This animation illustrates the geocetric model of the Surya Siddhantha. The Surya Siddhantha models both the diurnal as well as orbital motions of the celestial bodies around the Earth.
Diurnal motion is modeled by making all the celestial bodies including the fixed stars of the zodiac (i.e. Nakshatra Mandala) orbit the Earth at a rapid rate. Sidereal orbital motion of the celestial bodies is modeled by the relative "fall-back" of the celestial bodies with respect to the fixed stars (since the fixed stars have the highest orbital speed). This concept is explained in greater detail in here using the motion of the Sun as an example.
This model illustrates the movement of the celestial bodies as observed from a point on the equator (i.e. the celestial bodies rise in the East, pass overhead and set in the West, daily). It uses the orbital parameters specified in Chapter 1 of the Surya Siddhantha and hence these orbits are mean orbits and not true orbits (the true orbits will of course be elliptical).
This model also illustrates the orbital periods of the various celestial bodies. The reset checkbox initializes the model to a hypothetical grand alignment of all the celestial bodies at the start of Mesha. From there, the celestial bodies start "falling back" wrt the Nakshatra Mandala with time. The time taken by a celestial body to return to the start of Aries is by definition its sidereal orbital period. Clicking on a check box placed against a celestial body in the Legend positions the model to the end of the first sidereal orbit of that celestial body, i.e. on the model you will see the celestial body placed once again at the start of Aries.
Feel free to check Wikipedia and compare these Surya Siddhantha sidereal orbital periods with the modern values. The correspondence is amazing considering the Surya Siddhantha was written over 1800 years back!