verse.

1)s.s^2/(2^2+2)r^2,
2)s. s^2/(2^2+2)r^2. s^2/4^2+4)r^2
3)s.s^2/(2^2+2)r^2.s^2/(4^2+4)r^2. s^2/(6^2+6)r^2

Place the arc and the successive results so obtained one below the other, and subtract each from the one above to get jiva:

Jiva = s-(1-2-3)

When we transform it to the current notation

If x is the angle subtended by the arc s at the center of the Circle, then s = rx and jiva = r sin x.

Sin x = x - x^3/3! + x^5/5! - x^7/7!...., which is the infinite power series of the sine function.

By courtesy www.wikipedia.org and we thank Wikipedia for publishing this on their site.

Calculus, India's gift to Europe

2011-08-21T01:18:00.001-07:00

The Jesuits took the trignometric tables and planetary models from the Kerala School of Astronomy and Maths and exported it to Europe starting around 1560 in connection with the European navigational problem, says Dr Raju.

Dr C K Raju was a professor Mathematics and played a leading role in the C-DAC team which built Param: India’s first parallel supercomputer. His ten year research included archival work in Kerala and Rome and was published in a book called " The Cultural Foundations of Mathematics". He has been a Fellow of the Indian Institute of Advanced Study and is a Professor of Computer Applications.

“When the Europeans received the Indian calculus, they couldn’t understand it properly because the Indian philosophy of mathematics is different from the Western philosophy of mathematics. It took them about 300 years to fully comprehend its working. The calculus was used by Newton to develop his laws of physics,” opines Dr Raju.

The Infinitesimal Calculus: How and Why it Was Imported into Europe

By Dr C.K. Raju

It is well known that the “Taylor-series” expansion, that is at the heart of calculus, existed in India in widely distributed mathematics / astronomy / timekeeping (“jyotisa”) texts which preceded Newton and Leibniz by centuries.

Why were these texts imported into Europe? These texts, and the accompanying precise sine values computed using the series expansions, were useful for the science that was at that time most critical to Europe: navigation. The ‘jyotisa’ texts were specifically needed by Europeans for the problem of determining the three “ells”: latitude, loxodrome, and longitude.

How were these Indian texts imported into Europe? Jesuit records show that they sought out these texts as inputs to the Gregorian calendar reform. This reform was needed to solve the ‘latitude problem’ of European navigation. The Jesuits were equipped with the knowledge of local languages as well as mathematics and astronomy that were required to understand these Indian texts.

The Jesuits also needed these texts to understand the local customs and how the dates of traditional festivals were fixed by Indians using the local calendar (“panchânga”). How the mathematics given in these Indian ancient texts subsequently diffused into Europe (e.g. through clearing houses like Mersenne and the works of Cavalieri, Fermat, Pascal, Wallis, Gregory, etc.) is yet another story.

The calculus has played a key role in the development of the sciences, starting from the “Newtonian Revolution”. According to the “standard” story, the calculus was invented independently by Leibniz and Newton. This story of indigenous development, ab initio, is now beginning to totter, like the story of the “Copernican Revolution”.

The English-speaking world has known for over one and a half centuries that “Taylor series” expansions for sine, cosine and arctangent functions were found in Indian mathematics / astronomy / timekeeping (‘jyotisa’) texts, and specifically in the works of Madhava, Neelkantha, Jyeshtadeva, etc. No one else, however, has so far studied the connection of these Indian developments to European mathematics.

The connection is provided by the requirements of the European navigational problem, the foremost problem of the time in Europe. Columbus and Vasco da Gama used dead reckoning and were ignorant of celestial navigation. Navigation, however, was both strategically and economically the key to the prosperity of Europe of that time.

Accordingly, various European governments acknowledged their ignorance of navigation while announcing huge rewards to anyone who developed an appropriate technique of navigation. These rewards spread over time from the appointment of Nunes as Professor of Mathematics in 1529, to the Spanish government’s prize of 1567 through its revised prize of 1598, the Dutch prize of 1636, Mazarin’s prize to Morin of 1645, the French offer (through Colbert) of 1666, and the British prize legislated in 1711.

Many key scientists of the time (Huygens, Galileo, etc.) were involved in these efforts. The navigational problem was the specific objective of the French Royal Academy, and a key concern for starting the British Royal Society.

Prior to the clock technology of the 18th century, attempts to solve the European navigational problem in the 16th and 17th centuries focused on mathematics and astronomy. These were (correctly) believed to hold the key to celestial navigation. It was widely (and correctly) held by navigational theorists and mathematicians (e.g. by Stevin and Mersenne) that this knowledge was to be found in the ancient mathematical, astronomical and time-keeping (jyotisa) texts of the East.

Though the longitude problem has recently been highlighted, this was preceded by the latitude problem and the problem of loxodromes. The solution of the latitude problem required a reformed calendar. The European calendar was off by ten days. This led to large inaccuracies (more than 3 degrees) in calculating latitude from the measurement of solar altitude at noon using, for example, the method described in the Laghu Bhâskarîya of Bhaskara I.

However, reforming the European calendar required a change in the dates of the equinoxes and hence a change in the date of Easter. This was authorised by the Council of Trent in 1545. This period saw the rise of the Jesuits. Clavius studied in Coimbra under the mathematician, astronomer and navigational theorist Pedro Nunes. Clavius subsequently reformed the Jesuit mathematical syllabus at the Collegio Romano. He also headed the committee which authored the Gregorian Calendar Reform of 1582 and remained in correspondence with his teacher Nunes during this period.

Jesuits such as Matteo Ricci who trained in mathematics and astronomy under Clavius’ new syllabus were sent to India. In a 1581 letter, Ricci explicitly acknowledged that he was trying to understand the local methods of time-keeping (‘jyotisa’) from the Brahmins and Moors in the vicinity of Cochin.

Cochin was then the key centre for mathematics and astronomy since the Vijaynagar Empire had sheltered it from the continuous onslaughts of Islamic raiders from the north. Language was not a problem for the Jesuits since they had established a substantial presence in India. They had a college in Cochin and had even established printing presses in local languages like Malayalam and Tamil by the 1570’s.

In addition to the latitude problem (that was settled by the Gregorian Calendar Reform), there remained the question of loxodromes. These were the focus of efforts of navigational theorists like Nunes and Mercator.

The problem of calculating loxodromes is exactly the problem of the fundamental theorem of calculus. Loxodromes were calculated using sine tables. Nunes, Stevin, Clavius, etc. were greatly concerned with accurate sine values for this purpose, and each of them published lengthy sine tables. Madhava’s sine tables, using the series expansion of the sine function, were then the most accurate way to calculate sine values.

Madhava's sine series

sin x = x - x^3/3! + x^5/5! - x^7/7!+......

The Europeans encountered difficulties in using these precise sine values for determining longitude, as in the Indo-Arabic navigational techniques or in the Laghu Bhâskarîya. This is because this technique of longitude determination also required an accurate estimate of the size of the earth. Columbus had underestimated the size of the earth to facilitate funding for his project of sailing to the West. His incorrect estimate was corrected in Europe only towards the end of the 17th century CE.

Even so, the Indo-Arabic navigational technique required calculations while the Europeans lacked the ability to calculate. This is because algorismus texts had only recently triumphed over abacus texts and the European tradition of mathematics was “spiritual” and “formal” rather than practical, as Clavius had acknowledged in the 16th century and as Swift (of ‘Gulliver’s Travels’ fame) had satirized in the 17th century. This led to the development of the chronometer, an appliance that could be mechanically used without any application of the mind.

The Idea of Planetary Mass in India

2011-08-20T05:23:00.001-07:00

Many ancient cultures have contributed to the development of Astro Physics.

Some examples are

The Saros cycles of eclipses discovered by Egyptians
The classification of stars by the Greeks
Sunspot observations of the Chinese
The phenomenon of Retrogression discovered by Babylonians

In this context the Indian contribution to Astro Physics ( which includes Astronomy, Maths and Astrology ) is the the development of the ideas of planetary forces and differential equations to calculate the geocentric planetary longitudes, several centuries before the European Renaissance.

Natural Strength is one of the Sixfold Strengths, Shad Balas and goes by the name Naisargika Bala. It is directly proportional to the size of the celestial bodies and inversely proportional to the geocentric distance. ( Horasara ).

Naisargika Bala or Natural Strength is used to compare planetary physical forces. When two planets occupy the same, identical position in the Zodiac at a given instant of time, such a phenomenon goes by the name of planetary war or Graha Yuddha,happening when two planets are in close conjunction. The Karanaratna written by Devacharya explains that the planet with the larger diameter is the victor in this planetary war. This implies Naisargika Bala.

The Surya Siddhanta says " The dynamics or quantity of motion produced by the action of a fixed force to different planetary objects is inversely related to the quantity of matter in these objects"

This definition more or less equals the statement of Newton’s second law of motion

M = Fa
or
a = F/M

So it strongly suggests that the idea of planetary mass was known to the ancient Indian astronomers and mathematicians.

Differential Equations used in Siddhantas

2011-08-18T21:33:00.001-07:00

Motional strength is one the sixfold strengths, known as Cheshta Bala. This motional strength is computed by the formula

Motional Strength = 0.33 ( Sheegrocha or Perigee - geocentric longitude of the planet ). This motional strength is known as Cheshta Bala.

Differential Calculus is the science of rates of the change. If y is the longitude of the planet and t is time, then we have the differential equation ,dy/dt.

During direct motion, we find that dy/dt > 0 and during retrogression dy/dt < 0. During backward motion of the planet ( retrogression) y decreases with time and during direct motion y increases with time. When there are turning points known as Vikalas or stationary points, we have dy/dt = 0 ( where planets like Mars will appear to be stationary for an observer on Earth ).

The quantity in bracket is the Sheegra Anomaly, the Anomaly of Conjuction, the angular distance of the planet from the Sun. This Anomaly or Cheshta Bala is maximum at the center of the Retrograde Loop. Cheshta Kendra is defined as the Arc of Retrogression and is the same as Sheegra Kendra, Kendra being an angle in Sanskrit. During Opposition, when the planet is 180 degrees from the Sun, Cheshta Bala is maximum and during Conjunction, when the planet is 0 degrees from the Sun, it is minimum

The Motional Strength is given in units of 60s, Shashtiamsas.

Direct motion ( Anuvakra ) 30
Stationary point ( Vikala ) 15
Very slow motion ( Mandatara ) 7.5
Slow motion ( Manda ) 15
Average speed ( Sama ) 30
Fast motion ( Chara ) 30
Very fast motion ( Sheegra Chara ) 45
Max orbital speed ( Vakra ) 60
(Centre of retrograde)

The Nine Oribtal Elements

2011-08-17T21:04:00.001-07:00

Mean and true planetary longitudes in the Zodiac is computed by Nine Orbital Elements, in Indian Astronomy.

Mean longitude of Planet, Graha Madhyama , M
Daily Motion of the Mean Longitude, Madhyama Dina Gathi, Md
Aphelion, Mandoccha, Ap
Daily Motion of Aphelion, Mandoccha Dina Gathi, Apd
Ascending Node, Patha, N
Daily Motion of Ascending Node, Patha Dina Gathi, Nd
Heliocentric Distance, Manda Karna, radius vector, mndk
Maximum Latitude, L, Parama Vikshepa
Eccentricity, Chyuthi,e

In Western Astronomy, we have six orbital elements

Mean Anomaly, m
Argument of Perihelion, w
Eccentricity, e
Ascending Node, N
Inclination, i, inclinent of orbit
Semi Major Axis, a

With the Nine Orbital Elements, true geocentric longitude of the planet is computed, using multi step algorithms.

There is geometrical equivalence between both the Epicycle and the Eccentric Models.

The radius of the Epicycle, r = e, the distance of the Equant from the Observer.

Astronomical Units of Time Measurement

2011-08-14T21:21:00.000-07:00

We find Yuga cylces mentioned not only in astronomical works, but also in mythological works in India.

Kali Yuga began on the midnight of 17th Feb 3102 BCE and the duration of this Kali Yuga is said to be 4.32 K solar years. Dwapara is 2*Kali Yuga years. Treta is 3*K Y and Krita Yuga is 4*K Y.

Krita Treta Dwaparascha Kalischaiva Chaturyugam
Divya Dwadasabhir varshai savadhanam niroopitham

Thus an Equinoctial Cycle, Mahayuga is equal to 4+3+2+1 = 10 KYs.

E C = 10 KYs.

A Greater Equinoctial Cycle ( Manvantara ) = 71 Equinoctial Cycles

There are cusps happening in between Manvantaras, each equal to a Krita Yuga in duration. A Krita is equal to 4 KYs or 2/5 of a Maha Yuga. Since there will 15 such cusps happening amongst the Fourteen Manvantaras, they are equal to 15*2/5 = 6 Mahayugas.

Hence 14*71+6 = 1000 Mahayugas = 4.32 Billion Years

Sahasra yuga paryantham
Aharyal brahmano vidu
Ratrim yugah sahasrantham
The Ahoratra vido janah ( The Holy Geetha ).

This is one Cosmological Cycle, called Brahma Kalpa.

Chaturyuga sahasram indra harina dinam uchyathe

From one second, it can be logarithmically shown, upto 10^22 seconds. This is what the above diagram shows. This diagram is by courtesy of Wikipedia.

From 10^0 it goes upto 10^22 seconds. One day of Brahma is 4.32 billion years and 100 years of Brahma therefore is 311.04 trillion years, which is shown logarithmically above.

One Asu is 4 seconds, one Vinadi is 24 seconds and one Nadi is 24 minutes. 60 such Nadis make up one day. This is the Sexagesimal division of a day into 60 Nadis ! In Astronomy, one degree is sixty minutes and one minute is sixty seconds. Hence sexagesimal division is justified ! 365.25 such days constitute a year and Hindu calculation goes upto 311.04 trillion years !

The Geometric Model of Paramesvara

2011-08-13T23:07:00.001-07:00

The Indian astronomers were interested in the computation of eclipses, of geocentric longitudes, the risings and settings of planets,which had relevance to the day to day activities of people.

Did not Emerson say?

"Astronomy is excellent, it should come down and give life its full value, and not rest amidst globes and spheres ".

They were not bothered about proposing Models of the Universe and gaining publicity. But then they did discuss the geometrical model, the rationale of their computations.

The above diagram explains the Geometric Model of Parameswara, another Kerala astronomer. Paramesvara and Nilakanta modified the Aryabhatan Model.

By Sheegroccha, he meant the longitude of the Sun." Sheegrocham Sarvesham Ravir bhavathi ", he says is his book Bhatadeepika . For the interior planets, the longitude of the Sheegra correction is to be deducted from the Sun's longitude, Ravi Sphuta to get the Anomaly of Conjunction.

The Manda Prathimandala is the mean angular motion of the Planet, from which the trignometric corrections are given to get the true, geocentric longitude.

