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Vedic Astronomy & Trignometry
In the Great Circle of Light which is 360 degrees, ( the Bha Chakra, the
Kala Chakra, the Zodiac ), the first 90 degrees are Oja Pada ( Odd Tri
Signs ) and the next 90 degrees are Yugma Pada ( Even Tri Signs ). The
degrees traversed by a planet is called Bhuja and the degrees yet to be
traversed by a planet is called Koti in an Oja Pada. In a Yugma Pada, the
degrees traversed by the planet is called Koti and the degrees yet to be
traversed by a planet is called Bhuja. In other words, the degrees
traversed by a planet is the same in the first 0  90 degrees and in the
second Pada, it is 180  degrees traversed. In the 180270 degrees arc, it
is distance traversed  180 degrees and in the 270360 degrees arc, it is
360  distance traversed. This is known in Vedic Astronomy as the equation
of Bhuja or Sin. Bhujajya is radius multiplied by modern Sine.
In the Mighty Circle of Light
The First 90 degrees is Oja called
The distance traversed is Bhuja
Koti is the untraversed degree !
( Oja Yatra Bhujaira Kotirapara Meshadi Jookadhi Kau )
Brahmagupta, in his mathematical treatise, the Brahmasphuta Siddhanta used
the word Jya which means 5 degrees of a 360 degree circle which is the
Zodiac, which is the Ecliptic. Suppose a planet has traversed 42 degrees in
the first Oja Pada ( From Aries to Gemini end ).The Bhuja is 42 degrees and
the Bhujajya is the 9th Jya or the 9*5 th degree. Bhujajya by Trijya is
Opposite Side by Hypotenuse or the modern Sine.
Jya Ganitha means Trignometry. The equation for Koti is different. It is
Kotijya by Trijya or Adjacent Side by Hypotenuse ( the modern Cos ). As per
Indian Learning it was Aryabhata, one of the greatest mathematicians ever,
who first computed the celestial longitudes of planets ( Aryabhato Graha
Ganitham ).
The calculations given for the perturbations of Moon, Jupiter and Saturn are
as follows. First find out the Bhuja of the planet, the degrees traversed.
Find out its Bhujajya or Sin ( Bhuja ). Multiply it by the value given (
which is in seconds) and add it to the mean longitude of the planet.
Meshadi , Thuladi, Karkyadi & Makaradi ( The First Points of Aries, Cancer,
Libra & Capricorn )
From Aries to Libra is the Northern Celestial Hemisphere ( NCH ) and from
Libra to Aries is the Southern Celestial Hemisphere ( SCH ). If the planet"s
Kendra is in NCH, the values are to be subtracted and if in the SCH, it is
to be added.
Karkyadi is the First Point of Cancer and the beginning of Dakshinayana, the
Southern course of the Sun, his declination South. Makaradi is the First
Point of Capricorn and the beginning of Uttarayana, the Northern course of
the Sun , his declination North. At Meshadi, the Sun"s declination is 0
degrees and Right Ascension is 0 degrees. At Karkyadi, the Sun"s declination
is +23 degrees 27 minutes and Right Ascension is 90 degrees. At Thuladi, the
Sun"s declination is 0 degrees and Right Ascension is 180 degrees. At
Makaradi, the Sun"s declination is 23 degrees 27 minutes and Right
Ascension is 270 degrees.
The Perturbations of Jupiter
The equations given for Jupiter"s perturbations are as follows: Five major
perturbations are included along with a major perturbation which is given
below. ( The great Jupiter  Saturn perturbation ).
Kendra means an angle in Sanskrit . Manda Kendra means Mean Anomaly, the
angle between position and perihelion and Sheeghra Kendra is the last angle
formed before the ultimate reduction to perihelion. All Kendras are zero at
perihelion.
The English Era + 3102 gives the Kali Era, the Era of the Hindu Calender.
From that value 4660 is deducted and the value is divided by 918. This gives
the Beeja Kendra. Find out the Sin ( Bhuja ) of that, multiply it with 1187
seconds and add it to Jupiter"s longitude if the Kendra is in NCH and
subtract it if it is in SCH.
There are other minor perturbations which can be ignored.
