Eccentric And Epicyclic Theories Of Indian Astronomy
All planets traverse in ellipses and epicycles and this came to be known as the Epicycles Theory.
In the above diagram, the circle A is the mean orbit of the planet. P is the mean Position of the planet and the small circle P is the epicycle.
The small epicycles traversed by a planet are calculated and the mandaphala, the equation of center is computed and added if the Manda Kendra is in between 180 and 360 and subtracted if the M K is < 180. Manda Kendra is the angle between Position and Aphelion.
From the perspective of the Epicyclic theory & the Hindu astronomers, the radius of the epicycle was given instead of PQ and the circumferences of the epicycles. Both circumferences and radii are given in degrees, minutes and seconds, so that the equation of the center may be computed in deg min and secs. The epicycle in the case of the Equation of Center is given as Manda Nicha Uccha Vritta.
Manda - Manda Phala or Equation of Center
Uccha - Apogee
Nicha - Perigee
Manda Kriya is a Jya Ganitha Kriya, a trignometric reduction of the mean longitudes and distances of the planets to their heliocentric longitudes and distances.
The declination of the Sun is computed by the formula
Sin J = Sin L Sin w
where J is the Sun's declination of that particular date and time, L is the tropical longitude of the Sun and w, the Sun's maximum declination, which is 23 degrees and 27 minutes.
The Sun's maximum declination will be reached during Karkyadi ( The First Point of Cancer ) and Makaradi ( The First Point of Capricorn ). At Karkyadi, it will be +23 d 23 m and at Makaradi, it will be -23 d 27 minutes.
And at Meshadi ( The First Point of Aries ) and Thuladi ( The First Point of Libra ), the solar declination will be zero. Days and nights will be of equal duration and hence they are called Equinoxes.
Yada Mesha Thulayo varthathe thada ahoratranam samanani bhavanthi
We have said in our columns that the Indian astronomers said that the planets revolve around a point different from that of the Earth and Indian Astronomy is heliocentric.
The above diagram depicts the Eccentric Theory and Reduction of the longitude of the planet to the heliocentric coordinate system ( known as Manda Kriya ).
In the above diagram
The angle NAP = Manda Kendra or Mean Anomaly
The Circle A is the mean orbit of the planet
The Circle B is the true orbit
The mean planet moves on the mean orbit, known as the deferent.
When the planet is at N in the mean orbit, he is at M in the eccentric and this is calledMandoccha ( Aphelion ).
When the planet is at R in the mean, he is at S in the eccentric.
M and S correspond to Apogee and Perigee in the case of Manda Phala correction ( otherwise known as the Equation of Center ).
When the planet is at M in the eccentric, the position of the true planet coincides with N, the mean planet and so the Manda Phala correction is Zero.The Equation of Centre at both perigee and apogee becomes zero.
When the Mean Anomaly lies between 0 and 180 degrees, the Equation of Center is negative and this is known in Vedic Astronomy as Meshadi Rinam, Rinam meaning minus. And when it is between 180 and 360, it is additive and it is known in Indian Astronomy as Thuladi Dhanam, dhanam meaning additive.
Anomaly has been defined in Western Astronomy as the angle between position and perihelion. Manda Kendra here is the angle between Position and Aphelion, aphelion being mandoccha. The term manda explains that planets move slower at Aphelion !
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