Vikshepa Koti, the cosine of celestial latitude

2011-08-11T20:40:00.003-07:00

Jyeshtadeva was a Kerala astronomer who helped in the calculation of longitudes, when there is latitudinal deflection. In his Yukti Bhasa, he calculates correctly the cos l, the cosine of latitude, which is important in the Reduction to the Ecliptic.

There is a separate section in the Yukti Bhasa, which deals with the effects of the inclination of a planet's orbit on its latitude. He describes how to find the true longitude of a planet, Sheegra Sphutam, when there is latitudinal deflection.

"Now calculate the Vikshepa Koti, cos l, by subtracting the square of the Vikshepa from the square of the Manda Karna Vyasardha and calculating the root of the difference."

In the above diagram,

N is the Ascending Node
P is the planet on the Manda Karna Vritta, inclined to the Ecliptic

Vikshepa Koti = OM = SQRT( OP^2 - PM^2 )

Taking this Vikshepa Koti and assuming it to be the Manda Karna, sheegra sphuta, the true longitude, has to be calculated as before.

Vikshepa, the Celestial Latitude

2011-08-11T20:40:00.001-07:00

l, Vikshepa, is the Celestial Latitude, the latitude of the planet, the angular distance of the planet from the Ecliptic.

i is the inclination, inclinent of Orbit.

Sin l = Sin i Sin( Heliocentric Long - Long of Node ).

Celestial Latitude is calculated from this equation.

The longitude of the Ascending Node, pata, is minussed from the heliocentric longitude and this angle is called Vipata Kendra.

Sidereal Periods in the Geocentric Model

2011-08-08T01:51:00.000-07:00

In the last post we said that Angle AES is Sheegroccha, which is the longitude of the Sun. ( Sheegrocham Sarvesham Ravir Bhavathi ). The Angle AEK is the Heliocentric longitude of the planet.

Sidereal Periods of superior Planets in the Geocentric = Sidereal periods in the Heliocentric.

Sidereal Periods of Mercury and Venus = Mean Sun in the Geocentric

In the Planetary Model of Aryabhata, we find the equation

Heliocentric Longitude - Longitude of Sun = The Anomaly of Conjunction ( Sheegra Kendra ).

As Astronomy is Universal, we are indebted to these savants who made astro calculation possible. Even the word " genius " is an understatement of their brilliant IQ !

Development of the Planetary Models in Astronomy

Hipparchus 150 BCE
Claudious Ptolemy 150 ACE
Aryabhata 499 ACE
Varaha 550 ACE
Brahmagupta 628 ACE
Bhaskara I 630 ACE
Al Gorismi 850 ACE
Munjala 930 ACE
Bhaskara II 1150 ACE
Madhava 1380 ACE
Ibn al Shatir 1350 ACE
Paramesvara 1430 ACE
Nilakanta 1500 ACE
Copernicus 1543 ACE
Tycho Brahe 1587 ACE
Kepler 1609 ACE
Laplace 1700 ACE
Urbain Le Verrier 1850 ACE
Simon Newcomb 1900 ACE
E W Brown 1920 ACE

Reduction to the Geocentric for superior planets in the Eccentric Model

2011-08-06T22:16:00.001-07:00

In the above diagram,

A = Starting Point, 0 degree Aries
P = Planet
S = Sun
E = Earth

Angle AEK = Manda Sphuta, heliocentric longitude, after manda samskara
Angle AES = Sheegroccha, mean Sun, mean longitude of Sol
Angle AEP = True geocentric longitude of planet
Angle KEP = The Sheegra Correction or sheegra phalam

The Anomaly of Conjunction = Sheegra Kendra = Angle AES - Angle AEK

x = Angle AES - Angle AEK

Sin ( x ) =

r sin (x)
_______________________
((R + r cos x)^2 + rsin x^2 ))^1/2

which is the Sheegra correction formula given by the Indian astronomers to calculate the geocentric position of the planet.

Aslesha Njattuvela brings rains !

2011-08-05T20:56:00.001-07:00

It was Monsoon Tourism, as Aslesha Njattuvela was on. It was raining heavily, cats and dogs in Kerala. I got the rains when I reached Kochi. I had some work at the Passport Office and I finished the work at Noon. Then I went on a tour of the famous Goshree Islands.

I went by boat yesterday to the beautiful Bolgatty Island. A two minutes walk saw me entering the lovely Bolgatty Palace, a resort by the Kerala Tourism Development Corporation.

I walked to the Bolgatty Bus Stand and took a bus to Vallarpadam International Container Terminal. Now everything is in place and one ship, OEL Dubai, was unloading. The progress of the ICTT is slow, but steady.

The Bolgatty Palace is beautiful and well situated in the Mulavukad Island. This island is connected to Vallarpadam by a bridge. Vallarpadam is in turn connected to Vypin by a bridge. In fact these bridges are known as Goshree Bridges, as these beateous islands are known as Goshree Islands. In Vypin, one can see the GAIL LNG terminals, which adorn Puthuvypin.

A new bridge, parallel to the existing Vallarpadam bridge, is being built to ease the traffic. I saw a barge jetty at Bolgatty and a barge carrying containers there.

Kochi is a cauldron of world cultures. A versatile land where visitors from abroad, right from Arabs and Phoenicians to the Chinese, Italians, Portugese, Dutch and British have left indelible marks. A great Port, universally known as the Queen of the Arabian Sea. The newly renovated Bolgatty Palace has 4 palace suits, 6 waterfront cottages, 16 well maintained rooms and one can enjoy four star faciliites and a range of leisure options.

Said a honeymooner, Asmita, Calcullat about Bolgatty " We went to Kerala for our honeymoon and Kochi was our first stop. We reached the resort at around 3:30pm after a long flight and were famished. Since we reached post lunch timings none of the restaurants were open, however the room service was very prompt and we had an amazing keralite food. The rooms are large, and built in a princely way. The property is equipped with all the modern facilities and the stay was really comfortable.
We enjoyed the Kerala body message in the resort . The location is also great. Overall its a great place to stay ".

The Bolgatty Palace was built in 1744 by the Dutch and is a short boat ride away from the Ernakulam Mainland. This is one of the oldest Dutch Palaces outside Holland the only Palace Hotel of its kind in Kerala. Now she has a Palace block and a resort block, called Bolgatty Island Resort. Amenities here comprise Swimming Pool, 9 hole Golf Course and is a destination of choice for select Indian corporates for their conference. It is a favourite destination for Indian elite and overseas tourists. The Kochi Airport is just 32 kms away and the rail and bus terminals just 2 km away.

Kochi International Marina is a KTDC venture located on the eastern coast of Bolgatty Island in the Bolgatty Palace Heritage Hotel. It is the first full fledged marina of international standards in Bharat. It provides berthing facilities to 37 yachts and also offers services like electricity, water and fuel for boats. It is close to the international sea route at the South West Coast of peninsular India , with minimum tidal variations and favorable conditions.

The Bolgatty Event Center overlooks the backwaters of Cochin Seaport and is an exotic venue for conducting Conferences, Exhitions, Wedding Receptions, Conventions and theme dinners. Imbued with resplendent greenery, the Arabian Sea and the ICTT at Vallarpadam gives an easy access to the Center.

Another Indian Astronomical Treatise

2011-08-03T20:50:00.001-07:00

Siddhanta Darpana by Samanta is a great treatise on Astronomy. The placing of the five major planets in the Tychonic Model of the solar system is in agreement with the Titius-Bode Law and even with Kepler's third law. This is a great contribution from Samanta. Epicycles for Solar Anomaly, known as Ugra Phala give correct distances of planets, in both Indian and Greek Astronomy.

Here we give the modern values of the radii of the orbits of the planets and those given in his magnum opus, the Siddhanta Darpana.

Planetary distances in astronomical unit

Planet Distance according to Bode’s law Actual distance

Mercury 0.4 0.387

Venus 0.7 0.732

Earth 1.0 1.0

Mars 1.6 1.524

Asteroid belt 2.8 2.68

Saturn 10.0 9.539

Uranus 19.6 19.19

Neptune 38.8 30.1

Pluto 77.2 39.5

Siddhanta Darpana

Even Odd

quadrant quadrant

Sun 1.00 1.00

Mercury 0.386 0.388

Venus 0.725 0.727

Mars 1.5126 1.5184

Jupiter 5.1428 5.2173

Saturn 9.230 9.4773

The Obliquity of the Ecliptic !

2011-07-31T22:48:00.000-07:00

The Earth's Axial tilt is called the Obliquity of the Ecliptic and the is angle between the perpendicular to Orbit and the North Celestial Pole.

The Equatorial coordinate system is based on the 360 degree Celestial Equator Circle. The Ecliptic coordinate system is based on the 360 degree Ecliptic circle.

The mathematical conversion from Equatorial to Ecliptic is effectuated by the equation for the Ascendant

Lagna = atan ( Sin E / Cos E Cos w - Sin w Tan A )

L is the Lagna on the Ecliptic. E is the Lagna on the Celestial Equator, the Sayana Kala Lagna. The Sayana Kala Lagna, E, is reduced to the Ecliptic by this equation. The Lagna is the intersecting point between the Eastern Celestial Horizon, the Kshitija with the Ecliptic.

w is the Sun's maximum declination and A is the latitude of the place.

The above diagram is by courtesy of Wikipedia

Reduction to the Heliocentric Coordinate System

2011-07-27T01:21:00.000-07:00

In the Concentric Equant Model, reduction to the Heliocentric was easy.

In the above diagram, OM was the Radius of the Epicycle. And q is the Equation of the Center.

The word Equation in Astronomy is the angle between mean planet and true planet. It is got by the formula

q = arcsine ( e* sin (M) )

In the above diagram, BOM is the mean Centrum or the Mean Anomaly and SOM is the true Centrum or the True Anomaly.

t - m = q, the Equation of Center.

This diagram is by courtesy of Jean-Pierre Lacroix and Robert Baywater, www.ancientcartography.net

The Munjala Coefficients

2011-07-23T20:57:00.000-07:00

w was an important angle in the Munjala Model and the solution to the problem of a difference of 2.5 degrees in the lunar longitude had to be solved. So Munjala brought in an angle, w, angle between the Mean Sun and the Moon's Apogee.

The angle n is the elongation of the Sun from the Mean Moon and so the

Manda Anomaly, Alpha = w + n

This diagram is by courtesy of Jean-Pierre Lacroix and Robert Baywater, www.ancientcartography.net

The Epicycle Model of Bhaskara

2011-07-22T23:30:00.001-07:00

The Model propounded by Aryabhata is an algorithm. The Khmers drew the diagrams of the Sun by using the epicyle equivalent of the model developed by Bhaskara in the seventh century. Eccentricity is variable in this Epicycle Model.

You can see a relevant animation of Dennis Duke at
http://people.scs.fsu.edu/~dduke/pingree2.html

Corrections to the Equation of Center for Moon

2011-07-22T03:19:00.001-07:00

The Indian astronomers could calculate the Manda Kendra ( The Equation of Center of Western Astronomy ) and the Manda Phala, but a problem presented itself when calculating the lunar longitude.

The Concentric Model and the Epicylic Model could not calculate Moon's longitude at quadrature, even though they could calculate the lunar longitude at the times of New Moon and Full Moon. There was a difference of 2.5 degrees between the longitude computed by the Concentric Equant and Epicyclic Models. So the ancients had to give a correction to the Equation of Center, which reached a maximum of 2.5 degrees.

So the Indian astronomers came out with a solution. They created a new Equant (E'), the true Equant, which moves on an epicycle, whose center is the Mean Equant, E. The epicycle has a radius e, equal to EoE., on the Line of Apsis, OA.

q1 = Equation of Center, first lunar inequality
q2 = Correction, second lunar inequality.

True Longitude = Mean long + Eq of Center + q2

The first lunar anomaly was the Evection and the second, the Variation. The first inequality was the Equation of Center and the Evection and the Variation became the second and third inequalities. Actually Indian Astronomy recognised 14 major perturbations of the Moon and 14 corrections are therefore given to get the Cultured Longitude of the Moon, the Samskrutha Chandra Madhyamam. Then Reduction to Ecliptic is done to get the true longitude of Luna !

This diagram is by courtesy of Jean-Pierre Lacroix and Robert Baywater, www.ancientcartography.net

The Concentric Equant Model of Aryabhata

2011-07-21T23:07:00.001-07:00

Aryabhata developed a Concentric Equant Model, in the sixth century. The Sun moves on a circle of radius R, called a deferent, whose center is the Observer on Earth. The distance between the Earth and the Sun, the Ravi Manda Karna, is constant. The motion of the Sun is uniform from a mathematical point, called the " Equant", which is located at a distance R x e from the observer in the direction of the Apogee ( e = eccentricity ).

All Indian computations are based on this Concentric Equal Model. The normal equation for computing the Manda Anomaly is R e Sin M and resembles the Kepler Equation, M = E - e Sin E.

This diagram is by courtesy of Jean-Pierre Lacroix and Robert Baywater, www.ancientcartography.net

The Lunar Model Of Munjala

2011-07-21T02:20:00.000-07:00

The Concentric Equant theory was developed by the Indian astronomer, Munjala ( circa 930 CE ).

The Geocentric theory of the ancient astronomers had the ability to produce true Zodiacal Longitudes for the Moon. But the perturbations of the Moon were so complex, that the early Indian and Greek astronomers had to give birth to complicated theories.

The simplest model is a concentric Equant Model to compute the lunar true longitude.

In the above diagram

M = Moon
O = Observer
Eo = Equant , located at a distance r from the observer , drawn on the Line of Apsis and the Apogee.

A = Apogee, Luna's nearest point to Earth

Angle Alpha = Angle between Position and Apogee
Angle q1 = Equation of Center . Angle subtended at Luna between Observer and Equant
Equation in Astronomy = The angle between true and mean positions.

These diagrams are by courtesy of Jean-Pierre Lacroix and Robert Baywater, www.ancientcartography.net

Indian Astronomy Original

2011-07-19T22:08:00.001-07:00

The Physics Professor of Florida State University, Dennis Duke remarks

"The planetary models of ancient Indian mathematical astronomy are described in several texts. These texts invariably give algorithms for computing mean and true longitudes of the planets, but are completely devoid of any material that would inform us of the origin of the models. One way to approach the problem is to compare the predictions of the Indian models with the predictions from other models that do have, at least in part, a known historical background. Since the Indian models compute true longitudes by adding corrections to mean longitudes, the obvious choices for these latter models are those from the Greco-Roman world. In order to investigate if there is any connection between Greek and Indian models, we should therefore focus on the oldest Indian texts that contain fully described, and therefore securely computable, models. We shall see that the mathematical basis of the Indian models is the equant model found in the Almagest, and furthermore, that analysis of the level of development of Indian astronomy contemporary to their planetary schemes strongly suggests, but does not rigorously prove, that the planetary bisected equant model is pre-Ptolemaic. "

The mutli step algorithms of Indian Astronomy never approximated any Greek geometrical model. Ptolemy's Almagest was the first book, according to Western Astronomy. We have now the information that Ptolemy did not invent the equant.

