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