Rosh Chodesh
“This month shall mark for you the beginning of the months; it shall be the first of the months of the year for you."
Exodus 12:2 JPS
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Shabbat Mevarchim
Shabbat Mevarchim is any Shabbat that precedes and begins the week during which there will be a day or days of a new Hebrew month (Rosh Chodesh).
Shabbat Mevarchim (mevarchim means "they [the congregation] bless" [the forthcoming new month].")
This prayer is recited after the Torah reading before the Torah scroll is carried back to the Torah ark, where it is stored.
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Rosh Chodesh
Molad (מולד, plural Moladot, מולדות) is Hebrew and it’s meaning "birth" also refers to the time at which the New Moon is "born" or begins its new cycle and is announced based on the time in Jerusalem.
The molad is 29 days, 12 hours, and 793 chalakim (approximately 44 minutes, as a chelek is 3 1/3 seconds.) after the previous one, which is a little more than 29 and a half day.
Rosh Chodesh, the true beginning of the month is synchronous with the instant of the molad.
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Kiddush Levanah
Kiddush Levana (קִדּוּשׁ לְבָנָה), the Sanctification of the Moon, is performed once a month, during the first part of the lunar cycle.
The traditional time to say kiddush levana is after Shabbat but not before the third day (three periods of 24 hours) after the molad and up until 14 days and 18 hours after the molad. Ideal is after seven 24-hour periods.
Kiddush Levana is said outdoors at night facing east and looking into our prayerbooks, With a unobscured crescent moon visible we begin by reciting the first six verses of Psalm 148, giving praise to G‑d for the moon, sun, stars and heavens, “for He commanded and they were created.” and is often followed after Kiddush Levana by joyous dancing.