The Many Facets of Asarah B'Teves
Although to many the only notable aspect of the upcoming fast of Asarah B’Teves (the 10th of Teves) is that it is by far the shortest fast day in the Jewish calendar for anyone in the Northern Hemisphere (my heartfelt sympathies to the South Americans, So’Africans, Aussies, and Kiwis), nonetheless, the Fast of Asarah B’Teves is quite unique. For example, exclusive to this fast is that it is the only one that we do actually observe as a fast on a Friday. Even Tisha B’Av, which commemorates the actual destructions of our Batei HaMikdash, gets pushed off. Yet, obviously, to maintain this distinction of being the only Fast Day that we actually do observe on Friday, there must be much more to the Fast of Asarah B’Teves than meets the eye. In turns out that Asarah B’Teves has several exceptional characteristics that are not found in any other fast day.
Why This Fast?
The reason given for fasting on Asarah B’Teves is that it is the day that the wicked Babylonian king Nevuchadnetzar started his siege of Yerushalayim, foreshadowing the beginning of the end of the first Beis Hamikdash, which culminated with its destruction on Tisha B’Av several years later. Therefore, Chazal declared it a public fast, one of four public fast days that memorialize different aspects of the catastrophes and national tragedies associated with the destruction of both Batei HaMikdash.
Three Day Fast?
According to the special Selichos prayers said on the fast, a unique aspect of Asarah B’Teves is that we are actually fasting for two other days of tragedy as well; the 8th and 9th of Teves. In fact, both the Tur and Shulchan Aruch assert that if possible one should try to fast on all three days. Nevertheless, of the three, only Asarah B’Teves was actually mandated as a public fast day.
The 8th of Teves
On the 8th of Teves, King Ptolemy II (285 - 246 B.C.E.) forced 72 sages separately to translate the Torah into Greek (the Septuagint). Although miracles guided their work and all of the sages made the same slight but necessary amendments, nevertheless this work is described as “darkness descending on the world for three days”, as it was now possible for the uneducated to possess a superficial, and frequently flawed understanding of the Torah, as well as providing the masses with a mistaken interpretation of true morality.
The 9th of Teves
Although several decisors write that the reason for fasting on the 9th of Teves is unknown, nonetheless many sources, including the Kol Bo and the Selichos recited on Asarah B’Teves, as well as many later authorities, explain that this is the day on which Ezra HaSofer (as well as possibly his partner Nechemiah) died. Ezra, the Gadol HaDor at the beginning of the time of the Second Beis HaMikdash, had a tremendous impact upon the nascent returning Jewish community of Eretz Yisrael. He drastically improved the spiritual state of the Jewish people and established many halachic takanos, many of which still apply today. With his passing, the community started sliding from the great spiritual heights Ezra had led them. Additionally, since Ezra was the last of the prophets, his passing signified the end of prophecy.
Other sources attribute fasting on this day to the passings of other specific Tzaddikim on this day, including Shimon HaKalphus and Rav Yosef HaNaggid, or to the birth of ‘Oso HaIsh’, the founder of Christianity, in whose name myriads of Jews over the millennia were r”l murdered (see extensive footnote 8). The Sefer HaToda’ah posits that it’s possible that “the darkness descended on the world for three days” alludes to the triple woes of these three days: the 8th, 9th, and 10th of Teves.
Fasting on Friday?
Another exclusive characteristic of Asarah B’Teves is that, as mentioned previously, it is the only fast that can fall out on a Friday. This is fairly interesting as there is a whole debate in the Gemara about how to conduct fasts on a Friday, when we also must take kavod Shabbos into account, implying that it is a common occurrence. However, according to our calendar, a Friday fast is only applicable with Asarah B’Teves, and it happens quite infrequently. The last few times Asarah B’Teves fell out on a Friday were in 1996, 2001, 2010, and 2013. It is next expected to occur in 2020 (5781). After that, 2023 (5784), 2025 (5785), 2034 (5795), and 2037 (5798).