Bhaskara II was an astronomer-mathematician par excellence and his magnum opus, the Siddhanta Siromani (" Crown of Astronomical Treatises") , is a treatise on Astronomy and Mathematics. His book deals with arithemetic, algebra, computation of celestial longitudes of planets and spheres. His work on Kalana ( Calculus ) predates Liebniz and Newton by half a millenium.

The Siddanta Siromani is divided into four parts

1)The Lilavati - ( Arithmetic ) wherein Bhaskara gives proof of c^2 = a^ + b^2. The solutions to cubic, quadratic and quartic indeterminate equations are explained.

2)The Bijaganitha ( Algebra )- Properties of Zero, estimation of Pi, Kuttaka ( indeterminate equations ) , integral solutions etc are explained.

3)The Grahaganitha ( Mathematics of the planets ).

For both Epicycles

The Manda Argument , Mean Longitude of Planet - Aphelion = Manda Anomaly

The Sheegra Argument, Ecliptic Longitude - Long of Sun = Sheegra Anomaly

and the computations from there on are explained in detail.

4)The Gola Adhyaya ( Maths of the spheres )

Bhaskara is known for in the discovery of the principles of Differential Calculus and its application to astronomical problems and computations. While Newton and Liebniz had been credited with Differential Calculus, there is strong evidence to suggest that Bhaskara was the pioneer in some of the principles of differential calculus. He was the first to conceive the differential coefficient and differential calculus.

Khagola, the Celestial Coordinate System

2011-07-19T01:54:00.001-07:00

( Above diagram by courtesy of www.wikipedia.org )

A 360 degree Circle is a coordinate System. And Khagola is the Celestial Coordinate System.

Like the Geographical Coordinate System, the Celestial Coordinate System is another coordinate system, which computes the coordinates of the Khagola, the Celestial Sphere.

The Ascending Sign is called the Ascendant ( Raseenam udayo lagnam ) and is the intersecting point of the Ecliptic ( at the East Point) with the Celestial Horizon. The Descending Sign is the Descendant ( Astha Lagna ) and lies 180 degrees West on the Khshithija, the Celestial Horizon.

Like the Geographical Meridien ( the Prime Meridien ) and the Geographic Equator, the Celestial Coordinate System has a Celestial Meridien ( Nadi Vritta ) and a Celestial Equator.

The Vernal Equinox and the Autumnal Equinox are two intersecting points of the Ecliptic with the Vishu vat Vritta, the Celestial Equator, known as Meshadi and Thuladi.

The Hindu Zero Point of the Ecliptic starts from 0 degrees Beta Arietis, Ashwinyadi, which is the beginning point of the Sidereal Zodiac. This is the Nirayana System, sidereal. The Tropical System, Sayana, also has its adherents in India and starts from Meshadi, 0 degree Aries.

The Galactic Center, the Vishnu Nabhi, lies in Sagittarius. NEP is the North Ecliptic Pole, NGP is the North Galactic Pole and NCP is the North Celestial Pole.

It is raining cats and dogs in Kerala

2011-07-18T17:22:00.001-07:00

On Saturday, the heavens brimmed with pessimistic prophecies and then came the downpour. ( Today is 19th Jul 2011 )

The Sun has disappeared and it is now raining cats and dogs here. As a concomitant result, I got cold !

This SW Monsoon, defined as a failure this season, may perk up, compensating for the lack of rains during the earlier Mrigasira and Aridra Solar Periods ( Njattuvelas ). Now Punarvasu Njattuvela is on, as the Sun transits Beta Geminorum.

Now the paddy fields are full of water and it rained heavily at night day before yesterday. The ocean became hostile on Chavakkad Beach and surrounding areas, wreaking destruction.

The Double Epicyclic Model of India

2011-07-17T20:58:00.001-07:00

This diagram is by courtesy of Jean-Pierre Lacroix and Robert Baywater, www.ancientcartography.net

We have the Double Epicyclic Model - that of Manda Epicycle and Sheegra Epicycles - in Indian Astronomy, which explain the Zodiacal and Solar anomalies. One Epicycle explains the Zodiacal Anomaly and the other the Solar Anomaly.

( Zodiacal Anomaly - That all planets move slower at Aphelion and faster at Perihelion.
Solar Anomaly - The astronomical phenomenon of Retrogression. Backward Motion. When a planet changes its course from perihelion to aphelion, it retrogrades in order to gain the Sun's celestial gravity )

Dennis Duke, of Florida State University, says " We have only to conclude that Ptolemy did not invent the equant. " If Ptolemy did not invent the equant, as Westerners widely believe, then who did ?

"The bisected Indian equant model is pre-Ptolemaic' says he. Other Greek books, prior to Ptoemy, may have influenced Indian Astronomy,says he. Then what are those books, prior to the Almagest, which had influenced the Indian system? The answer is "unknown sources".

Remarks Duke " Indeed, since the very earliest investigation of the Indian models by Western scholars it has been presumed that the models are somehow related to a double epicycle system, with one epicycle accounting for the zodiacal anomaly, and the other accounting for the solar anomaly (retrograde motion) This perception was no doubt reinforced by the tendency of some Indian texts to associate the manda and sighra corrections with an even older Indian tradition of some sort of forceful cords of air tugging at the planet and causing it to move along a concentric deferent . Since our goal in this paper is to investigate the nature of any connection with ancient Greek planetary models, it is only important to accept that the models appear in Indian texts that clearly pre-date any possible Islamic influences, which could, at least in principle, have introduced astronomical elements that Islamic astronomers might have derived from Greek sources. ( "The Equant in India: the Mathematical Basis of Ancient Indian Planetary Models" By Dennis Duke, Florida State University )

Computation of Geocentric Distance, Sheegra Karna

2011-07-17T00:45:00.000-07:00

In the diagram above, the geocentric distance, EQ called X here , the distance of the planet from the Earth is calculated by the equation

X^2 = EQ^2(EP+PL)^2 + QL^2

or = EN^2 + QN^2

In a trignometric correction, called Sheegra Sphashteekarana, this equation is given by Bhaskara.

where

E = Earth
P = Planet in its Orbit
Q = Planet on the Epicycle
QL = Sin
PL = Cos

We have said that Sheegra Kriya reduces the heliocentric postions to the geocentric.

According to this oscillating Epicyclic Model of Bhaskara, EP = R ( Called Thrijya ), PQ is the Sheegra Phala, QL is the Bhujaphala and PL is Kotiphala.

The Hindu algorithms for the computation of mean and true celestial longitudes seems to be totally different from the Western, from the methods adopted by Kepler, Laplace and Co. Hence the Hindu Planetary Model is original and not influenced by Greco Roman sources, as some Western scholars believe.

Calculation of the geocentric longitude of Mercury

2011-07-15T20:39:00.000-07:00

Different equations have been given for superior planets ( Mars, Jupiter and Saturn ) and inferior planets ( Mercury and Venus ) in Astronomia Indica.

In the case of Mercury, an inferior planet in the diagram above, the center of the Sheegra Epicycle is located on the straight line running through the Sun and the observer, on the geographical parallel of the observer.

The above diagram is by courtesy of Jean-Pierre Lacroix and Robert Baywater, www.ancientcartography.net

The Sheegra Phalam, x, in the equation 1/2 Tan ( A -x ), where A is the Elongation or Sheegra Kendra, obtained is deducted from the Sun's longitude, to get the geocentric longitudes of Mercury and Venus.

Indian Astronomy Pre-Ptolemaic

2011-07-15T02:36:00.000-07:00

This diagram is by courtesy of Jean-Pierre Lacroix and Robert Baywater, www.ancientcartography.net

In the above diagram, Saturn, a superior planet, is on the circumference of the Sheegra Epicycle, where it is met by a radius drawn parallel to the direction of the Sun from the observer.

To the Western scholars, Indian Astronomy is mysterious. Let us see what astro scholars have said about IA.

Dennis Duke, of Florida State University suggests that Indian Astronomy predates Greek Astronomy

"The planetary models of ancient Indian mathematical astronomy are described in several texts.1 These texts invariably give algorithms for computing mean and true longitudes of the planets, but are completely devoid of any material that would inform us of the origin of the models. One way to approach the problem is to compare the predictions of the Indian models with the predictions from other models that do have, at least in part, a known historical background. Since the Indian models compute true longitudes by adding corrections to mean longitudes, the obvious choices for these latter models are those from the Greco-Roman world. In order to investigate if there is any connection between Greek and Indian models, we should therefore focus on the oldest Indian texts that contain fully described, and therefore securely computable, models. We shall see that the mathematical basis of the Indian models is the equant model found in the Almagest, and furthermore, that analysis of the level of development of Indian astronomy contemporary to their planetary schemes strongly suggests, but does not rigorously prove, that the planetary bisected equant model is pre-Ptolemaic" says he.

The earliest Indian Planetary Models are two sets from the writer Aryabhata, both dating from 6th Century AD.

1) The Sunrise System , after the Epoch, which is taken from the sunrise of 18th Feb 3102 ( Arya Paksha ). It appears first in Aryabhatiya

2) The Midnight System, after the Epoch, which is taken from the midnight of 17/18 FEB 3102 ( Ardha Ratri Paksha ). It appears first in Latadeva's Soorya Siddhanta

The Local Meridien is taken as Lanka, Longitude 76 degrees, Latitude 0 degrees.

Of Manda and Sheegra Epicycles

2011-07-14T04:29:00.000-07:00

This diagram is by courtesy of Jean-Pierre Lacroix and Robert Baywater, www.ancientcartography.net

In the above diagram, both the theories of Manda Kriya and Sheegra Kriya are given.

In the case of a superior planet, a deferent is drawn from an earth based observer. The Center of the Manda Epicyle rotates around the terrestrial observer, travelling around the deferent.

The peripheral end of one radius of this Manda Epicycle determines the center of another epicyle called the Sheegra Epicycle.

Vyasardha, the Radius of the Circle

2011-07-13T20:50:00.000-07:00

Aryabhata, one of the earliest mathematicians and astronomers, ( circa 476-550 CE ) postulated that Vysasardha, the Radius of the Circle is 3438 minutes and Arc is 5400 minutes.

Circumference = 2 Pi R
R = 360/2 Pi
R = 57.3 degrees
R = 57.3 * 60 = 3438 arcminutes
R = 3438 * 60 = 206265 arcseconds

Half Chord of 90 degrees = 90*60 = 5400 arcminutes.

In his astronomical treatise, the Aryabhatiya, he postulated that the Circumference of the Circle is 360*60 = 21600 minutes. All these formulae are useful for the computation of half chords of certain sets of arcs in a circle and became the base of Hindu Trignometry.

In his Sine Tablest, he called 3 degrees 45 minutes divisions by many Sanskrit names, given below.

मखि भखि फखि धखि णखि ञखि ङखि हस्झ स्ककि किष्ग श्घकि किघ्व |
घ्लकि किग्र हक्य धकि किच स्ग झश ङ्व क्ल प्त फ छ कला-अर्ध-ज्यास् ||

Aryabhata's Sine Table is not a set of values of the trignometric sine functions, but rather is a table of the first differences of the values of trignometric sines expressed in arcminutes. Because of this, this Table is referred to as the Table of Sine Differences.

Hindu Trignometry

2011-07-13T02:08:00.000-07:00

In Hindu Trignometry ( which is derived from Trikonamithi, trikona = triangle and trignon = triangle ), Jya resembles the modern Sine and Koti Jya, the cosine.

But in actuality, Jya is R Sin, that is Radius multiplied by modern sine.

By Jya, Brahmagupta meant 5 degrees of a circle. In Hindu Sine Tables and Tan Tables, the values are given for 5 degrees, 10 degrees, 15 degrees etc so that the Astro Maths students need not bother about using the Indian trignometric and inverse functions. Aryabhata's sine tables are found to be accurate, when compared to modern sine tables.

In other words, one Zodiacal Constellation, which is 30 degrees is made up of 6 jyas and a total of 72 Jyas constitute the Zodiac.

Koti Jya is R Cos, that is Radius multiplied by modern cosine.

Utkram Jya is the reverse sine, defined as 1- cos x. Since the Reverse sine resembled an arrow, Brahmagupta called it Sara. And since the Arcsine resembled a bow, he called it Chapa.

Bhujajya is radius multiplied by modern sine and bhujachapa is the arcsine. Kotijya is radius multiplied by modern cosine and Kotichapa is arccos. Sparshjya is tan and sparshachapa is arctan.

Aryabhata's Sine Table was the first ever constructed sine table in the History of Maths.

This is Aryabhata's Sine Table given for different Kakshyas ( One Kakshya is 3 degrees 45 mins, one eighth of 30 degrees Zodiacal Sign )

Sl. No Angle ( A ) (in degrees, arcminutes) Value in Āryabhaṭa's numerical notation
(in Devanagari) Value in Āryabhaṭa's numerical notation (in ISO 15919 transliteration) Value in Arabic numerals Āryabhaṭa's value of jya (A) Modern value of jya (A)
(3438 × sin (A))

1 03° 45′ मखि makhi 225 225′ 224.8560
2 07° 30′ भखि bhakhi 224 449′ 448.7490
3 11° 15′ फखि phakhi 222 671′ 670.7205
4 15° 00′ धखि dhakhi 219 890′ 889.8199
5 18° 45′ णखि ṇakhi 215 1105′ 1105.1089
6 22° 30′ ञखि ñakhi 210 1315′ 1315.6656
7 26° 15′ ङखि ṅakhi 205 1520′ 1520.5885
8 30° 00′ हस्झ hasjha 199 1719′ 1719.0000
9 33° 45′ स्ककि skaki 191 1910′ 1910.0505
10 37° 30′ किष्ग kiṣga 183 2093′ 2092.9218
11 41° 15′ श्घकि śghaki 174 2267′ 2266.8309
12 45° 00′ किघ्व kighva 164 2431′ 2431.0331
13 48° 45′ घ्लकि ghlaki 154 2585′ 2584.8253
14 52° 30′ किग्र kigra 143 2728′ 2727.5488
15 56° 15′ हक्य hakya 131 2859′ 2858.5925
16 60° 00′ धकि dhaki 119 2978′ 2977.3953
17 63° 45′ किच kica 106 3084′ 3083.4485
18 67° 30′ स्ग sga 93 3177′ 3176.2978
19 71° 15′ झश jhaśa 79 3256′ 3255.5458
20 75° 00′ ङ्व ṅva 65 3321′ 3320.8530
21 78° 45′ क्ल kla 51 3372′ 3371.9398
22 82° 30′ प्त pta 37 3409′ 3408.5874
23 86° 15′ फ pha 22 3431′ 3430.6390
24 90° 00′ छ cha 7 3438′ 3438.0000

Sine Table by courtesy www.wikipedia.org

The Epicyclic Theory of Indian Astronomy

2011-07-11T21:01:00.000-07:00

All planets traverse in ellipses and epicycles and this came to be known as the Epicycles Theory.

