Reduction to Geocentric Coordinates By
Vedic astronomers never said like Kepler that planets traverse in elliptical
orbits. But then they talked about Eccentric and Epicyclic theories. They said
for the luminaries, the Sun and the Moon, reduction to the geocentric (Sheegra
Kriya ) coordinate system was not necessary. But for the Tara Grahas, like
Mercury, Venus, Jupiter, Mars and Saturn, both thejya
trignometric corrections ) are necessary.
The Vedic astronomical texts say that the planets go in an epicycle, whose
center moves along the mean circular orbit from west to east. This theory came
to be known as the Epicyclic Theory. There is another theory called the
Eccentric Theory, which states that a planet goes in a circle whose center is
not the Earth, but a different point other than the Earth.
Bhaskara says " The Center of the Celestial Sphere coincides with the
center of the Earth. The circle in which a planet goes does not have its
center coinciding with the Center of the Earth". Hence the Vedic
astronomers like Bhaskara, Brahmagupta and Aryabhata, prescribedbhujaphalam (
otherwise called Equation of Center for mandaphala, whereas
in the case of the five Tara Grahas, this bhujaphala,
despite connoting Equation of Center or mandaphala,
also stands for corrections required to reduce their longitudes from the
Heliocentric Coordinate System to the Geocentric Coordinate System ).
the above diagram,
m is the Sheegra Anomaly
and the angle EJS is the Sheegra Phalam
where E = Earth, S = Sun and J = Jupiter
In order to get the geocentric longitude, the longitude of the Sun is deducted
from the Ecliptic longitude and then we get the Sheegra Kendra, the angle
between the planet and the Earth Sun plane.
Ecliptic longitude - Long Sun = Sheegra Kendra
Arka Sphutnoniham Kheda Manda
Sheegra Phalam is the angle EJS ( Earth, Jupiter, Sun ) and this Sheegra
Phalam is deducted to get the true, geocentric longitude. ( Added if Sheegra
Anomaly > 180 and deducted if Sheegra Anomaly < 180 ).
Like Kepler, the Indian astronomers may not have said that all planets move
fastest at perihelion but this principle was known to them as they called
Sheegra in Sanskrit means fast. Similarly they called Aphelion Mandochcha, manda meaning
slow, and it implies that all planets move slowly at Aphelion !
Indian Astronomy, Chara is the Ascensional Difference and is the difference
between Right Ascension and Oblique Ascension.
And is calculated by the equation
Sin ( Chara ) = tan ( decl ) tan ( latitude ).
Here Theta is Chara.
Sin C is called Chara Jya
Right Ascension means the longitudes measured along the Celestial Equator, the
Vishu vat Vritta.
Oblique Ascension means the longitudes measured along the Ecliptic, the Kranti
Chara is used in the computation of Sunrise and Sunset.
The formula for Sunrise = 6 H + Equation of Time - Chara - Refraction
The formula for Sunset = 18 H + Equation of Time + Chara + Refraction