Halachos of a Friday Fast
The halachos of a Friday fast generally parallel those of a regular fast day. In fact, even though there is some debate in the Rishonim as to the Gemara’s intent that ‘Halacha - Mesaneh U’Mashlim - a Friday fast should be completed’ whether or not one may be mekabel Shabbos early and thereby end the fast before nightfall, nonetheless, the halacha follows the Shulchan Aruch and Rema that since Asarah B’Teves is a public fast (Taanis Tzibbur) and not a Taanis Yachid, one must fast the whole day and complete it at nightfall (Tzeis HaKochavim) before making Kiddush.
There are those who maintain it is preferable to daven Maariv earlier than usual on such a Friday night, to enable making Kiddush, and breaking the fast, exactly at Tzeis HaKochavim.
A Shabbos Fast?!
The third and possibly most important attribute of Asarah B’Teves is that according to the AbuDraham, if Asarah B’Teves would potentially fall out on Shabbos, we would all actually be required to fast on Shabbos! (Notwithstanding that with our calendar this is an impossibility.) He cites proof to this from the words of Yechezkel referring to Asarah B’Teves (Ch. 24, verse 2) that the siege transpired “B’Etzem HaYom HaZeh”, implying that the fast must always be observed on that exact day, no matter the conflicting occurrence. This would also explain why it is observed on Friday, as opposed to any other fast.
Yet, the AbuDraham’s statement is astounding, as the only fast that halachically takes precedence over Shabbos is Yom Kippur, the only Biblically mandated fast. How can one of the Rabbinic minor fasts push off the Biblical Shabbos? Additionally, Asarah B’Teves commemorates merely the start of the siege, and not any actual destruction. How can it be considered a more important fast than Tisha B’Av, which commemorates the destruction and loss of both of our Batei HaMikdash? In fact, the Beis Yosef questions this declaration of the AbuDraham, stating that he “does not know how the AbuDraham could know” such a ruling. As an aside, this does not seem to be the actual halacha, as other Rishonim, including Rashi and the Rambam, both explicitly state that if Asarah B’Teves falls out on Shabbos it gets pushed off.
Commencement Is Catastrophic
Several authorities, including Rav Yonason Eibeschutz and the Bnei Yissaschar, understand the AbuDraham’s enigmatic statement as similar to the famous Gemara in Taanis (29a) regarding Tisha B’Av. It seems that historically the Beis HaMikdash only started to burn toward the end of the 9th of Av (Tisha B’Av) and actually burned down on the 10th. Yet, Chazal established the fast on the 9th, since Aschalta D’Paranusah Adifa, meaning that the beginning of a tragedy is considered the worst part. Likewise, they maintain that since the siege on Asarah B’Teves was the commencement of the long chain of tragedies that ended with the Beis HaMikdash in ruins and the Jewish people in exile, its true status belies the common perception of it as a minor fast, and potentially has the ability to push off Shabbos. Indeed, the MidrashTanchumateaches that it was already fitting for the BaisHaMikdash to actually be destroyed on AsaraB’Teves, but Hashem, in His incredible mercy, pushed the destruction off to the summertime, so that we would not have to be exiled in the cold. Hence, AsarahB’Teves’s role as the ‘beginning of the end’ underlies the severity of this fast day.
The famed Chasam Sofer takes this a step further. He wrote that the reason Chazal established a fast for the siege on Asarah B’Teves, as opposed to every other time Yerushalayim was under siege over the millennia, is that on that day in the Heavenly Courtroom it was decided that the Bais HaMikdash was to be destroyed a few years hence. There is a well known Talmudic dictum that any generation in which the Beis HaMikdash has not been rebuilt is as if it has been destroyed again. Therefore, he explains, every Asarah B’Teves the Heavenly Court convenes and decrees a new Churban. He adds though that, conversely, a proper fast on Asarah B’Teves has the potential to avert future Churbanos. We are not fasting exclusively due to past calamities, but rather, similar to a Taanis Chalom, a fast for a dream, to help prevent a tragedy from occurring. [He even refers to such a fast as an oneg, a delight.] That is why the fast of Asarah B’Teves, even though it is considered a minor fast, nonetheless has the potential to possibly override Shabbos. These explanations would also certainly elucidate why we would fast on a Friday for Asarah B’Teves.
