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During the beginning of the lunar month the moon is situated between the earth and the sun, thus causing the illuminated side of the moon to face away from the earth. A few days into the new month, the moon makes it's appearance gradually until it reaches it's fullness, when it then wanes again. Our Sages instituted that upon seeing the moon at it's first stages after renewal one is to recite a blessing called Birkat Halevana (Hebrew: ברכת הלבנה, tran. Blessing of The Moon), or Kiddush Levana (Hebrew: קידוש לבנה, trans. Sanctification of the Moon).
This monthly ritual is performed outdoors at night in the first half of the month, in which this blessing along with a series of additional prayers are recited for the new moon.
The source of this blessing appears in the Talmud (Sanhedrin 42a) where the sages equate one who blesses the new moon on its proper time to one who greets the Divine Presence. The commentators explain that by reciting this blessing of the new moon, one in essence recalls that it is God who created the universe, and this realization in turn is tantamount to experiencing the Divine Presence.
- Since this blessing is involves the greeting of the Divine Presence, it is most proper, when possible, that it's recital be in standing.  When not feasible (eg. elderly or sick persons) this blessing may be recited in a sitting position.
- It is also preferable, when possible, that this blessing not be recited indoors, but rather outdoors under the open skies, as is the way to go out toward to greet one of prominent stature.  Preferably one should also not be positioned beneath a roof or overhang. When not feasible, this recommended condition may be waived, provided the moon's illumination is still visible indoors to the reciter (eg. through a window or door). 
- It is proper to be well clothed with dignity, as one would dress before greeting one of prominent stature. Some have the custom to clothe themselves with their special Shabbat garments, even when reciting this blessing during an ordinary weekday.
When It Should Be Said
The Molad for Tevet 5781 is 5:34pm Jerusalem time on Wednesday 13th January 2021 and the latest time for kiddush levana for Sephardim is 5:34pm Jerusalem time on Thursday 28th January 2021 and for Ashkenazim 11:56am Jerusalem time on Thursday 28th January 2021.
- According to Ashkenazim, one may say the Bracha 3 days after the molad, however according to Sephardim, in general one should wait until 7 days after the molad. For this halacha, days are counted by 24 hour periods. It’s proper to wait until Motzei Shabbat (Saturday night) to say Birkat HaLevana. 
- During the month of Tishrei, Birchat Levana isn't said prior to Yom Kippur. Rather it should be said right after Yom Kippur.
- During the month of Av, most have the minhag not to say Kiddush Levana prior to Tisha BeAv. Some say that it shouldn't be said right after Tisha BeAv, but in the next few days.
- One may say Birkat HaLevana until 15 days after the molad, however, on the 16th day one should say it without Shem UMalchut. Some say that one may only say it until 14¾ days after the molad.  A chart of the time of the upcoming molads is printed here (see note for calculation):
- The strict halacha allows saying birkat halevana on Shabbat and Yom Tov, but since the kabbalists recommend against it one shouldn't do it unless one is running out of time to say it.
Looking at the moon
- One should look at the moon prior to saying the Bracha. Some hold that one should only look at the moon once and not look at it again, whereas others are lenient to allow looking at it anytime during the Seder of Birkat HaLevana except during the Bracha itself. 
- If one made Birkat HaLevana without looking at the moon but said it as part of the tzibbur, one fulfills their obligation bedieved.
- The text of this blessing as appears in the Talmud, reads: Blessed are you God.. Who with his utterance created the heavens.. Who renews the months, etc. In this blessing we express our recognition of God awesome power over the universe. As such, one should be vigilant to recite this blessing with full intent, devotion and elation.  It is customary to also recite additional appropriate texts and passages, the "Shalom Aleichem" greeting  and the "Aleinu" prayer .