In the above diagram, the circle A is the mean orbit of the planet. P is the mean Position of the planet and the small circle P is the epicycle.

The small epicycles traversed by a planet are calculated and the mandaphala, the equation of center is computed and added if the Manda Kendra is in between 180 and 360 and subtracted if the M K is < 180. Manda Kendra is the angle between Position and Aphelion.

From the perspective of the Epicyclic theory & the Hindu astronomers, the radius of the epicycle was given instead of PQ and the circumferences of the epicycles. Both circumferences and radii are given in degrees, minutes and seconds, so that the equation of the center may be computed in deg min and secs. The epicycle in the case of the Equation of Center is given as Manda Nicha Uccha Vritta.

Manda - Manda Phala or Equation of Center
Uccha - Apogee
Nicha - Perigee

Manda Kriya is a Jya Ganitha Kriya, a trignometric reduction of the mean longitudes and distances of the planets to their heliocentric longitudes and distances.

Kranti, the Declination of the Sun

2011-07-09T20:01:00.000-07:00

The declination of the Sun is computed by the formula

Sin J = Sin L Sin w

where J is the Sun's declination of that particular date and time, L is the tropical longitude of the Sun and w, the Sun's maximum declination, which is 23 degrees and 27 minutes.

The Sun's maximum declination will be reached during Karkyadi ( The First Point of Cancer ) and Makaradi ( The First Point of Capricorn ). At Karkyadi, it will be +23 d 23 m and at Makaradi, it will be -23 d 27 minutes.

And at Meshadi ( The First Point of Aries ) and Thuladi ( The First Point of Libra ), the solar declination will be zero. Days and nights will be of equal duration and hence they are called Equinoxes.

Yada Mesha Thulayo varthathe thada ahoratranam samanani bhavanthi

The Eccentric Theory of Indian Astronomy

2011-07-09T02:07:00.001-07:00

We have said in our columns that the Indian astronomers said that the planets revolve around a point different from that of the Earth and Indian Astronomy is heliocentric.

The above diagram depicts the Eccentric Theory and Reduction of the longitude of the planet to the heliocentric coordinate system ( known as Manda Kriya ).

In the above diagram

The angle NAP = Manda Kendra or Mean Anomaly

The Circle A is the mean orbit of the planet
The Circle B is the true orbit

The mean planet moves on the mean orbit, known as the deferent.

When the planet is at N in the mean orbit, he is at M in the eccentric and this is called Mandoccha ( Aphelion ).

When the planet is at R in the mean, he is at S in the eccentric.

M and S correspond to Apogee and Perigee in the case of Manda Phala correction ( otherwise known as the Equation of Center ).

When the planet is at M in the eccentric, the position of the true planet coincides with N, the mean planet and so the Manda Phala correction is Zero.The Equation of Centre at both perigee and apogee becomes zero.

When the Mean Anomaly lies between 0 and 180 degrees, the Equation of Center is negative and this is known in Vedic Astronomy as Meshadi Rinam, Rinam meaning minus. And when it is between 180 and 360, it is additive and it is known in Indian Astronomy as Thuladi Dhanam, dhanam meaning additive.

Anomaly has been defined in Western Astronomy as the angle between position and perihelion. Manda Kendra here is the angle between Position and Aphelion, aphelion being mandoccha. The term manda explains that planets move slower at Aphelion !

Chara, the Ascensional Difference

2011-07-08T00:15:00.001-07:00

In Indian Astronomy, Chara is the Ascensional Difference and is the difference between Right Ascension and Oblique Ascension.

And is calculated by the equation

Sin ( Chara ) = tan ( decl ) tan ( latitude ).

Here Theta is Chara.

Sin C is called Chara Jya

Right Ascension means the longitudes measured along the Celestial Equator, the Vishu vat Vritta.

Oblique Ascension means the longitudes measured along the Ecliptic, the Kranti Vritta.

Chara is used in the computation of Sunrise and Sunset.

The formula for Sunrise = 6 H + Equation of Time - Chara - Refraction Correction

The formula for Sunset = 18 H + Equation of Time + Chara + Refraction Correction.

Sheegra Kriya for superior planets

2011-07-06T01:12:00.001-07:00

In the above diagram,

m is the Sheegra Anomaly
and the angle EJS is the Sheegra Phalam

where E = Earth, S = Sun and J = Jupiter

In order to get the geocentric longitude, the longitude of the Sun is deducted from the Ecliptic longitude and then we get the Sheegra Kendra, the angle between the planet and the Earth Sun plane.

Ecliptic longitude - Long Sun = Sheegra Kendra

Arka Sphutnoniham Kheda Manda Sphutamihodhitham

Sheegra Phalam is the angle EJS ( Earth, Jupiter, Sun ) and this Sheegra Phalam is deducted to get the true, geocentric longitude. ( Added if Sheegra Anomaly > 180 and deducted if Sheegra Anomaly < 180 )

Like Kepler, the Indian astronomers may not have said that all planets move fastest at perihelion but this principle was known to them as they called perihelion Sheegrochha. Sheegra in Sanskrit means fast. Similarly they called Aphelion Mandochcha, manda meaning slow, and it implies that all planets move slowly at Aphelion !

Reduction of Planetary Longitudes to Heliocentric and Geocentric coordinates

2011-07-04T03:40:00.001-07:00

The Vedic astronomers never said like Kepler that planets traverse in elliptical orbits. But then they talked about Eccentric and Epicyclic theories. They said for the luminaries, the Sun and the Moon, reduction to the geocentric (Sheegra Kriya ) coordinate system was not necessary. But for the Tara Grahas, like Mercury, Venus, Jupiter, Mars and Saturn, both the jya samskaras ( trignometric corrections ) are necessary.

The Vedic astronomical texts say that the planets go in an epicycle, whose center moves along the mean circular orbit from west to east. This theory came to be known as the Epicyclic Theory. There is another theory called the Eccentric Theory, which states that a planet goes in a circle whose center is not the Earth, but a different point other than the Earth.

Bhaskara says " The Center of the Celestial Sphere coincides with the center of the Earth. The circle in which a planet goes does not have its center coinciding with the Center of the Earth". Hence the Vedic astronomers like Bhaskara, Brahmagupta and Aryabhata, prescribed bhujaphalam ( otherwise called Equation of Center for mandaphala, whereas in the case of the five Tara Grahas, this bhujaphala, despite connoting Equation of Center or mandaphala, also stands for corrections required to reduce their longitudes from the Heliocentric Coordinate System to the Geocentric Coordinate System ).

The Jupiterian Law or Brihaspathi Neethi

2011-06-18T22:42:00.001-07:00

Suppose your son goes against you. Will you throw him out of the house ?

This is where Jupiterian Law or Brihaspathi Neethi or Jesusian Law comes into operation.

Love is giving and forgiving
Self is getting and forgetting !

Conquer by Love ! This is the message handed out to us by the millenial philosophers, millenial poets and millenial prophets !

Love is a Glory from Eternity's spheres
He is still the Godhead that can make all change

Love should never cease to be upon the Earth
Love is the bright link betwixt Earth and Heaven
Love is the far Transcendent's angel here
Love is man's lien on the Absolute !

Sai and Jesus say " Love your enemies, bless them that curse you and bless them that persecute you" !

Let us be arrayed from head to foot with their commandments. ' Conquer everything with Patience and Love" is their eternal message !

Byron said " Take away Love and the whole world becomes a tomb "

Jupiter is the preceptor of the celestials and represents the divine arts and sciences. The scientia intuitiva or intuive sciences are a great preparation for Eternal Liberation. Without the discriminative intellect or prajna imparted by him, no one can hope for Self Actualisation. He represents the Sreyo Marga ( the way of Being and of Bliss ) and Venus represents the Preyo Marga ( the way of Mammon and the flesh ). Both paths are followed by mankind !

Goethe echoed the same when he averred

Now lead me where some heavenly silence glasses
The purer joys around the Poet throng
Where Love and Friendship divinely fashion
The bonds that bless, the wreaths that crown his passion !

Yoga Sastra, Nyaya Sastra, Neethi Sastra, Vedanta Sastra, Jyothis Sastra and all such sciences are ruled by Jupiter or Brihaspathi. Sasanath Thrayathe ithi Sastram - meaning that Redeeming instructions are called Sastras ( like fatherly advice to a son ). Hence Jupiter or Brihaspathi is the greatest benefic, from the perspective of Self Actualisation. He represents Grace Divine, without which no Self Realisatoin is possible.

Love is a manna sent from Heaven, a spark of the Immortal Fire, sent by the Lord to elevate our low desire ! Let Almighty Love triumph on earth !

From the Center where the Heart of God is known
Let Love stream forth into the hearts of men
Let Love triumph on Earth !

Let us Love All, Serve All, Help Ever, Hate None and Hurt Never, thereby fulfilling the Jupiterian Law !

The Venusian Law ( Shukra Neeti )

2011-06-17T21:21:00.001-07:00

The Mosaic Law of Western Thought is known as Shukra Neethi ( Venusian Law ) in Indian Philosophy. The Jesusian Law corresponds to Brihaspathi Neethi, that is rising to a higher plane which returns good for evil !

Even though it is taught that lying is Sin and should be avoided, Shukra Neethi or the Venusian Law states that one can lie for virtue !

Kaliyil prana rakshakkum
Go brahmana hithathinum
Kanya Vitha rakshakkum
Poli Nindithamalledo !

In business, one cannot be trufhful all the time. There is a saying, Truth is ruinous, hence suppressio veriti, suggestio falsi ! In order to make profits, the biz man is given the licence to lie !

Milton said that Mammon was the first teacher of Man

By him first
Men also

The God and Mammon of Western Thought have their equivalents in

Brihaspathi or Jupiter - the Guru of the celestials and representer of the twelve positive sciences of the Vedas

Shukra or Venus - the Guru of the demons and representer of all modern sciences

Milton's " It is better to reign in Hell than serve in Heaven " is Venusian or Shukra Neeti and is widely followed by politicians, mafia chiefs, the priesthood and the captialists !

In Mythology Indian, Venus or Sage Shukra was born to Bhrighu and Usana. He was born on the day of Freya or Venus, Friday. He was born in the constellation of Swathi. Freya is Venus in Norse Mythology and Freya's day became Friday. Shukravar is Friday and is named after Shukra. Shukra was sent to learn the Vedas from Angiras, who was partial to his son, Brihaspathi. However, Shukra learnt the Vedas from Gauthama. He later performed penance to Lord Shiva and obtained the Sanjeevani Mantra, a mantra which can resurrect the dead.

When Jupiter or Brihaspathi became the Guru of the celestials, Shukra competed and became the Guru of the demons ! He exhorted the demons to win the war against the celestials !

When King Bali was tested by Lord Vishnu in the form of the dwarf Vamana, Shukra immediately knew of the deceipt and warned King Bali. He sat in the spout of a vase, which was spotted by Lord Vishnu. Vishnu picked a straw from the ground and directed it on the spout, with the result Shukra became half blind !

Shukra corresponds to Machiavelli. Machiavelli opined that to be feared is better than to be loved. ( "Love is preserved by the link of obligation which men in their baseness break off at every opportunity for their own advantage, whereas fear preserves you with the dread of punishment which never fails " ). Machiavelli opined that men are base and ugly. ( " This has to be asserted in general for men, that they are cowardly, covetous, ungrateful, fickeminded and false and as long as you succeed, they are yours entirely"). Armed prophets had succeeded, whereas the unarmed had failed !

The Jesus and Machiavelli of Western thought, both dialectial opposites, correspond to Brihaspathi and Shukra of Indian thought !

Shukra in Sanskrit means brightness, clearness, purity. These mythological figures are planets and Vedic Symbolism was used by the Rishies. Astrologically, he represents the mundane arts and the mundane sciences, whereas Jupiter or Brihaspati represents the divine sciences and the divine arts.

The Periods of the Sun !

2011-06-15T20:48:00.001-07:00

The Malayalam Agri Calender has it that the Sun transits the 27 constellations of the Ecliptic and these came to be known as the Njattuvelas. The word Njattuvela is derived from Njayar meaning the Sun and Velas meaning the Times. In short Njattuvela means the Times of the Sun, as it passes through the 27 constellations of the Sidereal Zodiac.

Now the Sun is transiting Mrigasira or Makiryam Njattuvela is on. It is raining incessantly in Kerala. Makiryam mathi ariyathe peyyum meaning that rains will be galore during Mrigasira Njattuvela. On June 22nd, the famous Thiruvathira Njattuvela will be on and Kerala will be graced by bursts of rain with sunny interludes.

Monsoon Tourism is on the upswing in the state. People from Arab lands and tropical countries find Kerala a haven. Westerners find it as a gorgeous Paradise, because of the immense greenery which adorn the state.

More rains are expected during the solar transits of Punarvasu and Pushya. These four Njattuvelas are fierce and destructive. Many have lost their homes in the villages, many paddy fields have been inundated, as the Rains of Life and Death simultaneously bring relief from the blistering heat and at the same time wreack havoc on the poor infrastructure of the state.

Medical Astrology Verses

2011-05-25T03:46:00.001-07:00

With great body and looks
The Sun rules Bile
Luna rules Wind and Phlegm
And is equal eyed

Madhu pingala drik
Chathurasra Thanu
Pitha prakriti savithatpakacha
Thanu vritta thanu bahu vata kapha
Prajnascha sasi sama dukh sama bhak

With looks cruel and with body young
With hair long, Mars rules Bile
Mercury is humourous
And represents the humors three !

Kroora drik tharuna moorthir udara
Paithika su chapala krisa madhya
Slishta vak sathatha hasaruchi jna
Pitha marutha kapha prakritischa

With massive body and great looks
With intellect noble, Jove rules Phlegm
Venus is hedonist and with lovely body
And rules Phlegm and Bile.

Brihat Thanu pingala moordhajekshana
Brihaspathi Sreshta mathi kaphatmaka
Bhrigu sukhee kanti vapu sulochana
Kapha nilatma sitha varka moorkaja

Lazy is Saturn and with hairs long
He represents humours Bile & Wind
The Seven Revolving Heavens
Represent the Tissue Elements Seven
Tendons are signified by Saturn
Bones by Sol
Blood is ruled by Luna
Skin is Mercury's portfolio
Fat by high Jove
Semen is the poet Venus
And Mars, Bone Marrow !

Mandalasa kapila drik krisa deergha gatra
Sthooladwija parushaloma kachanilatma
Snay vasthi sruk thvak aja sukla vase cha majja
Manda arka chandra budha sukra suredya bhauma

India's Transfiguring Hour !

2011-04-05T07:50:00.001-07:00

As we said in our columns before, 1030 PM on 02042011, proved to be India's
transfiguring hour !

Some idol worshipping Indians have not acknowledged the role played by
Gambhir. He came in when Sehwag was out second ball and when he got out, the
score was 223/4 and the dew had set in !