The Rambam famously exhorts us to remember the real meaning underlying a fast day. It’s not just a day when we miss our morning coffee! The purpose of fasting is to focus on the spiritual side of the day and use it as a catalyst for inspiration towards Teshuva. In this merit may the words of the Navi Zechariah, “The Fast of the Fourth (month, 17th of Tamuz), the Fast of the Fifth (month, Tisha B’Av), the Fast of the Seventh (month, Tzom Gedalyah), and the Fast of the Tenth (month, Asarah B’Teves) shall be (changed over) for celebration and joy for the household of Yehuda” be fulfilled speedily and in our days.
This article was written L'iluy Nishmas the Ohr Somayach Rosh HaYeshiva - Rav Chonoh Menachem Mendel ben R' Yechezkel Shraga, the Kedoshei Har Nof and R’ Chaim Baruch Yehuda ben Dovid Tzvi, L’Refuah Sheleimah for R’ Shlomo Yoel ben Chaya Leah, Henna Rasha bas Yitta Ratza and Rochel Miriam bas Dreiza Liba, and l’zechus Shira Yaffa bas Rochel Miriam v’chol yotzei chalatzeha for a yeshua sheleimah teikif u’miyad!
For any questions, comments or for the full Mareh Mekomos / sources, please email the author: email@example.com.
Rabbi Yehuda Spitz serves as the Sho’el U' Meishiv and Rosh Chabura of the Ohr Lagolah Halacha Kollel at Yeshivas Ohr Somayach in Yerushalayim. He also currently writes a contemporary halacha column for the Ohr Somayach website titled “Insights Into Halacha”. http://ohr.edu/this_week/insights_into_halacha/.
 See AbuDraham (Hilchos Taanis), Magen Avraham (Orach Chaim 550, 4), Ba’er Heitiv (ad loc. 4), Aruch Hashulchan (ad loc. end 2), and Mishna Ber ura (ad loc. 10).
 Melachim II (Ch. 25, verse 1), Yirmiyahu (Ch. 52, verse 4), Yechezkel (Ch. 24, verses 1 & 2).
 See Zecharia (Ch. 8, verse 19), Gemara Rosh Hashana 18b, Rambam (Hilchos Taaniyos Ch. 5, 1- 5) and Tur & Shulchan Aruch (O.C. 549 & 550).
 See the Selicha for Asarah B’Teves that starts with the word Ezkerah.
 Tur and Shulchan Aruch (Orach Chaim 580).
 Tur and Shulchan Aruch (Orach Chaim 549 & 550).
 As told at length in Gemara Megillah 9a. For a slightly different version see Maseches Sofrim (Ch. 1, 7 - 8). This quote is found in Megillas Taanis (Ch. 13); and cited by the Tur and Shulchan Aruch (Orach Chaim 580). See Sefer HaToda’ah (vol. 1, Ch. 8, Chodesh Teves, par. Yom Kasheh) at length.
