Surya Siddhantha - Diurnal and Annular Motion
The Surya Siddhantha describes a geocentric model of the solar system. It places the Earth at the center of the celestial sphere, fixed and immobile. Planets such as Mercury, Venus etc., as well as the Sun and the Moon orbit the Earth, with the Sun's orbit defining a solar year. So far so good.
Since the Earth is immobile at the center, the Sun's movement has to be made to serve two purposes viz. one annular movement (stated above) and the other the daily movement that creates day and night. How does the Surya Siddhantha achieve this?
Firstly, the outermost level of the celestial sphere, i.e. the fixed stars (asterisms) is modeled as revolving from East to West extremely fast, this simulating the diurnal motion.
Second, the Sun too is modeled as revolving extremely fast from East to West (simulating sunrise and sunset), but not as fast as the asterisms. As a result, with respect to the asterisms, the Sun "falls back" resulting in an apparent West to East movement of the Sun (with respect to the asterisms). This apparent motion models the annular motion of the Sun which defines a solar year, i.e. after 365.25 days the Sun is effectively lapped by the asterisms (like a fast race car laps a slow one on a racing track) and hence returns to its starting position with respect to the asterisms, thus starting a new year (this model ignores the effect of the precession of the equinoxes).
"The planets, moving westward with exceeding velocity, but constantly beaten by the asterisms, fall behind, at a rate precisely equal, proceeding each in its own path" - Surya Siddhantha, 1.25
Confused? Take a look at the animation below. This animation shows sunrise and sunset at the equator. The "One Month" animation shows the Sun positioned at Mesha (Aries) at the beginning at sunrise but falling behind and eventually crossing over to Vrushabha (Taurus) after 30 days. The "One Year" animation shows this process extended over 365 days by which time Mesha comes around one full circle and catches up with the Sun again!
Complicated? Yes, but this is an accurate model of the motion of the Sun and the asterisms from the Earth; and Indian astronomers circa 500 AD had this figured out!
This model is created using the following orbital parameters of the Sun and the asterisms as specified in Surya Siddhantha:
"In a Yuga, the revolutions of the Sun, Mercury and Venus, and of the conjunctions of Mars, Saturn and Jupiter, moving eastward, are four million, thre hundred and twenty thousand." - Surya Siddhantha, 1.29
"Of the asterisms, one billion, five hundred and eight two million, two hundred and twenty seven thousand, eight hundred and twenty eight. The number of risings of the asterisms, diminished by the number of the revolutions of each planet respectively, gives the number of risings of the planets in a Yuga" - Surya Siddhantha, 1.34
Use the slider to position the solar day to any starting value, but be sure to view the animation to observe the nuances of the movements. When you drag the slider around in the One Year mode, it given an illusion of the movement being from West to East. Ignore that and focus on the animation to see the correct East - West movements.