"The 97 in the World Cup final was not the best innings in my career but no
doubt the most important one so far," the 29 year old Gambhir told reporters
after reaching Delhi

"It was a special knock for me as it came in a special situation. The whole
country was expecting us to win the World Cup and I have contributed my bit
in India's triumph. So, it was the most important innings of my career."

His Delhi team mate Kohli supported him in a vital 83 run stand for the
third wicket.

"Obviously, a century in the final would have been the icing on the cake.
But winning was more important for the country. If you had hit a century but
your team lost there was no point," said the dashing left hander.

Normally he opens, but when he came in at No 3, India were 0/1, and his
experience as an opener served him well, particularly against the fast
slinging deliveries of Slinga Malinga !

"On the other hand, if you missed a century but helped your team win the
World Cup, that I will take."

One billion people were worried that the Little Master may score a century
and India may lose. One billion minds were worried that Indian batting may
collapse. But when Gambhir and Dhoni took over the responsibility of
steering India to victory, gone were the worries from the minds of the one
billion. One billion felt like World Champions from then on.

Jup Sun MarMer Moo Ket
Ven RASI LA

Rah
Sat

The map of the Heavens at 0230 PM, 02042011, Mumbai.

LA means Lunar Ascendant ( Here Cancer Moon )

On April 1, Moon was the only planet adverse for India. On Apr 2, Moon moved
over to India's House of Fortune and all planets became beneficial.

It was as if the heavens stood ranged to say
"Be Thou The World Champions" !

Saturn in the benign Thirld represented the Crown

Jupiter, Mercury, Moon, Sun, Mars in the Ninth represented Divine Grace

Venus in the Eighth represented Wealth

And the Nodes in the 6/12 represented Conquest

Jupiter in the 9th gives India victory !

2011-03-30T17:53:00.001-07:00

Providence ( Jupiter in the House of Fortune ) saved India yet again. Master Batsman Sachin Tendulkar got Man of the Match Award for his blistering 85, but then he had as many as six lives.

Four Paki fielders let him off, Misbah, Y Khan, Afridi and Akmal. He survived two close calls for lbw and stumping. Today was his day.

Let us see the astrological factors.

Yesterday was Dhanishta, his kshema tara or 4th star or Lucky Star. But Dhanishta, which ruled for 57 Nadis ( 23.5 hours ) or right throughout the day was not so good for India or Dhoni. For Dhoni, it was his vipat tara, or adverse star. Hence the nervousness of the Indian spectators and viewers !

For Sehwag, this was his sampat tara or favourable star. Even though he scored only 38, he hit the premier Pak bowler, Umar Gul, for five fours in one over. He hit Gul off his length !

When we analysed, we knew that some factors were adverse and we did remedial measures to overcome those adverse factors. We knew that the Transit positions of Jove and Saturn are benign and so ultimately India will triumph. ( As for me, I fasted in the afternoon, as I badly needed an Indian triumph. I indulged in prayers and meditation right throughout the day and relief came from tension at 1000 PM ).

For Pak, the transits of Jupiter and Saturn are not so benign. Jupiter in the Tenth is Dasame Darika Vadham or adverse for their Ego. Saturn in the 4th is also disconcerting and affected their batting performance in this WC. Not even one Paki batsman had scored a century and they were reckoned formidable because of their excellent bowling !

On 25th, Mars moved over to Pisces, ending some bad luck for India. After then Indian bowling became efficient and fielding improved. Indian fans were afraid that bowlers and fielders might put Sachin & Co down ! But in the QF and SF, Indian bowling and fielding rose to the occasion. The mighty Australians were restricted to 260 in QF and in SF, Pak were bowled out for 231 !

On 30th, yesterday when India won, the Birth Number is 3, represented by Jupiter. Hence it is safe to assume that it was the No 3 in Numerology, or Jupiter in Astrology favourable, which gave India victory. It was also a diplomatic victory, as the Indian and Pak PMs shared lunch together and we hope many bilateral issues will be resolved !

Panic not as Super Moon will not harm Earth !

2011-03-18T23:06:00.001-07:00

Now that Super Moon has already harmed ( the tsunami ), it will not harm
furthur !

Here we give the dates of the Super Moon from 1950 to 2050

November 10, 1954
November 20, 1972
January 8, 1974
February 26, 1975
December 2nd, 1990
January 19, 1992
March 8, 1993
January 10, 2005
December 12, 2008
January 30, 2010
March 19, 2011
November 14, 2016
January 2nd, 2018
January 21st, 2023
November 25, 2034
January 13, 2036

To make one revolution of the earth, the moon takes 27.3 days . Since, as the earth has motion and has moved in the heavens, it takes further two days to catch up with the earth. ( Full moon-new moon lunar cycle takes 29.5 days.

The moon's orbit around the Earth is elliptical, and its orbit is inclined at 5.14 deg to the elliptic (earth's path around the sun) with a substantial eccentricity of 5.49 percent (earth's is 1.67 per cent). The Moon at Super Full Moon will be at 217 K kms and at Apogee it is more than 300 K. A difference of more than 100 K kms. The Moon will be Full when it is near Perigee and will appear brighter. Yesterday Moon was a great sight in the heavens.

Jupiter in Pisces will see to that the Earth is not harmed. The Sun Moon
Opposition takes place in Pisces/Virgo and Jupiter is there, posited in
Pisces. Hence we dont see any devastation happening on the 19th in US and
20th in India !

Anyway the Gayathri mantra should be recited for the welfare of humanity !

Jove will save Earth !

2011-03-18T00:33:00.001-07:00

Should one worry about the Super Moon? NO!

The Super Full Moon occurs when Sun is in Pisces and Moon comes diametrically opposite at ( 180 degree from the Sun's longitude ) Virgo. This is the Full Moon, the Pournami of Indian Astronomy.

Now Jupiter in Pisces is the Redeeming Grace. Jupiter, the indicator of Divine Grace will save this planet from catastrophes.

Some devastation has already taken place, as the Tsunami hit Japan on the 11th. Still Japan is in a mess. Burning nuclear rectors , earthquakes and tsunamis ravaged Japan and Japan looks like a devastated area.

Jupiter is the divine planet, the wisdom planet and He will not allow this planet to be destroyed !

It will not be the end of the world, as some Doomsday theorists make out. Vedic Astrology does not support Doomsday theories. The sum total Energy in the Universe is a constant and cannot be destroyed ! So no end of the world !

One need not bother unnecessarily about this phenomenon. There were Doomsday theories that the world was going to end in 2000 ! ( There was one grand father of Pongo Twistleton in Wodehouse, who gave all his shirts and pants to a passerby, saying that the end of the world was coming at 1030 AM sharp ! ).

The Sun Moon Opposition !

2011-03-16T20:36:00.001-07:00

The Sun Moon Opposition is called Pournami in Sanskrit, when the Moon is 180 degrees away from the Sun.

The Sun Moon Conjunction is called Amavasya in Sanskrit, when the Moon is conjunt 0 degrees with the Sun.

The Super Moon is a Full Moon. The Super Moon is a term coined by the astrologer Richard Nolle.

Yesterday, there was an earthquake in Japan, measuring about 6 on the Richter scale. Japan is devastated by explosions in nuclear reactors, earthquakes and tsunamis or harbour waves !

In 2005, Tsunami struck fifteen days before the Super Moon date. This time almost one week before.

One has to be wary of this week.

Super Moon devastates !

2011-03-16T02:28:00.001-07:00

Those who decry Astrology should see the post on Super Moon which we posted on 10th. The Tsunami ( japanese for harbour wave ) struck on 11th, causing widespread destruction.

The Super Moon is a Full Moon. Full Moon means that the Moon is away from the Sun in Opposition and New Moon means the Moon is near the Sun in conjunction.

This phenomenon is known to astro savants and to the Indian mind, Astronomy, Astrology and Mathematics are epistemically correlated.

Some people, due to the influence of Anti Paganism, decry Astrology. This is because during early childhood, they have been taught by the ignorant priesthood that Astrology is hog wash !

The priesthood, sunk in Nescience, believes in the phenomenon of water turning into wine and such irrational miracles. They believe in the Immaculate Conception, which is not physiologically possible ! Another dogma is the Resurrection, which is not scientifically possible.

Tsunami caused by Super Moon ?

2011-03-11T19:37:00.001-08:00

JupMerSun		Ket
Mar	RASI
Ven	RASI	Moo
Rah		Sat

The Lunar Perigee ( when the Moon is closest to earth ) is called Supermoon and is believed to cause earthquakes and natural disasters.

That Moon causes tides is well known and Supermoon may affect tides.

On Mar 19, the Moon will be 221,567 miles from earth, the nearest point in 20 years.

There were Superomoons in 55,74,92 and 2005 and these years were characterised by extreme weather conditions.

Weatherman John Kettley said about the phenomenon on Mar 19th."A moon can't cause a geological event like an earthquake, but it will cause a difference to the tide. If that combines with certain weather conditions, then that could cause a few problems for coastal areas."

Astrologically, Sun will be at 334 degrees and Moon at 143 degrees.

As a remedial measure, the mantra of the Moon Om Saum Somaya Namah can be chanted. Also the Gayatri mantra, as natural calamities affect the psyche of universal humanity !

Om Bhoo Bhuvah Swah
That savithur varenyam
Bhargo Devasya Dheemahi
Dhiyo yo no prachodayath

Some astronomers, who decry Astrology, says there wont be much problem during this phenomenon of Extreme Super Moon.

We are giving the Anti Thesis ( to the Astrological Theory of Lunar Perigee) here, the opinion of Pete Wheeler of the International Centre for Radio Astronomy.

Wheeler stated, "(The Earth will experience) just a lower than usual low tide and a higher than usual high tide around the time of the event, but nothing to get excited about."

"Remember in the past, planetary alignments were going to pull the sun apart. It didn't. Astrologers draw a very long bow most times. Normal king tides are about all I would expect out of this Super Moon prediction," he added.

The Web world is in fact, influenced by the Super Moon phenomenon and this is very much evident in Google trends, a public facility of Google Inc, based on Google Search, that shows how often a particular search-term is entered relative to the total search-volume across various regions of the world, and in various languages.

Within a few day, the Earth could be headed for a big showdown. Some experts also claimed that huge storms, earthquakes, volcanoes and other natural disasters will occur on Saturday, Mar 19. On the very day, the moon will swing around Earth more closely than it has in the past 18 years.

Extreme Super Moon is the term coined by those who are well versed in the Art of the Nine Revolving Heavens ( Astrology ).

Sensex rises due to favourable Saturn & Jove !

2011-03-01T21:45:00.000-08:00

The Sensex rose, when the FM announced that FII investment is welcome in Mutual Funds. This will pave the way for billions coming in to the mutual funds sector.

The Sensex rose 623 points yesterday, an inordinate rise. Experts feel that more dollars will find its way into the Indian stock market.

The Budget was said to be populist, but it will not hurt Industry. It comforts the middle class man ( IT limit increased to 1.8 lk ) and Industry.

On the whole, an industry friendly budget and the initial euphoria has led to the inordinate rise of the Sensex !

The FM has done a balancing act, he has to please both Industry and the Common Man.

Ridham Desai, the MD, Morgan Stanley India, said that the move to allow global investors in mutual funds is very positive. Another positive factor is the infra spending of 27% more. He expects a positive impact of 50-60 bps on earnings. He expects the markets, Sensex and Nifty, to perk up by a furthur 20%.

"I think the budget was okay, there was nothing bad in the budget. I guess market expectations were a little bit on the lower side. So, I think there is a sigh of relief that there is nothing untoward in the budget.

I think he has done a decent balancing act. There were a lot of constituencies to serve. I think there is a bit of skepticism on the numbers, maybe the revenue side is a tad aggressive and on the subsidy side, he has been maybe a little bit too aggressive on the downside. So, maybe eventually he is going to have a tough fight on his hand to meet these numbers.

But apart from that, I think there were a few positive takeaways, which the market I don’t think has immediately paid attention to, I don’t see a lot of investors have paid attention to it. This whole thing about the Nandan Nilekani Committee is a very positive signal. The move to allow foreign individuals to invest in domestic mutual funds is positive.

I think there is a fair bit of infrastructure. If we look at the split of expenditure, he is budgeting for a 27% increase in infrastructure spending. Now, in a budget where overall spending is rising 3.5%, that is a huge skew towards a particular sector in terms of spending. Ofcourse the skeptics will come back and say but he didn’t do it last year, he had spending increased last year and he underdelivered. But the fact is that he has chosen to discriminate all his spending basket. He has picked out infrastructure for his spending, which I think is the key area where we need the spending.

So, he is doing the right things. Now, it is all down to execution. It is easy to stand up now and say, “They will not execute and be skeptical about it.” I think the other way of looking at it, which is my way of looking at it, is we will see we will wait and watch and give them the benefit of doubt right now and come back late to check whether the executions have happened or not. So, I am reasonably okay with the budget. I think it is pretty okay for the market."

"The market interest rates, to me, at various levels look like we are almost done. The only caveat here is what happens to oil. In 2008, when oil went up, we responded with the very sharp increase in rates. If oil does go up to USD 130-140 per barrel then that may have some implication on short-term rates. Otherwise, I think deposit rates we are mostly done, lending rates may go up a little bit. The RBI definitely needs to move a little bit maybe another 75-100 bps over the next nine-twelve months, but not a lot left on short rates. I think we are dealing with almost peak rates across various market interest rates."

We had said in our columns that India is running a good time, astrologically. Jupiter in the 9th and Saturn in the 3rd are both favourable. Period wise, India is running Sun Dasa/ Rahu Bhukthi. The ICTT Terminal at Vallarpadam became operational during this phase. Vibrant Gujarat mopped up 450 billion during this time. The Sensex is going up, thanks to the govt allowing global investors to invest in the mutual funds sector. Bullish news will come in during favourable times and during unfavourable times, bearish news ! The markets normally go down after budgets. But this time, due to the pragmatism of the FM, it is otherwise !

Jove in the 9th heralds good news !

2011-02-26T02:10:00.001-08:00

FDI in Retail has been advocated by the Economic Survey of 2011. There can be private participation in the social sector.

It is good that the farm sector has clocked in 5.4% growth. Forex reserves at $297 billion. The foodgrain production has gone up to 232 million tonnes.

With the financial planet, Jupiter, in the favourable House of Fortune, this good news has come in.

As food prices rise, there is an imperative need for immense investment in the agri sector. It is due to the good performance of the agri sector that the economy has clocked in 8.6% growth.

The survey calls for a second green revolution. As the world is undergoing a Food Crisis, the solution is to upgrade agriculture so that India becomes the granary of the world.

As far as the stock market is concerned, every correction is good.

Mars and Cricket Astrology

2011-02-23T20:18:00.001-08:00

In Cricket Astrology, Mars is the planet of Cricket and the 3,6,7 and 11 houses are very important.

