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 the
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 ). In 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 Sphutamihodhitham
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 perihelion Sheegrochha. Sheegra in Sanskrit means fast. Similarly they called Aphelion Mandochcha, manda meaning slow, and it implies that all planets move slowly at Aphelion !