Rosh Hashanah begins at sundown on Sept 12th.
The new moon can be seen on Sept 11th but at a certain of the day the crescent may be visible. Here is a better explanation of it than I can give:
The new moon occurs when, from the point of view of the Earth, the moon is between the Earth and the Sun. If it's in a direct line there's a solar eclipse. At the exact moment if new moon, the lunar disc is totally dark.
This occurred at 14h45 UAE time on Friday 22nd September. The new moon occurs at the same time everywhere.
As the Earth rotates, it causes the Sun and Moon to apparently track across the sky from east to west. Sunset in Dubai was at around 18h15 on Friday. And moonset was at 18h12. The Sun and Moon are more or less in line, so at a New Moon sunset and moonset must occur at the same time
Now, because of the Moon's monthly orbit, every day at sunset the moon is slightly higher in the sky. Around 13 degrees higher, in fact. So as the Sun and Moon go out of line, the crescent starts to show. If the New Moon is only a few hours old the cresent will be very tiny. Sunlight is so much brighter than the Moon, so unless the crescent is fairly large and/or the sun has set, it is very difficult to see the moon at all.
For the purposes of declaring the start of a new lunar month, it must be possible to see the crescent just before the Moon drops below the western horizon.
I have already noted that last Friday moonset in the UAE was 3.5 hours after new moon. An observer further west, say in Riyadh or Cairo, would get sunset (and moonset) a couple of hours later, meaning that the lunar crescent has chance to get that little bit bigger and therefore more observable.
According to The Dubai Astronomy Group 11 Sept is the date of the New Moon and Sept 11th and 12th is the date of the New Crescent. Ramadan officially starts at the sighting of the New Crescent.
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