The Third House signifies ability, courage, hands, energy, fitness, mental strength, intelligence. The Sixth House represents enemies, victory, action and competition. The Seventh House represents the opponent. The Eleventh House represents fame, gain, fulfillment of desire, ambitions, profits, wishes and desires.

Sagittarius represents ground playing games and the Signs which trine Sag like Leo and Aries also become significant. Aries is the natural Ascendant of the Cosmic Man or Kalapurusha and Leo, the sign of sports and games.

Mars represents the organising ability, administration, competition, determination and energy ( sathvam kujo ) . Mars is the most important planet in Cricket Astrology and you will find powerful Mars in the horoscopes of Cricketers. The power of 3,6,7 and 11 Houses also denote cricketing success.

Mars is in the 7th House in Aries, forming Ruchaka Maha Yoga, in the horoscope of Kapil Dev.

Mars is exalted in the horoscopes of Wadekar, Gavaskar and Tendulkar.

Mars is powerfully posited in Scorpio in the horoscope of the Wall ( Dravid ).

In Ganguly's horoscope, Mars aspects the 6th and 7th Houses.

Mars tenants the Ascendant in Srinath's horoscope.

Mars is powerfully posited in the 3rd in Sehwag's horoscope.

Mars aspects the 5th House, in Yuvraj's horoscope.

Mars is powerfully posited in own sign, in C K Nayudu's horoscope.

Mars is placed in the 5th, in Leo, in Bradman's horoscope.

Aquarius Rains !

2011-02-22T19:41:00.001-08:00

Yesterday it rained heavily for more than two hours. Started from 0600PM and lasted till 0830 PM.

There is a saying in Malayalam " Kumbha mazhayil kathirum pookam " - that anything will sprout during the summer rains in the sidereal months of Aquarius.

Temperature may rise to more than 40 degrees win the sidereal months of Aquarius ( Kumbha ) and Pisces ( Meena ).

Kerala receives more than 400 mm rains during the summer. This comes as a big relief from the blistering heat. And when Kala Varsha ( South East Monsoon ) comes, people welcome it as a merciful release, even though it can wreak havoc on the "rural infrastructure" !

Jupiter in the Ninth augurs well for Indian Cricket

2011-02-01T22:25:00.001-08:00

JUP		KET

MARMER SUN
VEN RAH	MOO	SAT

Till May 6, Jupiter will be in Pisces, in the 9th. The World Cup, therefore, will take place when Jupiter transits the 9th. Saturn will be in the favourable third. The only negative factor is that Mars will be moving over to the 8th, on 20th March. So things are looking good for India ! There may be slices of bad luck after 20th March.

Jupiter was in the Fifth, a favourable house, in Scorpio when India won the 1983 World Cup.

Imran Khan, the former Pak skipper, was on TV yesterday contradicting Petersen's view that the WC longish schedule is negative.

On the other hand, it is positive, he feels. The greatest threat a team can face is injuries. He cited the example of the Pak defeat in the 1987 final, when their 3 major players were injured.

Now India is also smarting from injuries. Praveen Kumar is flying to England for treatment and Sreeshant may be roped in. Asked about Sreeshanth, Imran said that Sreeshant is not a bad replacement. His oustwingers are excellent.

About the Pak skipper problem, Imran said that Misbah does not have adequate experience. The World Cup will be fiercely competitive, and Misbah simply do not have the experience to handle tough situations, which may arise. Misbah did play well yesterday, scoring 93 no and winning the match for Pakistan.

Imran said India are favourites and Sri Lanka are second favourites. But he warned that Pakistan can be the dark horse. Pak may enter the semis, upsetting the theory that Sri Lanka or SA, Australia, England and India may reach the semis.

Dhoni said he will convert pressure into responsibility.

There is a theory that India in 1983 had nothing to lose, as they were written off as underdogs, and hence they performed well, as they played without pressure. They were not a star studded side, like the present one, and was a team of bits and pieces players. Bits and players players are players capable of taking one or two wickets, and can score 30/40 runs. Not people who score 200 not out !

The present Indian team is star studded, with a lot of watchwinners. Sachin is the top scorer in ODIs with 200 no against SA, we have Yuvraj who created a record in the T20s by hitting six sixes in an over ( overtaking Sobers' and Shastri's performances, which was only in county cricket ), an explosive batsman in Sehwag and a blitzkreig batsman in Y Pathan. More experienced is this team than the 1983 squad. The only enemy India will face is pressure. As Trevor Bailey used to say " It is the situation". It is pressure which will be the no 1 enemy. Look at Pathan's last innings. When India were 113/8, the game was almost over. And Yathan played without any pressure. When he scored a hundred with 8 sixes and 8 fours, then pressure crept in. There was a chance for India to win and then when pressure came, he got out, giving the match on a platter to the South Africans !

It is easy for Dhoni to say he will change pressure into responsibility. If Indian players do not perform well, they would have let the 1 billion Indians down. They are playing before a 100,000 crowd, watched avidly by miliions of cricket crazy Indians. There is tremendous pressure on all teams, but more on India. When everybody thinks that India is favourite, pressure becomes enormous. But then, India are on their home ground and home ground advantage can be benign !

India's strength lies in her spinning allrounders. Yuvraj, Pathan, Sehwag, Sachin, Raina all can bowl and they are fairly well experienced. Another factor in their favour is the position of the heavens. Jupiter in Pisces is in the 3rd in India's national horoscope. Saturn in the 3rd is a redeemer !

India is currently placed 2nd in ODIs, ICC Rankings. Retaining that spot brings in another pressure situation ! Complacency should be avoided at all costs and anything can happen in one day cricket. Most of the teams are more or less equal. Australia, England, South Africa and Sri Lanka can stage upsets at any time. They have better fast bowlers than India !. ( Allan Border is of the view that Aussies with three genuine fast bowlers will lift the Cup )

It is to be noted that this will be Sachin's last World Cup. He has created all records except one. He is not like, like Kapil Dev, a member of the WC victors ! What greater gift can be there than consecrating the WC to Sachin Tendulkar ?

Stock Market Astrology

2011-01-30T20:26:00.001-08:00

The stock investors have lost 11 lk crores in the last two months and the Sensex has lost more than 2600 points !.

Looking like a bubble which bursts every now and then, the Indian stock market, like all stock markets, is highly risky.

It rose from 3000 to 21000, then fell back to 7000 and then rose again to 21 K. It is now hovering around the 18 K mark and has lost 2600 points since Diwali.

Runaway inflation and high food inflation, lack of infrastructure, less agri produce due to climate change, lack of human resources - all these plague the Indian economy.

Political instability due to India Shaming ( widespread corruption ) has added fuel to the fire.

If Technical Analysis states that all scrips display regular and recurrent patterns of behaviour ( also the Sensex and the Nifty ), then we can say that the coming days are tough for the Indian market. Even though GDP may quadruple and the Sensex may go beyond the 50 K mark in ten years time, now we cannot see a surge in the Sensex or the Nifty for the time being.

Ms Gita Gopinath, Professor of Economics at Harvard and hailed as the successor to the Nobel Laureate Amartya Sen, feels that India has to improve infrastructure and human resources to overcome the negative traits in the Indian economy.

Food inflation ( 18%) has been brought about by Asian affluence, rising incomes and great demand and less supply. Consumerism is the main causative factor. Agri produce do not go up due to Climate Change. Lack of infra is another factor.

We have to do agriculture on lands which lie barren now, increase productivity and yield and improve vital infrastructure like road, rail and inland waterways.

The Decoupling Theory is true. Only the BRIC nations have not been much affected by the global meltdown ( Brazil, Russia, India, China ). India still could grow at 9%.
Neither the European nations nor the US have escaped from recession. Unemployment also rose in these countries. India and other BRIC nations have not been so affected, mainly because of the governmental controls and a strong domestic market. Controls are less in the developed economies. There is some control on Banks, but not on other financial institutions and they are suffering as a result. Now the US is thinking of brining in controls to save the ailing economy.

The dollar is falling now. So is the Euro. Until the dollar stabilises, gold will continue to rise. This is because China is investing in gold, because of their high dollar reserves.

In the future, the Indian presence will be felt in the economic field. BRICs will rise in the next ten years. India has the maximum working people in the age group 25-55 years. If India improves infrastructure and human resources, she may well become the third economic power in the world, by 2020 !

Astrologically, even though Jupiter in the 9th augurs well for India, she is running the period of the Sun, who is posited in the 3rd.So let India be on guard !

Anizham Njattuvela wreaks havoc !

2010-11-22T02:15:00.001-08:00

Meteorology may say it is a depression in the Bay of Bengal called La Nina which is responsible for the rains, but to those well versed in Astro Meteorology, it is the Sun's transit of Scorpio and the constellation of Delta Scorpi, which is the cause, as heavy rains lashed Trichur. From 0500 PM it was raining till 1100 PM, when I went to sleep.

According to Meteorology, La Nina is a coupled ocean-atmosphere phenomenon of El Nino, as a part of the El Nino Southern Oscillation Climate pattern. La Nina is defined as the dialectial opposite of El Nina !

These depressions happen only during the Monsoon season, when the Sun transits the constellations from Eta Tauri to Alpha Scorpi ! So Astro Meteorology is right !

Why do these depression not happen during the summer season?

Climate Change, triggered by Global Warming, is creating havoc throughout the world. Sea levels rose by 1.8 mms from 1961 to 2003. All snowy mountains are melting. Co2 levels are increasing. Forest fires increased. When hot air creates lightning, forest fires are more. More cyclones and thunderstorms. Extreme climatic patterns are produced. More floods and more draughts than usual.

Jupiter blocks progress !

2010-10-22T21:52:00.001-07:00

The banking sector has recorded good corporate performance. While the State Bank of Mysore post a growth in net of 13%, Indian Bank recorded 11.8% net rise and Vijaya Bank 33% !

Biocon, the blue chip BT co, recorded 20% growth in Q2. Wipro, the IT major, recorded a 10% rise in net profit !

There are some negative factors, like FDI falling, slipping down to 1.33 billion USD in August, from 3.28 b ! Overall, there is a slump in FDI.

Jupiter, the financial planet, moves over to the adverse 8th for India and this indicates some financial stringency. This is only a temporarary phase, as Indian stock market will go upto 50 K Sensex, within a decade. Let us not be bothered by temporary setbacks. Ultimately the victory will be India's !

Indians have mastered web designing skills, programming skills and English language skills, with the result India is the largest English speaking nation in the world. More engineering and medical graduates are produced nowadays and India will be the third largest economy in the world in 2020, after China and the US !

Housing units shortage is estimated at 20 to 70 million units and this is a huge opportunity for Housing Finance. Residential space price is rising in all urban and rural ares. Also commercial space, as India industrialises !

Now the stock market has fallen as expected, after companies mopped up 4800 crores as IPOs. From a long term perpective, this is only a temporary lull !

Sidereal Libra means rains !

2010-10-18T01:13:00.001-07:00

The Sun entered the first degree of Sidereal Libra, thus heralding the North East Monsoon or Thula Varsham, as per Astro Meteorology.

This is the Retreating Monsoon. Coming as a depression from the Bay of Bengal, it takes the moisture laden winds and then sweep down on the Himalayas and Indo Gangetic plains, and then pours over peninsular India ! Mainly caused by the heat generated by the overhead Sun on the Tropic of Capricorn. The places of the Indian Ocean becomes hot and the northern parts of India become cool. Cool winds from the Bay of Bengal cause this and the result is Thula Varsham !

Expected to rain till the end of the sidereal month of Vrischika or Scorpio, NEM is a boon to states like Tamil Nadu. Kerala gets both SWM and NEM !

A must book for creating Astrology Software

2010-10-06T21:09:00.001-07:00

No study of Astronomy is complete without Kepler ! Did he not bequeth the Laws of Planetary Motion to the world ?

Astronomy is nothing but Mathematical Astrology and Kepler gave the world the three laws of Motion.

1) The planets move in elliptical orbits.

20 Planets move fastest at perihelion ( nearest point to Helios, the Sun ) and slowest at Aphelion ( the farthest point from the Sun ).

3)The squares of their sidereal periods ( orbital periods ) is equal to the cubes of their semi major axes.

The base of Western Astronomy is Kepler. First we study Kepler and then we study Laplace !

Previousy astronomers ( Hipparchus, Ptolemy, Brahe, Copernicus ) have used many geomertical models to give a mathematical account of the movement of the luminaries. Astronomy is a branch of Physics, declared Kepler. In this great book, Kepler's Physical Astronomy, Bruce Stephenson demonstrates the importance of Kepler's physical principles of planetary motion. A must book for students of Astronomy and Mathematical Astrology. Also for the creation of Astronomy and Astrology softwares. In any type of Astro software, let it be Indian, Western or Chinese Astrology, or Yahoo Astrology, this book contains great info which is good for the developer.

Great Njattuvelas trigger rise in Sensex !

2010-10-03T20:40:00.000-07:00

Atham Njattuvela is good and it is raining well in Kerala. Other parts of India also received excellent rains.

Good monsoon means that the agriculturist's income will be up. They will be investing in farm equipments, which is good for such equipment manufacturing companies. As India is an agrarian economy, a good monsoon ensures good industrial growth. The GDP growth is expected to be 8.5%.

Jupiter in Pisces is favourable for India and the Sensex moved to 20.4 K on reports of good monsoon, an expected 8.5 GDP growth and surging car sales. The Index of Industrial Production has gone up. The market capitalisation has gone upto 71,22514 crores. This is a great Value Addition as far as investors are concerned. But then the small investors have booked profits and hence they could not exploit the current bull surge.

$19 b was invested by the FIIs so far in 2010 and the cash flow has triggered the surge in both Sensex and Nifty. In Sep end they invested 43107 crores. Simultaneoulsy the Indian Financial Institutions have sold their holdings, in order to book profits. We hope that furthur momentum will be maintained. Most brokers feel that the Sensex will create new record this Deepavali, the Festival of Lights. They maintain that the record 21.4 K level of the Sensex ( on Jan 10, 2008 ) will be surpassed within one month. Adverse factors like Global Recession and rising crude prices may halt the slide. On 10, Jan 2008, the market capitalisation crossed 72 lakh crores and this wil be surpassed easily.

On Friday, Nifty closed at 6143 and the Sensex 20,445 ! SBI and Infy crossed 3000 INR. L&T crossed 2000 !.

IIP will will the highest in these 18 months. This is another bullish factor. The good monsoon comes as a boon to consumer companies.

Not only is this phase good for the secondary market, the primary market is also rising. 4000 crores were mopped up within 2 weeks.

Machiavellis say that companies will collect about 4800 crores as IPOs and the market has been manipulated. Once the IPOs are over, the market may react sharply. More info at Stock Market Astrology

Jupiter will be moving over to Aquarius and this does not augur well for India. He will be in the 8th in India's national horoscope from Nov 1 onwards. So be careful !

