Amavasya in October 2027

In Delhi: the fast on Friday, 29 October, with the śrāddha the same day.

The new moon: the thirtieth tithi, which ends the dark half (Krishna) of the lunar month. A tithi is the time the Moon takes to gain 12° on the Sun. In the amānta reckoning the Amāvasyā is the last day of the month. Surya Siddhanta 2.64, 2.66

The fast is kept on the later of the two days, the one joined to the next Pratipadā, and never on the day joined to Chaturdaśī. The Sāvitrī vrata is the exception and keeps the earlier day. Nirṇaya-sindhu p. 73

On the day whose aparāhṇa, the last third of the daytime, the Amāvasyā touches. When it touches both afternoons, the day whose kutapa, the 8th of the day’s 15 muhūrtas, it covers. Hemādri makes the kutapa the first test for households without sacred fires, and Hārīta’s rule by Vedic branch decides equal coverage. Nirṇaya-sindhu pp. 81⁠–⁠87

Each date is worked out for the city’s own sunrise and afternoon. The Amāvasyā begins and ends at the same moment everywhere, but which sunrise and afternoon it reaches depends on the city, so cities far apart can keep different days.