Astronomy is said to be the Science of the Heavens and Astrology, the Wisdom of the Heavens. The subtle difference between physical Science and intuitive science is the only difference between the two, even though some astronomers in their ego will say Astrology is not a science. Without the basic knowledge of Astronomy,  the knowledge of an astrologer is not complete. Ganita  means Astronomy and the mathematical aspect of Astrologia Vedica. Gnosis means Knowledge or Wisdom and the true Astro Gnosis is the knowledge  of all the three branches, Astronomy, Mathematics and Astrology, Siddhanta, Samhitha and Hora.  Jyothishastra praveeno graha ganitha padu, so thra daivajna uktha . The Kerala Mathematicians gave the KSAM algorithms, based on the Geometrical Model. They calculated planetary longitudes by the triune method of correction of the mean longitude of the planet. The planet on the Mean Circle was brought to the Heliocentric Circle, then to the Ecliptic Circle and finally to the Geocentric !


The planet on the Mean Circle is known as Griha Madhyama and the reduced planet to the Heliocentric Circle is known as Vikshepa Vriteeya Sphuta Griha. Then it is brought ot the Ecliptic Circle and he is known as Kranti Vritteeya Sphuta Griha. Then it is brought to the Geocentric Circle and he is known as Sheegra Vritteeya Sphuta Griha. This is totally different from the Western calculations, propagated by Kepler, Laplace, Schlyter or Keith Burnett, where the True Anomaly of the planet is found and then the Argument of Perihelion added  ! So let no one claim that Indian Astronomy is derived from Greek sources !

We have the Pingree and Van der Werden Hypothesis, the Naugbauer 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 


This is the Longitude corrected thrice Method of Kerala Astronomy
While the Western method is brilliant, finding out the True Anomaly of the Planet ( Theta = v + w ) and then converting it into Cartesian coordinates, x,y and z and then converting them into Spherical Coordinates, r, Theta and Phi ( vide Paul Schlyter, Computing Planetary Positions.htm ), the Kerala Method is no less effective.

In the Kerala Method, after computing the Mean Longitude of the planet, Graha Madhyamam, the Manda Anomaly, the angle between Position ( of the planet ) and Aphelion is computed.  The formula used is Manda Anomaly = Mean Longitude of the Planet - Aphelion. Then Manda jya phalam, x, the angle between the planet on the Mean Circle and the planet on the Heliocentric circle, is computed by the formula x = R e Sin M and x is then added ( if long > 180 ) or subtracted ( if long <180 ) to the Mean Longitude of the planet.
Then Vipata Kendra, the angle between Position and the Node is computed ( Vipata Kendra = Ecliptic longitude - Ascending Node ) and h, the Parinathi Phalam, the angle between the planet on the Heliocentric Circle and the planet of the Ecliptic is computed and then h is added or subracted ( added if mean longitude is in even signs and subtracted if mean longitude is in odd signs )  to the Mean Longitude of the planet.  And finally the Sheeghra Anomaly, the angle between Position and the Earth Sun Vector ( Sheegra Anomaly = Ecliptic Longitude - Longitude of Sun )  is computed to get the true longitudes of planets and x, the Sheegra phalam, the angle between the planet on the Ecliptic and the Geocentric Circle is added ( if long >180 ) or subtracted ( if long <180 ) to the mean longitude !
These are the terms used in Kerala algorithms for the calculation of planetary longitudes.
Vikshepa Vritta = Heliocentric Circle.

Vikshepa Vritteeya Manda Sphutam =  Heliocentric Longitude, l
Vikshepa Vritteya Manda Karna =  the Radius Vector, r
Kranti Vritta = The Ecliptic
Kranti Vritteeya Manda Sphuta =  Ecliptic Longitude
Kranti Vritteya Manda Karna     =  Ecliptic Vector
The Sheeghra Pratimandala = Geocentric Circle.

The Sheeghra Karna = Geocentric Vector, Delta
The Sheeghra Sphuta = Geocentric Longitude, Lamda
Vikshepa = Celestial Latitude.


The Concentric Equant Model of Aryabhata

Indian Astronomy Pre Ptolemaic

Differential Equations and Planetary Mass

Intercalary Months

Positive and Negative Regions of the Zodiac

Madhava Trignometric Series

Madhava Sine Series Astronomical Units of Time Measurement
Reduction to Geocentric Coordinates

Vedic Trignometry

Indian Astronomy III 

Eccentric and Epicyclic Theories of  Indian Astronomy

Indian Astronomy 

Kerala School of Astronomy and Mathematics

Calculus, India's Gift to Europe

Mathematics and Philosophy

Longitude Corrected Thrice Method

Indian Spherical Trignometry 

Astronomia Vedica Part IV Indian Astronomy IV 
Astronomia Vedica Part III   
Astronomia Vedica Part II

Mathematica Indica



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