The Astronomical Foundations of Astrology
The Ascendant is defined as the intersecting point between the Ecliptic and the Celestial Horizon and is the Eastern Celestial Horizon. It is represented by the formula
Tan L = Sin E / cos E cos w - Sin w Tan A
where A is Latitude of the place, w is the maximum declination of the Sun, E is the Right Ascension of East Point ( Sayana Kala Lagna ) & L - the Lagna.
Raseenam Udayo Lagnam - Udaya Lagna, the Ascendant, the pivot of the horoscope, is the Eastern Celestial Horizon. In Astrology everything is based on Lagna, Sarvam Lagnepi Chinthayel.
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180 degrees opposite to the Ascendant is the Descendant, the Astha Lagna and is the Western Celestial Horizon.
Bhujamsa is the degrees traversed by the planet in the Zodiac. In the mighty 360 degree Circle, the planet may be anywhere and its position is its mean longitude. The planet actually is in the ellipse and its position is the true longitude of the planet.
If the planet is say at 42 degrees, then the Equation of Bhuja states that its Bhujamsa is 42 degrees. That is in the first Oja Pada, in the first quarter of 0-90 degrees, the Bhujamsa is the same.
If the planet is say at 110 degrees, then the Equation of Bhuja states that its Bhujamsa is 70 degrees. That is in the first Yugma Pada, in the second quarter of 90-180 degrees, the Bhujamsa is 180 - bhuja.
If the planet is say at 200 degrees, then the Equation of Bhuja states that its Bhujamsa is 20 degrees. That is in the second Oja Pada, in the third quarter of 180-270 degrees, the Bhujamsa is bhuja - 180.
If the planet is say at 300 degrees, then the Equation of Bhuja states that its Bhujamsa is 60 degrees. That is in the second Yugma Pada, in the fourth quarter of 270-360 degrees, the Bhujamsa is 360 - bhuja.
Bhuja Jya is Sin ( M ) and is the sine value of the Kendra. Bhuja Jya is used in the calculation of Epicycles, in calculating the Equation of Center for Moon, Jupiter and Saturn.
The Manda Phala, the Equation of Center is given by the formula
Equation of Center, Mandaphala =Circumference of the Epicycle ( Parama Phala ) * Manda Kendra Jya ( Sin M ).
This is the equation used in calculating the 14 perturbations of the Moon, the five of Jupiter and the six of Saturn.