- The phases of the moon are equated to the Davidic dynasty, where we are confident that our nation's "diminished" power will soon end and its light will soon illuminate to fullness. It is therefore the custom to recite the verse "David, King of Israel, is alive and enduring". Some communities then follow the recital of this verse with the recital of the word "Amen", three times. (These verses are repeated three times in order to give emphasis to this special message.) One should make sure to pause between each Amen unless one is saying it in private in which case one doesn’t need to pause. 
- Women are exempt from Birkat HaLevanah. Even though Ashkenazic women usually are permitted to volunteer to make a bracha even when they are exempt, the minhag is that they don't say Birkat HaLevanah. Others argue that they should really recite it.
- Blind men should recite birkat halevana even though they cannot see the moon.
- Ashkenazic text of Kiddush Halevana: Wikisource.org.
- Sephardic text of Birchat Halevana: Sefaria.org
- Some Ashkenazic greats termed this blessing "Kiddush Halevana, see for instance Maharil (Rosh Chodesh, Siman 9) and Rama 426:2. Rabbi Yosef Qafih (The Guide for the Perplexed, 2:5 fn. 15) however, writes that the name "Birkat Halevana" is more correct as that is what is found in all earlier sources. See Hegyonei Haparsha Shemot (p. 132) who documents that the Or Zaruah (456), Shibolei Haleket (167) and Tur (426) all use the title Birkat Halevana, as opposed to the Eshkol (Birchot Hodah 23:3) and Maharil (Rosh Chodesh) who termed it Kiddush Levana. In explaining the term this latter term, he cites the To'ameha Chaim (37) who brings that Midrash Rabba (Shemos Rabba 15) states that God gave the Jewish people the moon as his betrothal gift, with that he explains that this term highlights the relationship between God and the Jewish people which is comparable to an Halachic marriage, kiddushin.
- Sanhedrin 42a. See Divrei Yatziv (Orach Chaim 278) for a discussion as to why this blessing is only first introduced here.
- Levush (426:1) explains that this blessing was specifically designated to the moon over other stars or planets because it is the moon that is closest to us on earth, easily enabling us to constantly recognize God's control over the universe. Aruch Hashulchan 426:2 also cites this reason. C.f. Sefer Hachinuch 403 for a similar idea. Alternatively, Hegyonei Haparsha (Shemot p. 133) quotes To'ameha Chayim (Rosh Chodesh n. 8) that the moon is awarded this blessing as an appeasement for it's minimization by God at the beginning of creation (See Rashi Beresheet 1:16).
- Gemara Sanhedrin 42a, Shulchan Aruch 426. The Gemara relates that Mereimar and Mar Zutra in their later years would be supported by their attendants in order to recite this blessing while standing, see Rashi there.
- Shiltei Ha'giborim (Berachos 189:3), Bach 426 and Responsa Teshuvos Ha'bach (no. 80)
- Rama 426:4 with Mishnah Brurah (21). Orchos Rabbenu (v. 1 p. 178) however, brings from the Chazon Ish that this optimal condition is only to refrain from it's recital in indoor structures, but once outside one may recite the blessing under an overhang. See Responsa Yaskil Avdi for a discussion on it's recital under a tree's branch, and Mishnah Berura Dirshu (42) regarding it's recital under an umbrella.
- Bach 426 with Mishnah Berurah (21).
- Shulchan Aruch 426:4 writes that one shouldn’t say Birkat Halevana until 7 days have passed from the molad based on the Shaarei Orah. However, the Bach 426 rules like the Rabbenu Yonah who says that one may say it after 3 days. Taz 426:3, Magen Avraham 426:13, Aruch HaShulchan 426:13, and Mishna Brurah 426:20 agree with the Bach. Sh”t Yabia Omer 6:38(1) rules like Shulchan Aruch but adds that if Motzei Shabbat is a few hours less than 7 days one may say it and in places where majority of the month is cloudy one may say it after 3 days. Mishna Brurah 426:17 clarifies that for this halacha days are counted as 24 hour periods and not from sunset to sunset.
