Mandaphala is the epicycle theory in Hinduism. According to description, while the movement of mean sun, or moon, is along a big circular orbit of radius, R, the actual (or true) sun or moon moves along another smaller circle of radius, r, called the epicycle, whose center is on the bigger circle. The bigger circle, called kaksavritta, has the earth as its center.
It is assumed that as the center of the epicycle (mean sun) moves the bigger circle in the direction from west to east with the velocity of the mean sun, the true sun itself moves along the epicycle with the same velocity but in the opposite direction (from east to west). Also, the time taken by the true sun to complete one revolution along the epicycle is the same as that taken by the mean sun (i.e the center of the epicycle) to complete one revolution along the orbit.
Then the arc on the epicycle joining the Madhya (or the mean sun) and spashta (or sphurta) Ravi is called mandaphala (the equation of center).