Humanistic Astrology

2010-09-29T20:40:00.001-07:00

Did you know that the 360 degrees of the Zodiac has 360 different symbols? These Sabian symbols (a set of astrological notations representing each degree of the zodiac ) can be used for divination. Discusses origins of the symbols. Learn from the great Dane Rudhyar, a Titan in the field of Astrology.

Rudhyar integrated Jungian Psychology with Astrology and called it Harmonic Astrology. He postulated that the stars do not cause the effects ( like Dante who said planets impel and they do not compel ) and that but were pictures synchronistically aligned to human beings. Detailing psychological forces working in individuals. He did not override human freedom in responding to these forces. His magnum opus "The Astrology of Personality" was published in Lucis Publishing.

Astro Software Books

2010-09-26T04:43:00.000-07:00

If you want to calculate the longitudes of planets and create an Astro Software, then the best book for you is Laplace's CelestialMechanics. You can find out the mean longitudes of the planets, calculate the perturbations, the epicycles and then calculate the Heliocentric Longitudes of planets. You can use Laplacian equations to then reduce it to the Ecliptic Coordinates and then reduce them to Geocentric Coordinates, thus computing the true longitudes of the planets. A must for Astro software developers.

Kepler's Formulae

Kepler represents Old Astronomy. If you want to creat an Astro Software, you have to solve the Kepler problem. The Kepler Equation, M = E - e Sin E, may sound easy, but it is a transcendental equation and the most difficult amongst Kepler's equations. We can find out the True Anomaly of the planet, that is the angle between the planet and perihelion. The next step is to find the Argument of Perihelion, which is the angle between the Node and perihelion.

Laplace - Advanced Astronomy

Laplace's Celestial Mechanics is one of the best books ever written. If you read this magnificent book, you can handle Astronomy and Maths easily.

A good book to possess !

2010-09-20T20:49:00.001-07:00

Vedic Astrology, a guide to the fundamentals of Jyothish, is a great book by Ronnie Dreyer, for those hungering for the knowledge of Jyothish. Ronnie Dreyer has made the tough subject light by explaining in simple terms the mighty science of Astrology. Dreyer is well versed in Western Astrology, despite having profound knowledge of Jyothish. She can fathom the complexities, the pitfalls and the perplexities that veteran Western astrologer encounter while they deal with Jyothish. Throughout the book, there are warnings and hints that guide astrologers in the proper path, saving them from the interpretative calamities experienced by many astro savants.

Vedic Astrology is explained in simple terms to the student, without much technical jargon. Vedic Astrology is similar to Western Astrology and differs only by 23.5 degrees, which is the difference between the Zodiacs now.

Foreword is by James Braha, another veteran Vedic Astrologer.

This book is a must for the novitiate, as it contains immense information to the students of Evolutionary Astrology.

Lunar Mansions !

2010-09-19T06:28:00.001-07:00

Astrology has 108 lunar mansions. That is 27 constellations multiplied by 4. Each asterism or Nakshatra is divided into 4 quarters. Nine such quarters tenant a Zodiacal Sign. Beta Arietis ( Aswini ) 1,2,3 and 4, 41 Arietis, 1,2,3 and 4 and the first quarter of Peiades ( Karthika ) tenant the constellation of Aries.

The quarters of Nakshatras are then the lunar mansion and the Sidereal Zodiac has 108 lunar mansions.

The book "Nakshatras, Lunar Mansions of Vedic Astrology" is a great book by Dr Dennis Harness and Dr David Frawley. It deals with the Sidereal Zodiac and contains a wealth of information about Vedic Astrology. A must for the novitiate.

Both are great scholars of Astrology and can enlighten the students about the great stellar science which is Vedic Astrology. Once the concept of Lunar Mansions is understood, the student can easily grasp the structure of the Sidereal Zodiac, upon which Vedic Astrology is based.

Equation for Saturn in the great Jup-Sat perturbation

2010-08-02T03:07:00.001-07:00

We will now deal with the equation for Saturn in the Jupiter- Saturn inequality.

3102 is added to the Year of Birth and then 4660 is deducted from it. Then that value is subtracted by 918 and multiplied by 360. Then that value is mulitplied by 2873 seconds and then the resultant value is minussed from Saturn's longitude ( if his longitude is less than 180 ) and added ( if his longitude is greater than 180 ).

Mathematically,

KY ( kali year ) = Year ( Date of Birth ) +3102
kyb = KY - 4660

x, bhujamsa = ( kyb )/918 * 360
y, bhujajya = sin (x )

satvalue = sin (x ) * 2873

If Mean Longitude of Saturn < 180
Sat's corrected Long = Sat's long - satvalue

If Longitude of Saturn > 180
Sat's corrected Long = Sat' long + satvalue

Western Astronomy gives the perturbation amplitude as .812 degrees which is similar to the Indian value of 2873 seconds. Similar values are not exactly the same and hence neither borrowed from each other !

Computation of Ayanamsa

2010-08-02T02:55:00.001-07:00

In India, Chaitra Paksheeya Ayanamsa is widely followed. The Indian Govt gave the job of standardising the Almanacs to the great N C Lahiri. It is also known as Lahiri's Ayanamsa.

The Year of Coincidence of the Tropical and the Sidereal Zodiacs was at 285 AD, according to Chaitra Paksheeya Ayanamsa. There are 13 other Ayanamsas, with different scholars differing as to the dates. The great Dr B V Raman opined that the two Zodiacs coincided at 398 ACE, but the followers of Chaitra Paksha Ayanamsa are more.

According to Cheiro, the Precession was one degree in every 72 years.

According to C P A, the precession is 50.24645 secs per year.

Mathematically

y = year(xdate)-Year of Epoch

x = 50.25645+(.00022229)*y + ((0.00000000027)*y^2)

Chaitra Paksha Ayanamsa = 22.436+ (x/3600)*y

Computation of the great Jupiter-Saturn perturbation !

2010-07-15T07:00:00.000-07:00

In Indian Astronomy, the great Jupiter - Saturn perturbation, is calculated using the formula given below.

The Kali year, ky, is calculated and 4660 is deducted from it to get the kyb, the kali year balance. Its Bhujamsa,x is calculated using the Equation of Bhuja and then its Bhujajya ( Sin x ) is calculated to get the value of Manda Phala, a.

Mathematically, it can be written as

Y, (Year of Birth) + 3102 = ky, the Kali Year of Birth

kyb ( kali year balance ) = ( ky - 4660 )

x = kyb*360/918

b, bhujajya = sin(x)

Since the duration is 918 years and perturbation amplitude is 1187 seconds,

Manda Phala, a = sin(x) * 1187

( Example - My year of birth is 1955. Add 3102 and we get 5057. Less 4660 is 397. 397*360/918 is 155.6 and its Bhujamsa is 25 degrees roughly ( 180-155). So Sin (25 ) is 0.41. Manda Phala, therefore is 0.41*1187 seconds or Vikalas. )

This value, Manda Phala, a is added to Jupiter's mean longitude, if Jove's long is less than 180 and subtracted if Jove's long is greater than 180.

In the West, this discovery is attributed to Laplace. The duration of the perturbation of 918 years is known as Laplace period. Its amplitude of .332 degrees is similar to the Indian value of 1187 seconds.

Laplace gives the equation 2 nj - 5 ns, bringing to light the 5:2 Resonance in the orbits of the two celestial giants. 2 revolutions of Saturn = 5 revolutions of Jupiter = 60 years !

Computation of Ahargana

2010-07-14T02:56:00.001-07:00

Ahargana is defined as the no of days elapsed after the start of the Iron Age, the Kali Yuga, which began on 3102 BC.

Kali Era = English Era +3102

The no of days elapsed from Kali Start was 1822903 on 01/01/1890.

Hence

Ahargana = ( xdate - 01/01/1980 ) + 1822903

where xdate is the date of birth.

This Ahargana is printed on every V A Horoscope. All calculations in Indian Astronomy is based on Ahargana. Ahas means day in Sanskrit and gana means calculation.

The present Kali Era is therefore

3102 + 2010 = 5112

The difference between the Malayalam & English eras are 825. Malayalam Era is 1185 now and if you add 825 to Malayalam Era, you get English Era.

Definition of Ascendant

2010-07-11T23:44:00.001-07:00

The Ascendant is defined as the intersecting point between the Ecliptic and the Celestial Horizon and is the Eastern Celestial Horizon. It is represented by the formula

Tan L = Sin E / cos E cos w - Sin w Tan A

where A is Latitude of the place, w is the maximum declination of the Sun, E is the Right Ascension of East Point ( Sayana Kala Lagna ) & L - the Lagna.

Raseenam Udayo Lagnam - Udaya Lagna, the Ascendant, the pivot of the horoscope, is the Eastern Celestial Horizon. In Astrology everything is based on Lagna, Sarvam Lagnepi Chinthayel.

180 degrees opposite to the Ascendant is the Descendant, the Astha Lagna and is the Western Celestial Horizon.

THE EQUATION OF BHUJA

2010-07-11T23:35:00.000-07:00

Bhujamsa is the degrees traversed by the planet in the Zodiac. In the mighty 360 degree Circle, the planet may be anywhere and its position is the mean longitude of the planet. The planet actually is in the ellipse and its position is the true longitude of the planet.

If the planet is say at 42 degrees, then the Equation of Bhuja states that its Bhujamsa is 42 degrees. That is in the first Oja Pada, in the first quarter of 0-90 degrees, the Bhujamsa is the same.

If the planet is say at 110 degrees, then the Equation of Bhuja states that its Bhujamsa is 70 degrees. That is in the first Yugma Pada, in the second quarter of 90-180 degrees, the Bhujamsa is 180 - bhuja.

If the planet is say at 200 degrees, then the Equation of Bhuja states that its Bhujamsa is 20 degrees. That is in the second Oja Pada, in the third quarter of 180-270 degrees, the Bhujamsa is bhuja - 180.

If the planet is say at 300 degrees, then the Equation of Bhuja states that its Bhujamsa is 60 degrees. That is in the second Yugma Pada, in the fourth quarter of 270-360 degrees, the Bhujamsa is 360 - bhuja.

Bhuja Jya is Sin ( M ) and is the sine value of the Kendra. Bhuja Jya is used in the calculation of Epicycles, in calculating the Equation of Center for Moon, Jupiter and Saturn.

The Manda Phala, the Equation of Center is given by the formula

Equation of Center, Mandaphala =Circumference of the Epicycle ( Parama Phala ) * Manda Kendra Jya ( Sin M ).

This is the equation used in calculating the 14 perturbations of the Moon, the five of Jupiter and the six of Saturn.

The Auxiliary Circle, the Vikshepa Vritta

2010-07-05T21:38:00.001-07:00

In order to compute the celestial longitudes of planets, first the Graha Madhyamam, the mean longitude of the planet is computed.

We have to understand that the planets traverse in elliptical orbits. If their orbits are circular, then there is no need for jya samskaras ( trignometric corrections ).

Once the mean longitudes of the planets are ascertained, then we first start with the First Jya Samskara, the first trignometric correction. Manda Jya means Sin M in Western Astronomy.

The Kepler Equation is M = E - e Sin E, where e is eccentricity and E is the Eccentric Anomaly, an auxilary angle in Kepler's equations.

Like Kepler who brought in an auxiliary angle ( E, the Eccentric Anomaly ), Indian Astronomy uses Vikshepa Vritta, an auxiliary circle. The mean longitude of a planet reduced by Manda Kriya is the Vikshepa Vritteeya Sphuta, the once corrected longitude of the planet.

While Western astronomers compute the celestial longitudes using the formula Theta = v + w ( Celestial Longitude = True Anomaly + the Argument of Perihelion ), Indian astronomers use the Triune Trignometric Method. Longitudes are corrected thrice using Manda Kriya, Parinathi Kriya and Sheegra Kriya.

The perturbations of planets

All planets have perturbations. Moon has 300 perturbations, of which 14 are major. Hence for 14 perturbations, 14 jya samskaras have to be done ( Chatur Dasa Jya Samskara). The largest of them is the Evection. There are others like the Variation, the Annual Equation and the Parallactic Equation. When 14 trignometric corrections are done, we get the Reduced Longitude of the Moon, the Samskritha Chandra Madhyamam.

Jupiter has five major perturbations ( guror pancha kendrani bhavanthi ) and Saturn has six. So five jya samskaras and six jya samskaras have to be done for Jupiter and Saturn, before commencing the Triune Trignometric Method.

The four systems of Astronomy

2010-07-05T21:37:00.002-07:00

There are four major methods of calculation in Astronomy

They are

Longitudes calculated along the Zodiac or Ecliptic - The Ecliptic System
Longitudes calculated along the Celestial Equator - The Equatorial System
Longitudes calculated along the Celestial Horizon - The Horizontal System
Longitudes calculated along the Celestial Meridian - The Meridian System

Longitude measured along the Kranti Vritta, the Ecliptic or Bha Chakra , the Zodiac is known as Kranti Vritteeya Sphuta, the true longitude of the planet.

Longitudes measured along the Vishuvat Vritta, the Celestial Equator is known as Vishuvat Vritteeya Sphuta, Right Ascension.

Udaya Lagna, the Ascendent and Astha Lagna, the Descendent are measured along the Celestial Horizon,The Kshitija

And the Madhya Lagna, the MC and the Patala Lagna, the IC are measured along the Celestial Meridian, the Nadi Vritta.

About Sine, Cosine and Reverse Sine

2010-07-05T21:37:00.001-07:00

Jya ( Sine ), Kotijya ( Cosine ) and Utkram Jya ( Versine ) are the three trignometric functions introduced by the Indian astronomers and mathematicians.

In order to compute the celestial longitudes of planets, these functions were used by the trinity of Indian Astronomy, Bhaskara, Brahnmagupta and Aryabhata.

Thrijya, the Radius or R

If 360 = 2 Pi r
then, r = 360/2Pi in degrees

One degree is 60 minutes and one minute is 60 seconds and hence one degree is 3600 seconds.

R in seconds will be ((360/2pi)* 3600 ) Vikalas or 206265 seconds. This figure 206265 is known as the Magic Figure of Astronomy.

Bhujajya = R Sin
Kotijya = R Cos

The arc sine of the angle is Bhujachapa
The arc cosine of the angle is Kotichapa
The arc tangent of the angle is Sparshachapa

By Jya, Bramhmagupta meant 5 degrees of a sign of 30 degrees. Hence a Zodiacal Sign consists of 6 Jyas ( 30 degrees ) . The Zodiac of 360 degrees was divided into 4 quarters of 90 degrees each. Three Jyas of 30 degrees each becomes a quadrant of the Zodiac and was called Thrijya. Thrijya is also the Radius, the Vyasardha.

His magnum opus, the Brahmasphuta Siddhanta was translated by the Arabs as As Sind Hind. Jya became jiba and Kotijya became kojiba in Arabic. It was translated into Latin as sinus ( meaning " bosom " ). So Sinus and Co-sinus when translated into English became Sine and Cosine !

The Aryabhateeyam of Aryabhata was translated by the Arabs as Al Arjabhat. Trignometry is derived from the Sanskrit Thrikonamithi and Geometry from Jyamithi !

