The fast is broken only after sighting the moon and offering it arghya; the moonrise time varies by place. If it falls on a Tuesday it is Angarki, held especially powerful.
Monthly fasting on the 4th day of Krishna Paksha devoted to Lord Ganesha for removing obstacles.
Sankashti Chaturthi is the monthly vrat of Lord Ganesha, kept on the Krishna Paksha Chaturthi of every lunar month, and dedicated to Ganesha as Sankatahara — the remover of sankat, of troubles and obstacles. The one falling in this month, within the Ashwin fortnight, is worshipped with the special devotion of the season. Devotees keep a fast through the day, worship Ganesha with durva grass, red flowers and modak, recite his names and the Sankashti Vrat Katha, and — crucially — break the fast only after sighting the moon at night and offering it arghya, for the moon-sighting is the defining rite of Sankashti. Where a Sankashti Chaturthi falls on a Tuesday it becomes Angarki Chaturthi, held especially powerful. The vrat is kept for the removal of difficulties, success in endeavours, wisdom, health and the wellbeing of the family, and is among the most widely observed of Ganesha's monthly observances, particularly in Maharashtra and among Ganesha devotees everywhere.
The moon-sighting is the defining rite; the fast is not broken until the moon is seen and worshipped.
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