- Masechet Sofrim 19:10 (in some versions 20:1) writes that one should say Birkat HaLevana specifically on Motzei Shabbat. However, Rabbenu Yonah (Brachot 21a) quotes some who say this, rejects it, and concludes that one can say it anytime after 3 days. Bet Yosef 426:2 writes that probably Rabbenu Yonah didn’t have this girsa in Maasechet Sofrim. S”A 426:2 rules that one should say Birkat HaLevana on Motzei Shabbat. However, the Biur HaGra 426:2 cites the Gemara Yevamot 39a which says that we don’t delay performing Mitzvot. The Mishna Brurah 426:20 rules that it’s proper to wait until Motzei Shabbat but there is what to rely on to say it earlier and in the winter and rainy months those who are zealous to say it early are praiseworthy. Rama 426:2 writes that if Motzei Shabbat is the 11th night from the molad one doesn’t have to wait until Motzei Shabbat because it’s possible it will be cloudy the following 4 nights.
- Rama 426:2. The Beiur Halacha (sham d"h v'lo kodem), however, does quote the opinion of the Levush that by Yom Kippur, as opposed to Tisha B'Av, kiddush levana SHOULD be said BEFORE Yom Kippur as even one merit (one mitzvah) may tip the scales towards the positive during this period of judgement. He notes that this seems to be the opinion of the Beis Meir as well
- Rama 426:2, 551:8
- Rama 426:2, Mishna Brurah 426:10. However, Ish Matzliach footnote 3 on the Mishna Brura says that the minhag is most places is to say it on Motzaei Tisha B'av
- Shulchan Aruch 426:3 rules like the opinion of Nehardai in Gemara Sanhedrin 41b who say that one has 15 complete days. Chazon Ovadia Chanuka p. 349 agrees unlike the opinion of the Rav Poalim. However, the Rama 426:3 writes that one may only say it up to half of 29 days, 12 hours, and 793 chalakim. Beiur Halacha s.v. VeLo writes that if one is in such a situation where half of 29 days, 12 hours, 793 chalakim passed and 15 days have not, there is what to rely on to say the Bracha. Beiur Halacha adds that if it’s the 16th day one should say it without Shem UMalchut. Sh”t Yabia Omer 6:38 agrees with the Beiur Halacha that on the 16th day one should say it without Shem UMalchut.
- Rambam (Kiddush HaChodesh 6:3) writes that from one Molad (the astronomical time when the new moon can be seen) to another is 29 days, 12 hours, and 793 chelakim (and there's 1080 chelakim in an hour). The Rambam 6:8 also writes that the time with which to begin to calculate the Molads from the beginning of creation is the 2nd day, 5 hours, and 204 chelakim. To calculate the Molad of Rosh Chodesh Tishrei 5773, first let us calculate the number of months which passed from creation and then add the appropriate time for each month. Although there are 12 months in a regular year because there are 7 leap years in a 19 year cycle, there is an average of 12.3684 lunar months a year. By Tishrei 5773, 5772 complete years have passed, meaning that 71390 complete months have passed since creation. The chelakim for the molad of Tishrei 5773 should be 1034 (i.e. 204 + (71390 * 793) modulo 1080) which is equal to 57 minutes and 8 chelakim. Making similar calculations leads to conclude that the Molad for Tishrei 5773 is 1am (i.e. 5+12*71390+(204+71930*793-1034)/1080) mod 24 starting from 6pm) Sunday (i.e. 2+1*71390+(909103-37879)/24 mod 7). The other months can then be calculated from that starting point by either adding or subtracting the interval for each month (1 day, 12 hours, 793 chelakim. To confirm these calculations, one can check the Chabad.org page of Molad times.