The Celestial Meridian, the Nadi Vritta

2010-07-05T21:36:00.004-07:00

All celestial bodies appear to rise in the east, travel westward and set in the west, because of this relative diurnal motion. When the axis of the earth's rotation is extended, it meets the Celestial Sphere on two diametrically opposite points called Celestial Poles. The one in the direction of the Earth's north pole is called the North Celestial Pole and the one in the opposite direction is called the South Celestial Pole.

The Celestial Horizon, the Kshitija

To the observer standing at a place on the surface of the earth and looking around describing a full circle, the earth appears to meet the Heavens along a circle. From the observers' frame of reference, this circle is called the Celestial Horizon, the Khshitija.

The Celestial Meridian, the Nadi Vritta

Almost 90 degrees to the Celestial Horizon, you will find another circle ( the line perpendicular to the plane of the horizon ). This Circle is the Celestial Meridian. The highest point on this Celestial Meridian is called Zenith, the MC and the lowest, the Nadir or IC.

The 18 Siddhantas !

2010-07-05T21:36:00.003-07:00

Astronomical Knowledge is known in Sanskrit as Siddhanta. Transcendental Knowledge is Vedanta.

There are 18 astronomical treatises compiled by 18 Seers. Each Siddhanta is named after its author. They deal exhaustively with Astronomy.

They are

Surya Siddhanta
Pitamaha Siddhanta
Vyasa Siddhanta
Vasishta Siddhanta
Atri Siddanta
Parasara Siddhanta
Kashyapa Siddhanta
Narada Siddhanta
Garga Siddhanta
Marichi Siddhanta
Manu Siddhanta
Angira Siddhanta
Lomasa Siddhanta
Paulasa Siddhanta
Yvana Siddhanta
Chyavana Siddhanta
Bhrigu Siddhanta

These are the main astronomical treatises. There are others like Arya Siddhanta by Aryabhata II, Brahma Sphuta Siddanta by Brahmagupta and Maha Bhaskareeya by Bhaskara.

The Celestial Sphere, the Khagola !

2010-07-05T21:33:00.000-07:00

When we look up at the heavens on a clear night, we find a multitude of celestial bodies, illuminating the sky with their radiance. It looks like a large hollow hemisphere, with the observer at the center. The planets and the luminaries seem to be scattered thorough the heavens at large distances.

This picture of the observer, the sky as a large crystalline hemisphere , is a very convenient model for the study of the Heavens.

This hemispherical model of the heavens is called Khagola, the Celestial Sphere. Another geocentric model, the Khagola is an imaginary sphere of large radius.

Astronomy, Maths and Astrology ( Siddhanta, Samhita and Hora ) are considered to be Apaurusheya, divine in origin. They were revealed to the Rishies in higher states of Consciousness and hence are revealed sciences. Descendit e Caelo, they cometh from Heaven !

Their date of compilation is believed to be 12th century BCE

Rotation, Revolution & Diurnal Motion

The earth rotates about its own axis, from west to east in the course of a day. Due to this rotation, the observer is carried eastward. But the observer is unaware of his motion in space. To the observer, the Celestial Sphere with all the heavenly bodies, is seen as rotating from east to west. This apparent westward motion of the heavenly objects is known as the diurnal motion.

The Kepler Equation, M = E- e Sin E

2007-12-28T01:56:00.000-08:00

The Kepler equatio M = E- e Sin E can be used to compute planetary longitudes.

M is the Mean Anomaly of the planet and E, the Eccentric Anomaly. Eccentric Anomaly is an auxiliary angle used in Kepler's Equations.

e is Eccentricity of Orbit. The planet's orbit is elliptical and not circular and Eccentricity or e is always Zero at Circle, 0-1 at ellipse and one at Parabola !

The Kepler Equation can be put in a different way

E = M + e Sin E

Kepler's Laws of Planetary Motion

2007-12-28T01:51:00.000-08:00

Johannes Kepler expounded the principles of Planetary Motion thus

1)The orbit of a planet is an ellipse, with the Sun as the focus of the ellipse.

3)The motion of a planet is fastest at Perihelion and slowest at Aphelion.

4) p1^2 / p2 ^2 = a1 ^ 3 /a2 ^3

The periods of revolutions ( sidereal period ) of two planets is equal to the cubes of their semi major axes.

Long before Kepler Aryabhata expounded the Helio centric Theory of Gravitation, that all planets circle around the Sun due to celestial gravity. If it is terrestrial gravity which is the characteristic of the earth, then it is Celestial Gravity, which is the characteristic of the Sun

R, the Magic Figure in Astronomy

2007-12-27T23:45:00.000-08:00

R is the Radius of a Circle. It is 206265 secs and is an important figure is Astronomy

We talk about the Circles in Astronomy. The Ecliptic is a Circle, the Zodiac is a Circle and so on. And how do we measure the Radius of the Circle?

The Magic Figure of 206265 seconds is got by these derivations

Circumference = 2 Pi r

360 degrees = 2 Pi r

r = 360 degrees / 2 Pi

= 360 degrees / 2* 3.14

= 57.3 degrees

( One degree is 60 minutes and one minute is 60 seconds and hence one degree = 60*60 = 3600 seconds )

= 57.3 degrees * 3600 seconds

= 206265 seconds of arc

This is the how the Magic Figure in Astronomy, 206265 seconds, is derived !

Computation of Directional Strength

2007-12-11T01:17:00.000-08:00

Directional Strength or Digbala is one of the Sixfold strengths. Here we give the formula for computing Directional strength

First find out the Digbala arc. For instance Jupiter has full directional strength when he is on the Ascendant. That means 180 degrees from that point, on the Descendant he is zero.

So the equation for Digabala arc is

Digbala arc = Longitude of the planet - its powerless point.

( if the difference is more than 180, subtract it from 360 degrees ).

The midpoint of the House or Bhava is taken into consideration. The midpoint of the 7th House becomes the powerless point of Jupiter

Divide the Digbala arc by 3 and you get the Digbala or Directional strength.

Definitions of some Vedic terms

2007-12-05T03:33:00.001-08:00

Astrology is based on the Platonic Imitation Theory that the Earth
is an exact replica of Heaven. "As Above So Below" - was the form-
ula summed up by Hermes Trismegistes. We find that the pauper of
today is the prince of tomorrow and the prince of today is the
pauper of tomorrow. What is the base of all this ?

Astrology - the Science of Time - is the only science that has the
answer as it deals with natural causes and the corresponding cele-
stial causes. Since everything happens by Cause we can infer that
everything happense by two types of causes - natural & celestial.
We know the natural causes which has determined the present events.
This heavenly science deals with the celestial causes which has de-
termined the present events. Divine Providence coincides completely
with natural causes.

The Law of Correspondences of classical philosophy states that
everything on earth is an exact copy of that which is structured
in Heaven. Astrologers therefore analyse the heavenly archetype
( the horoscope ) to understand the earthly reflection.

GLOSSARY OF SANSKRIT TERMS USED
-------------------------------

LMT - Local Mean Time after the longitudinal correction is applied.

Nirayana - Sidereal viz based on the constellation of fixed stars.

Sayana - Tropical viz based on the Signs of the Zodiac.

Rasi - Zodiacal Sign . There are 12 signs of the Zodiac from Aries
to Pisces . 30 degrees of arc.

Sphutam - Celestial longitudes of planets.

Nakshatra - Star or asterism. There are 27 asterisms or stars which
tenant the Zodiac

Zodiac - A belt of the heavens 9 degrees to either sides of the
Ecliptic.

Eclipitic - The real path of the earth round the Sun.

Pada - Quarter of a star or asterism. A star is divided into 4
quarters or 4 padas.

Lord - Lord of the star. All stars have lords. For instance Alpha
Arietis or Aswathi is owned by Ketu. Revathi or Zeta Piscium is
owned by Mercury.

Ayanamsa - Precessional Distance. It was observed that the Tropi-
cal Zodiac precedes 1 degree in every 72 years. It takes 25920
years to precede 360 degrees and this is called the precession of
the Equinoxes.

Chitra Paksha Ayanamsa - The Indian Govt adopted this Ayanamsa for
all astronomical calculations. ( There are other Ayanamsas formulated
by scholars.)

Ahargana - No of days elapsed from the beginning of Kali Era which
started from 3102 BC as per the Hindu Calender.

Thithi - Lunation . When the Moon is within 12 degrees from the Sun
it is the First Lunation or Prathama. When Moon is within 24 degrees
from the Sun it is the Second Lunation or Dwitheeya.

Thriteeya - Third Lunation
Chathurthi - Fourth Lunation
Panchami - Fifth Lunation
Shasthi - Sixth Lunation
Sapthami - Seventh Lunation
Ashtami - Eighth Lunation
Navami - Ninth Lunation
Dasami - Tenth Lunation
Ekadasi - Eleventh Lunation
Dwadasi - Twelvth Lunation
Thrayodasi - Thirteenth Lunation
Chaturdasi - Fourteenth Lunation
Pournami - Full Moon. Moon 180 degrees from the Sun
Amavasya - New Moon. Conjunction of the Moon with the Sun.

Nithya Yoga - There are 27 Nithya Yogas. Period during which the
joint motion in longitude of Sun and Moon amounts to 13 degree 20
minutes of arc.

Shukla Paksha - Bright Fortnight - 15 days after the New Moon.
Krishna Paksha - Dark Fortnight - 15 days after the Full Moon.

Dasa - Period of Directional Influence. Saturn's period is 19
years Jupiter's 16, Mars 7, Moon 10 Sun 6 Venus 20 Rahu 18 Ketu 7.
When a person is born he is born in a certain star. It is ruled
by a planet. This planet is ruling at the time of birth. Say
a child is born in a star called Zeta Piscium or Revathi. Its
lord is Mercury and Mercury Dasa will be ruling at the time of
birth. After 17 years it will be replaced by Ketu Dasa for 7
years and after 7 years Venus dasa for 20 years.

KETU - Moon's Descending Node . Caput Draconis.

RAHU - Moon's Ascending Node . Cauda Draconis.

Ashtavarga - Benefic points of planets in a Rasi or Zodiacal
Constellation.

Sarvashtavarga - Total benefic points in the 12 signs.

Rasi Chart - Map of the heavens at the time of birth.

Navamsa Chart - 1/9th division of the Rasi Chart.

Bhava Chart - Chart based on the Ascending Degree. ex - Suppose
the ascending degree of a man is 20th degree of Cancer. This point
is taken as the mid-point of Bhava and 15 degrees to either side
is taken as the Ascendant House. So the Ascendant house or the
First House is from 5th degree of Cancer to the 5th degree of Leo.

LAGNA - Ascendant - The Eastern Horizon of the place. The Sign
rising at the eastern horizon. For instance if the date of birth
is say 05th JAN the sign rising at the Eastern Horizon at the time
of Sunrise is Sagittarius. This is known as Sagittarius Ascendant
or Dhanus Lagna.

GUL - Gulika a satellite of Saturn.

Bhava Sphutam - Longitudes of Houses ( Bhavas ).

Arambha _ Starting Point
Madhya - Mid-point
Anthya - End-point

Ayana - Solstice . There are 2 two types of Ayanas _ Uttarayana
and Dakshinayana ( Northern progress of the Sun and Southern
progress of the Sun). When the declination of the Sun is North
- Uttarayana. When the declination of the Sun is south - Dakshi-
nayana).

Rithu - 2 months. There are 6 Rithus in a Year.

Chandra Vela Chandra Kriya and Chandra Avasthas - Subtle States
of the Moon.

Saptha Varga - Points attained by planets.
Subha Varga - Benefic Points.
Papa Varga - Malefic Points.

Drekkana - Decanate . 10 degrees of a Sign.
Hora - 1 hour. 15 degrees of a Sign.
Sapthamsa - 1/7th Division of a Sign.
Dwadasamsa - 1/12th division of a Sign.
Trimsamasa - 1/30th division of a Sign.

Apahara or Bhukthi - Sub -period of a planet. In a ruling Dasa
there will be sub-periods of other planets.

Sevenfold Division Strength ( Sapta Vargaja Bala )

2007-11-28T03:09:00.000-08:00

A planet on account of its tenancy of certain divisions or vargas gets a certain amount of strength.

A planet in its Moola Trikona gets 45 Shastiamsas.

In own Varga, it gets 30.
In bosom friend's house, it gets 22.5 Shastiamsas.
In friend's house, it gets 15 Shastiamsas.
In neutral varga, it gets 7.5 Shastiamsas.
In inimical Varga, it gets 3.75 Shastiamsas

and in the varga of bitterest enemy, 1.875 Shastiamsas.

Odd/even Strength of Planets - OjaYugmaRasyamsa Bala

2007-11-26T02:13:00.000-08:00

Certain planets in odd signs gets a strength of 15 Shashtiamsas while some others get 15 Shashtiamsas strength in even signs.

The Sun, Mars, Jupiter, Mercury & Saturn, when they are in Odd Sings get a strength of 15 Shashtiamsas. Moon and Venus get the same strength in even signs.

This should be applied to both Rasi & Navamsa charts. Hence this strength is known as OjaYugmaRasyamsa Bala

Oja - Odd
Yugma - Even
Rasi -
Amsa - Navamsa

Computation of Quadrant Strength ( Kendra Bala )

2007-11-25T08:32:00.000-08:00

Quadrants ( Kendras ) are 1,4,7, 10 houses.

Panaparas - These are the signs next to quadrants, viz, 2,5,8 & 11.

Apoklimas - These are houses next to the Panaparas, 3,6,9 & 12

Quadrant strength is calculated by the rule that a planet in a Quadrant gets 60 Viroopas or Shashtiamsas, in a Panapara 30 Shastiamsas and in an Apoklima 15 Shashtiamsas.

Computation of Decanate Strength

2007-11-24T01:12:00.000-08:00

Planets are classified into 3 types

Masculine planets - Sun, Jupiter and Mars
Feminine Planets - Venus & Moon
Hermaphrodite " - Saturn and Mercury

A male planet in a first Decanate of 10 degrees
A hermaphrodite planet in the middle decanate
& female planet in last Decanate

gets a strength of 15 Viroopas or Shastiamsas

Computation of Exaltation Strength ( Uchaa bala )

2007-11-22T02:10:00.000-08:00

An exalted planet gets 100% strength. In Vedic Astrology 100% strength is 60 Shashtiamsas or Virupas or 1 Rupa.

When a planet occupies its deep exaltation point or Uchabhaaga, it gets a strength of 1 Rupa. Similarly, when it occupies its deep debilitation point, it gets zero strength.

Exaltation strength is given by the formula

Exaltation Strength = Planet's longitude - Its debilitation Point/180 * 60 ( in Virupas or Shastiamsas )

where the difference is more than 180, it is to be subtracted from 360

Jup Sun MarMer Moo		Ket
Ven	RASI	LA
	RASI
Rah		Sat