The first sighting of the crescent moon after Amavasya, for your city
Chandra Darshan is the first sighting of the waxing crescent moon after Amavasya (new moon), on the evening Shukla Pratipada is in effect, or, when the crescent is not yet visible then, the following evening (Dvitiya). Seeing the newborn crescent is considered auspicious: many observe a short fast until the sighting and offer arghya (water) to Chandra (the Moon) upon seeing it.
Right after Amavasya the crescent is extremely thin, low on the horizon, and sets soon after the Sun, so whether it can actually be seen with the naked eye on a given evening is a genuine astronomical question, not a fixed calendar date. This page checks each candidate evening using the Yallop crescent-visibility criterion (B.D. Yallop, HM Nautical Almanac Office Technical Note No. 69, 1997): a published method, also used internationally for other lunar-calendar moon-sighting determinations, based on the crescent's elongation, width, and arc of vision at sunset.
This is a scientific visibility estimate, not a substitute for an actual local sighting where community observance depends on it. Local horizon conditions (haze, elevation, obstructions) can affect what is actually seen on any given evening.
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