Thank you Shri Sangom ji for the clarification.
Your explanation has triggered two doubts in my mind. One, if the 'nirayana' system and 'saayana' system give rise to such a significant time gap of about three weeks in the calculations, then the positions of navagrahas, particularly the ones having only short stays in each Raasi like, Budha, Sukra and Ankaaraka, are bound to be so different that even the Raasi as per one system may not tally with the Raasi as per the other. In the case of Chandragraha, it would be quite very different, as it stays in each Raasi only for a little more than two days! Naturally, the birth charts of an individual, according to the two different systems would be very different from each other, and hence the astrological predictions based on the two different charts would also be very different. So, is it not possible to take the cases of a few aged individuals as samples, cast separate birth charts for them using the two different systems and make predictions also out of both charts about past events in their lives? This way it should be possible to verify which one of the systems is more dependable, astrologically.
Two, as the planetary positions and movements are tracked and recorded astronomically to a high degree of accuracy, using sophisticated instruments nowadays, can't we compare the astronomically observed data with the astrologically calculated data using both 'nirayana' system and 'saayana' system to find which one of the two systems is more 'truthful''?