ĀRKSky
The sky, the way the text describes it
The Sūrya-siddhānta, an ancient Sanskrit astronomical treatise, records how many times the Moon orbits across a vast cosmic cycle, and how many civil days that cycle holds. Dividing the days by the revolutions gives the exact length of a month, calculated centuries before the invention of the telescope.
Check it yourself
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You can check it directly. That is the whole purpose of this corner of the site. The numbers are ancient, the arithmetic takes two lines, and modern NASA measurements provide the standard to compare against.
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Several calculations agree to four decimal places. Where a figure diverges, it is stated openly on its own row rather than hidden in a footnote.
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Nothing here claims that ancient scholars predicted modern science. Historical calculations are placed side by side with modern observations for anyone to inspect.
Where the figures come from
The Sūrya-siddhānta and Siddhānta-śiromaṇi, translated from Sanskrit into Bengali by Bimala Prasāda Siddhānta Sarasvatī and edited by Dānavīr Gosvāmī (Rūpānuga Vedic College, 2007). Revolution counts are chapter 1, verses 29–34; the civil-day total is 1.37. That edition is under copyright and none of its English prose is reproduced here. The numbers are mathematical facts and the explanatory sentences are ours.