( Lj = Mean Longitude of Jupiter; Ls  Mean Longitude of Saturn. These
longitudes are Tropical or Sayana. ).
First Kendra (Sin ( Lj  Ls )  1. 15)* 81
Second Kendra Sin (( Lj  2 Ls)  13.08 )* 132
Third Kendra Sin ( 2 Lj  2 Ls  0.58 )* 200
Fourth Kendra Sin ( 2 Lj  3 Ls  61.57 )* 83
Fifth Kendra Sin ( 3 Lj  5 Ls  56.38 )* 162
The first value is to be added if the Kendra is Thuladi ( after the First
Point of Libra ) and deducted if it is Meshadi ( after the First Point of
Aries ). 2,3,4 & 5 are to be added if it is Meshadi and subtracted if
Thuladi
The Perturbations of Saturn
First Kendra Sin ( Lj  2 Ls ) 14.66 )*418
Second Kendra Sin ( 2 Lj  4 Ls + 56.90 )* 667
Third Kendra Sin ( 3Ls  Lj + 77.38 )* 48
These values are to be added if the Kendra is Thuladi ( after the First
Point of Libra ) and deducted if it is Meshadi ( after the First Point of
Aries ). In Sanskrit it is called Meshadi Rinam & Thuladi Dhanam. Meshadi
is the beginning of the Northern Celestial Hemisphere and Thuladi the
begining of the Southern Celestial Hemisphere.
There are other minor perturbations which may affect only the Vikala (
second ) of the planet"s longitude and hence can be ignored.
The Perturbations of the Moon
(Ms  Mean Anomaly of the Sun; Mm  Mean Anomaly of the Moon; Ls  Mean
Longitude of the Sun; Lm  Mean Longitude of the Moon; D = Lm  Ls (
Thidhi); Nm  Node of the Moon. These values are Sidereal or Nirayana )
14 Kendras are to be made and 14 trignometric corrections are to be given,
according to astronomical savants. These 14 reductions are mandatory and
only after these reductions can we get the true longitude of the Moon.
First KendraSin ( Ms + 180 ) * 658
Second KendraSin ( Lm  Ls ) * 121
Third Kendra Sin ( 2*D  Mm ) * 4467
Fourth Kendra Sin ( 2*D + 6 Signs ) * 2145
Fifth Kendra Sin (( 2*D  Mm Ms ) + 180)* 198
Sixth KendraSin ( 2*D  Ms ) * 155
Seventh KendraSin ( Mm Ms + 180 ) *112
Eighth KendraSin ( 2( Lm  Nm Mm +180))* 85
Ninth KendraSin ( 2*Ls  Nm ) * 81
Tenth Kendra Sin ( Mm  Ms )* 73
Eleventh KendraSin ( 2*D + Mm ) * 60
Twelfth Kendra Sin ( 2*Mm  2 D + 180 ) * 42
Thirteenth KendraSin ( 4*D  Mm ) * 35
Fourteenth KendraSin ( 4*D  2*Mm +180)* 30
These trignometric corrections should be added to Moon"s Mean Longitude if
the Kendra is in the Southern Celestial Hemisphere and deducted if the
Kendra is in the Northern Celestial Hemisphere and then we get the
Samskrutha Chandra Madhyamam or the Cultured Mean Longitude of the Moon.
Manda Kriya ( Reduction to True Anomaly ) must be done. Then Parinathi Kriya
( Reduction to Ecliptic ) should be done and what we get then is the
longitude of the Moon along the Ecliptic !
Viskshepa Vrittopa Gatho Vipatha
Thasmannayel Jyam Parinathyabhikhyam
Yugmaupada Swarnam Idam Vidheyam
Syath Kranti Vritteeya Ihaisha Chandra !
After the Reductions Fourteen, Sin M to be added or minussed thereby
To the Cultured Longitude Mean; The Node to be deducted &
Reduced to the Earth"s Path ( Ecliptic ); thus shall we get as the resultant
Value,
Luna"s true Sidereal Longitude !
Author Bio : Article by G Kumar, astrologer, writer & programmer of
www.eastrovedica.com. He has 25 years psychic research
experience in the esoteric arts. Stock market investment
advice can be got at http://www.stockmarketastrology.com

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