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Dear Sri Murthy,
Sorry for the delay in responding. I am not an astronomer by profession. But having spent number of years investigating Hindu astronomy prior to the siddhanta period, I venture to add a few points in response:
Uttarayana is defined as the movement of Sun (as seen from earth) towards North. This day is also the shortest daylight day of the year. That Sun has movement not only E-W but also N-S is evidenced in the Rigveda itself. But I will not go into that now. The Pnchangas (Five elements) to which you refer are too recent in our history. If you see the work Parashara tantra (ISBN 978-81-9209-924-8) and Vrddhagaargiya (unpublished) there were only four elements in their calendar without Vāra or week days. The earliest unambiguous reference to Uttarayana is in the Maitrayani Aranyaka
“Of the year one half (when the sun moves northward) belongs to Agni, the other to Varuna (when the sun moves southward). That which belongs to Agni begins with the asterism of Maghâ, and ends with half of the asterism of Sravishthâ, the sun stepping down northward. That which belongs to Soma (instead of Varuna) begins with the asterism (of Asleshâ), sacred to the Serpents, and ends with half of the asterism of Sravishthâ, the sun stepping up southward..”
Here it is said that the Uttarayana started when Sun was at the middle of the star Dhanishtha. In the more famous Vedanga Jyotisha of Lagadha
Here, the Uttarayana, shortest day and the sun being with the beginning of star Dhanishtha are unambiguously mentioned. This event has been dated to c1400 BC. From this it follows the Maitrayani Aranyaka statement belongs to 1600-1800 BC.
Varaha mihira mentions that during his time uttarayana started with sun at ¼ of uttarashadha, but in ancient times winter solstice was at the start of Dhanishtha. Varaha mihira lived during 505-590 AD. From this statement also the ancient date alluded by him can be shown to be 1300-1400 BC. For his time, as per his convention, the Makarasankranti coincided with uttarayana.
To discuss how the error has crept in between observation of the shortest day and the current panchangas, one has to go into too many other details and history of the present day “Raashi”. One reason in my opinion is “too much reverence to the letter at the cost of the spirit”.
When you have free time you may like to read my paper
thanks
RN Iyengar