- The Rashba (responsa 4:48) quotes someone who said that it is forbidden to say birkat halevana on Friday night since it is like travelling out of the techum above ten tefachim. The Rashba doesn't understand that opinion. He argues that there is no techum above ten tefachim and also it is greeting Hashem and not the moon; therefore, it isn't at all like travelling out of the techum and is permissible to be recited on Shabbat. The Mishna Brurah 426:12 rules that it is permissible to say kiddush levana on Shabbat and Yom Tov if it is necessary. In the Shaar Hatziyun 426:12 he adds a reason that everyone can agree with; since it is a mitzvah filled with happiness a person might come to dance and it is forbidden to dance on Shabbat.
- *Shulchan Aruch 426:2 writes that one should look at the moon prior to making the Bracha. Magen Avraham 426:8 quotes the Shlah who says that one should only look once and then it’s forbidden to look again (for Kabbalistic reasons). Shaarei Knesset HaGedolah 426:5 quotes the Sefer Charedim that one may only look at the moon at the time of the Bracha.
[However, the Sefer Charedim 45:5 actually writes that one may not look at the moon just like one may not look at a rainbow (and doesn’t mention anything about the Bracha). Thus, the Birur Halacha (Rabbi Yechiel Zilber, vol 5, pg 121) explains that the Sefer Charedim probably agrees with the Shlah.]
- However, Shaarei Knesset HaGedolah writes that the minhag is look at the moon during the entire Seder and it’s supported by the language of Maasechet Sofrim quoted by the Tur and S”A. Birur Halacha (vol 5, pg 122) writes that if one is looking at the moon in order to recognize Hashem’s wonders then it’s permissible.
- Mishna Brurah 426:13 quotes these three opinions and doesn’t give a ruling. The Aruch HaShulchan 426:5 writes that the minhag is like the Shlah. The Ben Ish Chai (Vayikra(2) 23), Kaf HaChaim Palagi 35:4, Kaf HaChaim Sofer 426:34, Mekor Chaim 426:2, Chesed Alafim 426:4, Yosef Ometz 474, Chida in Moreh Etzbah 6:186, Birkat Eitan (Birkat Levana pg 207), Yalkut Yosef (Birkat Levana pg 146), and Ateret Paz (Birkat Levana pg 65) agree.
- Birkat Eitan (Birkat Levana pg 200), Sefer Kiddish Levana (2 note 20) in name of Rav Elyashiv, Halichot Shlomo 15:13, Even Yisrael 426:1, Sh"t Shevet HaLevi Y"D 5:125(4)
- Sanhedrin 42a, Shulchan Aruch 426:1
- Ben Ish Chai (Vayikra 26) and More Be'ezbah 187
- Levush (426) explains that this greeting is included after the recital of this blessing, for after having greeted the Divine Presence, we then joyously bless one another.
- Mishnah Berurah 426. We recite this prayer after our greeting of the moon, to declare that this ritual is not to be interpreted as idolatrous heavenly worship, God forbid.
- *Yerushalmi (Megillah 4:10) says that one shouldn’t say Amen Amen just like one shouldn’t say Shema Shema. This is quoted by the Ohel Moed (Kriyat Shema 1:7). Bet Yosef 61 writes that he doesn’t know what the source of the Ohel Moed is and challenges this because there are pesukim with the words Amen VeAmen.
- Pri Chadash 61:12 answers that in the pesukim it’s permitted if one pauses between the two words Amen. Korban HaEdah (Megillah 4:10) writes that in a congregation it’s forbidden but the pesukim were said in private and then it’s permitted. Kiseh Eliyahu 61:3 and Yabia Omer 10:5 agree. Yaavetz (Mor UKesiyah 61) argues that the Yershalmi is against the Bavli it is totally permissible to say Amen Amen.
- Yabia Omer 10:5 concludes that when saying Amen Amen Amen in Birkat Halevana one should pause between each Amen. This is also the ruling of Kaf HaChaim 61:43.
- Sh"t Ateret Paz (vol 4 Chap 10 #37), Magen Avraham 426:1, Sh"t Haelef Licha Shlomo OC 193
- Rav Soloveitchik (cited in Nefesh Harav pg. 176)
- Mishneh Brura 426:1