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 ).
There are two major Indian Planetary Models – the Eccentric Model and the Epicycle Model. In the Eccentric Model, the Mean Circle is called Manda Pratimandala, that is the circle traversed by the mean angular motion of the planet. In the Epicycle Model, the Planet is on the epicycle, known as Manda Paridhi.
The Equation of Bhuja
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The degrees traversed by a planet is called Bhuja and the degrees yet to be traversed by a planet is called Koti in an Odd Sign. In an Even Sign, 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 180-270 degrees arc, it is distance traversed – 180 degrees and in the 270-360 degrees arc, it is 360 – distance traversed. This is known in Vedic Astronomy as the equation of Bhuja or Sine. Bhujajya is radius multiplied by modern Sine.
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The Mighty Circle of Light, Zodiac
Is divided by four into Four Quadrants
Distance traversed is Bhuja in Odd Sign
In Even Sign, it is Koti called !
Bhuja is Radius into modern Sine
Koti is Radius into modern Cos
From Aries to Libra is the Northern Hemisphere
And Southern from Libra to Aries !
( 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.
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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. ( Meshadi Rinam, Thuladi Dhanam )
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.