Thursday, March 14, 2013

Kerala Astronomy, on Argive heights divinely sang !



If the Tropicalists "tropicalise" the Vedic Zodiac ( "which is imported from the West" ), it will go the Gregorian Way. The Vedic Astro Calender will become the Gregorian Calender ( again to be rectified later ! )

We have the Pingree and Van der Werden Hypothesis, the Naugbuer Hypothesis that the multi step algorithms of Indian Astronomy approximated a Greek Planetary Model, an eccentre and epicyclical Model. We have to respect them, as at least they admitted that India has an Astronomy. Not like Thibeau or Whitney who said that the ancient Indians  had no knowledge of Astronomy or Maths, when they saw gigantic calculations like 311.04 trillion year cycles ( Maha Manvantara ) and the Cosmological Cycle (4.32 billion years ). They said these calculations are plagiarised from the Romans and the Greeks!

Dr Carl Sagan opined that while Christians were calculating in thousands, Hindus were calculating in trillions !

The Radius Vector, said Kepler, sweeps out equal areas in equal time. 

Parameswara in the 15th century and Nilakantha in the 16th talked about Vyasardha Manda Karna. Vyasa is Diameter. Vysardha is Radius and Vyasardha Mandakarna is nothing but Radius Vector.

Kepler's Second Law states that

All planets move faster at Perihelion and move slower at Aphelion. That was known to the Indian astronomers. Otherwise they wouldnt have called Aphelion, Mandoccha ( Manda - slow ) and Perihelion, Sheegrocha ( Sheeghra - fast ) !

Let us get the dates of the astronomers

Parameswara - 15th century C E
Nilakanta - 16th
Kepler - 17th
Laplacae - 18th

The Nine Orbital Elements of the Kerala School of Astronomy and Maths, from which planetary longitudes are computed.

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 

Wednesday, March 6, 2013

Of the Eleventh House, a House of Wealth



The Eleventh House rules Gains and is one of the Houses of Wealth. The 
others being 2,5 and 9, deshveanka.



If the Eleventh lord be
In angles or trines
And if Eleventh be tenanted by malefics
A wealthy man indicated !


If the Eleventh lord be
In House Second
And if Second lord be in Second
Rich man indicated !


If the lords of Second and Eleventh be
In angles or trines favorable
Wealthy the native becomes
Such is Astrology's decree !


If the Eleventh lord be
Powerful, posited in Eleven
This itself is a Regal Yoga
Rich the native becomes !


If House Eleven and the Eleventh lord
Be in Shubhakarthari Yoga
Hemmed in between benefics
Wealthy the native becomes !


If House Eleven and the Eleventh lord
Or the Eleventh lord's dispositor
Be in benefic Navamsas
Rich the native becomes !

If the Navamsa lord of Eleventh lord
Be powerful, angular or trinal
And aspected by the Second lord
Wealthy the native becomes !

If the Trimsamsa lord of Eleventh lord
Be powerful, posited with benefics
And aspected by the Tenth lord
Rich the native becomes !


If the planets mentioned above
Be with malefics and posited
In Trika houses, 6,8 and 12
Native will be devoid of wealth !

If the Eleventh be tenanted
By benefics natural
And if Eleventh lord be angular
Native will have good elder brothers !

If benefics natural be posited
In House Eleventh
Good friends the native will have
Such is Astrology's decree !

If the Eleventh lord be powerful
And if Eleventh is tenanted by benefics
Native will have friends sincere
Thus say the astro wise !

If contrary is the case
Eleventh House and lord weak
Native's friends will be cheats
Thus say the wise !

Tuesday, February 26, 2013

Bhagya or Fortunate Yogas



The most important House in Astrology is the Ninth House, as it deals with Fortune or Bhagya. It is said that Kunti prayed to the Lord to grant her fortunate children and not scholars or soldiers.



Here we give some verses for Bhagya Yoga.

If the Ninth lord be in
Eleventh and if the lord of 11
Be in House Ninth
Bhagya Yoga indicated !

If all malefics be
In 3, 8 and Eleven
Fortunate the native becomes
Such is Astrology's decree !


The significations of the planets
That tenant the Twelfth
Those significations get fostered
Such is Astrology's decree !

If the lords of 4,7,9 and Venus
Be in Eleventh or Ninth
And receive aspect Saturnine
Fortunate the native becomes !

If the lords of the 4th and Ascendant
Be angular, fortune indicated
During their periods/subperiods
Native enjoys fame and wealth

If a planet be exalted
And is in Fifth or Ninth
Fortunate the native becomes
Such is Astrology's decree !

Swochhopago Bhagy Grihe cha Bhogo
Narasya Jatham Kuruthe cha Lakshmya

If Sun, Mercury and Venus
Tenanth the Lakshmi Sthana
The House Fifth, with Jove in Eleven
Wealth and fame grace the native !

If Sun and the lord of the Ninth
Be in House of Expenditure
The Twelfth, native enjoys
Legacy from father !

If the Sun be exalted in Aries,
Father becomes fortunate
If he be in Libra debilitated
Ill fortune grace father of native !

But if Sagittarius rises
And Sun be debilitated
Native is blessed with wealth
Got as father's legacy!

If Moon be in the Twelfth
Gain from mother indicated !
If Venus be in the Twelfth
Gain from wife indicated !

If Mars be in the Twefth
Gain from brother indicated
Kuje Vyaye Sthitho yasya
Bhrathru bhagyam udheeritham !


If the lords of the Ninth and the Seventh
Be in mutual interchange,parivartana
Native will have gains via wife
And will be self made !

If Jupiter be the lord of the Fifth
And if he be exalted in Cancer
Native's children reach high positions
Such is Astrology's decree !

Wednesday, February 20, 2013

Kerala astronomers




This is the diagram of Manda Kriya, Reduction to the Heliocentric Coordinate System, given by the equation R e Sin M, where e is eccentricity, R is the Radius of the Circle, M is the Anomaly.

The Manda Anomaly is found out by subtracting Aphelion, Mandoccha from the Mean Longitude.

Mean Longitude - Aphelion = Manda Anomaly.

R = 360/ 2 Pi or 180/Pi or 57.3*60*60 = 206265 seconds or Vikalas.

This amount thus got is added to the mean longitude if ML > 180 and deducted if ML < 180.


The Kerala astronomers predate their Western counterparts, particularly Kepler and Laplace by centuries. In his Thesis " The Model of Planetary Motion in the works of the Kerala astronomers", Prof Ramasubramaniam, Physics Professor, Madurai University observes " In conclusion, it may be noted that there is a vast literature on astronomy, including mathematics, both in Sanskrit and Malayalam produced by the Kerala School during the period 14-19th century. Only a fraction of it has been published and so far only a few studies of these texts have appeared ".

The era and the astronomer

Parameswara   - 15th century
Neelakanta      - 16th century
Kepler                17th
Laplace               18


Monday, February 4, 2013

Modern Diagram for the Indian trig functions, Jya and Kojya.



Jya = R Sin

Kojya = R Cos

... R being Vyasardha, the Radius of the Circle = 206265 seconds.

...
These are the trig functions used in Graha Ganitha and is highlighted in Bhaskara's Ganitha Adhyaya.

As one Zodiacal Sign defines 30 degrees of Arc, three consecutive Signs constitue one Vritta Pada, Quadrant of a Circle = 90 degrees and Indian mathematicians used the term Trijya for Radius of the Circle.

Tuesday, January 29, 2013

India beat England !



India beat England in Ranchi, Dhoni's home town.


India does it again,third consecutive win against England and moves to Numero Uno position in ICC Rankings.