In an earlier post, I have written about the epicyclic motion of planets in a geocentric model of the solar system. In this post, I take a look at the Hindu approach to epicyclic motion which is significantly different from the Greek approach.
In this post I will focus on the inferior planets – Mercury and Venus.
The Hindu approach (as exemplified by the Surya Siddhantha) focuses on the ecliptical longitude of the planets rather than on their actual position. In other words it ignores the actual distance from the Earth to the planet. Such a focus immediately highlights the fact that the ecliptical longitudes of the inferior planets librate around that of the Sun, i.e. they lead and trail the ecliptical longitude of the Sun periodically and hence appear to be Morning and Evening Stars at various times.
In the following figure the actual position of Venus is marked as “Shigroccha” (more on this below) and the eclipitic longitude of that position is marked as Venus (this is what I mean when I say that the Hindus have shifted the focus from the actual position to the ecliptic longitude). The red arc then highlights the fact that Venus is trailing the Sun, i.e. the Zodiacal house of Venus is behind that of the Sun and hence Venus will rise and set after the Sun and hence appears to be an Evening Star (i.e. is visible in the western sky after sun set).
In the following figure, some 200 days later, the situation is reversed with Venus leading the Sun, i.e. the zodiacal house of Venus is ahead of that of the Sun and hence Venus rises and sets ahead of the Sun and hence appears to be a Morning Star (i.e. is visible in the eastern sky before dawn).
All this will make more sense if you see an animation of this model in action.
Another interesting aspect of this model is that it highlights the retrograde movement of the planets. Run the animation and observe the ecliptic longitude slider on the left and you will see it reversing direction periodically (happens more frequently for Mercury than Venus). Alternately, you can also observe the line segment connecting the Earth to the planet and see it sweeping backwards (i.e. clockwise) periodically. If you turn the trace on to create the actual geocentric orbit of the planet, you can also observe that the reversal / backward sweep coincides with the “looping” of the orbit, which is what one would expect.
Thus, while the Greek model presents wonderful spirographs which can never really be observed in the sky above us, the Indian model highlights aspects of planetary movements that can be observed and anticipated in the morning / evening sky.
That leaves us with the question: what are Shigroccha and Mandoccha?
Mandoccha (Manda Uccha) is the apex of slowest motion. This could either be the apogee / aphelion of a planetary orbit or it could also be the inferior conjunction of an inferior planet with the Sun in a geocentric model. The latter is the meaning intended in the Surya Siddhantha. When a inferior planet is between the Earth and the Sun, since both the Earth and the planet are orbiting the Sun in the same direction it (the planet) seems to move slower across the zodiacal background (“manda” in Sanskrit is “slow”).
Conversely Shigroccha (Shigra Uccha) is the apex of fastest motion. When a planet is on the opposite side of the Sun (from the Earth), since both the Earth and the planet are orbiting the Sun but in opposing directions it seems to move faster across the zodiacal background (analogous to the Doppler effect in acoustics).
In the case of inferior planets (Mercury and Venus), the above definition of Shigroccha is superseded and, as mentioned above, the Shigroccha is simply identified with the real position of the planet (hence turning on trace in the animated model will trace the Shigroccha and gives you the Spirographs).