Based on accurate astronomical calculations, the conjunction between the moon and the sun happens before the midday of Tuesday, May 11th based on the San Diego time zone. Hence, Wednesday, May 12th is the Eid al-Fitr. Eid al-Fitr means “returning to the true self”. We congratulate this great Eid to all of the Muslims.
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At the time of the prophet Muhammad (PBUH), people did not have any instruments to accurately calculate the beginning and the end of the lunar month. For this reason, the prophet instructed a simple method to people so that they can recognize the beginning and the end of each lunar month. This simple method was based on observing the moon at the time of sunset. You should however know that the lunar calendar and the lunar month was not invented and introduced by prophet Muhammad (PBUH). He only adopted it for instructing religious rituals. The lunar month has astronomical origins. Its astronomical origins are based on the conjunction of the sun and the moon. In other words, whenever, the moon, the earth, and the sun lie on the same line, it is the beginning of the month.
When these calculations are done, if this conjunction happens before mid-day, the crescent moon will be visible at sunset in the western sky. However, if the conjunction happens after mid-day, the crescent moon will not be observable. Based on astronomical rules, if the conjunction happens before the mid-day, the next day is the beginning of the lunar month, and if the conjunction happens after mid-day, the day after the next day is considered the beginning of the lunar month. At the present-day, the best and most accurate way to determine the beginning and the end of a lunar month is by finding the exact time of the conjunction through many globally known and credible astronomical websites.
At the time of the prophet, if these tools and accurate astronomical calculations were accessible for all of the people, the prophet would recommend referring to credible websites and finding out the time of the conjunction instead of observing the crescent moon.