 See Tur & Shulchan Aruch (Orach Chaim 580). However, many poskim, including the Ba’er HaGolah (ad loc. 4), Magen Avraham (ad loc. 6), Taz (ad loc. 1; who concludes ‘tzarich iyun rav’ on the Tur and Shulchan Aruch for not knowing that Ezra HaSofer died on that day), Elyah Rabba (ad loc. 5), Pri Megadim (ad loc. Mishbetzos Zahav 1), Ba’er Heitiv (ad loc. 6), Mishna Berurah (ad loc. 13), and Kaf Hachaim (ad loc. 20), all cite the Kol Bo (63), BeHa”G (Hilchos Tisha B’Av V’Taanis), or the Selichos of Asarah B’Teves (ibid.) that the tzara on that day is that Ezra HaSofer died. The Aruch Hashulchan (ad loc. 3) diplomatically states that originally they did not know which tragedy occurred on that day to mandate fasting, and afterwards it was revealed that it was due to Ezra HaSofer’s passing on that day. Rav Yonason Eibeschutz (Ya’aros Dvash vol. 2, 192 - 193) gives an interesting variation on this theme. He maintains that since Ezra’s role in Klal Yisrael in his time was akin to Moshe Rabbeinu’s, Chazal wanted to withhold publication of the day of his passing, similar to the Torah stating that “no one knows of Moshe’s burial place” (Devarim, V’Zos HaBracha Ch. 34, verse 6). However, the Chida (Birkei Yosef, Orach Chaim 580) points out that the statement in Megillas Taanis (and later cited by the BeHa”G) that ‘lo kasvu Rabboseinu al mah hu’ seems to be referring to a separate occurrence than its next listing, that Ezra HaSofer died on that day, and that they are not one and the same. The Chasam Sofer (Toras Moshe, Parshas Vayigash, Drush for 8 Teves s.v. kasav BeHa”G) answers that Ezra was similar to Moshe Rabbeinu, and drastically improved the spiritual state of the Jewish people, and yet, even after he died, Klal Yisrael felt satisfied and blessed simply to have been led by him when he was alive, and did not see any reason to fast on the day he died. Yet, when the Torah was later translated into Greek, enabling the “Tzaraas of the Minim”, only then did they realize the import of Ezra’s passing and established it as a fast day. Yet, previously, they did not know why to fast on the 9th of Teves. Rav Baruch Teumim - Frankel (author of the Imrei Baruch, in his glosses to Shulchan Aruch Orach Chaim 580) cites several other sources opining different tzaddikim’s passings on the 9th of Teves as the reason for fasting, including the enigmatic Shimon HaKalphus, ‘who saved Klal Yisrael during the days of the Pritzim’, and to whom ‘Nishmas’ and ‘Etein Tehilla’, a Piyut that is part of Yom Kippur liturgy, is attributed (see the Haggadah Marbeh Lesaper of Rav Yedidyah Weil, son of the Korban Nesanel, pg. 114; and Seder Avodas Yisrael, pg. 206, in the commentary to ‘Nishmas’). [Known as Patrus, it has been surmised that he was a Jewish pope, placed by Chazal to infiltrate the early Christians, to ensure that Christianity became a separate religion (see Otzar HaMedrashim [Eisenstein] pg. 557 and the Oz VeHadar edition of Gemara Avodah Zarah 10a, Haghos U’Tziyunim 30; citing an original manuscript of Rashi’s that had been censored for hundreds of years). Some opine that he was ‘Ben Patora’ mentioned in Gemara Bava Metzia 62b. Although we do find Shimon HaKalphus (or Kippa) mentioned derisively as ‘Shimon Petter Chamor’ by several Rishonim, including the Machzor Vitry (Pesach 66), and Rav Yehuda HaChassid (Sefer Chassidim 193), on the other hand and quite interestingly, while referencing the laws of the Yomim Noraim (325) the Machzor Vitry himself refers to Shimon Kippa quite approvingly, if not downright reverently. In the footnotes of the Berlin edition of the Machzor Vitry (from 1893; pg. 362, footnote 5) the editor, Rav Shimon HaLevi Ish Horowitz, posits that this is not actually an outright contradiction in the Machzor Vitry, but rather a machlokes between his mentors, Rashi and Rabbeinu Tam. He postulates that the first mention in the Machzor Vitry, that ‘Shimon Petter Chamor’ was certainly not the composer of ‘Nishmas’, and all who claim such will have to bring a Korban Chatas Shmeinah when the Beis HaMikdash will be rebuilt, was from a handwritten manuscript of Rashi’s. Conversely, the second mention, that Shimon Kippa was the one who set the order of the Yom Kippur tefillos and composed ‘Etein Tehilla’, was the opinion of Rabbeinu Tam (whom the Machzor Vitry quoted as the source of the ruling of that paragraph about allowing Piyutim and personal additions during Shemoneh Esrei), who held that Shimon Kippa’s kavanna in all that he did was exclusively Lesheim Shamayim. The Sefer Chassidim (ibid.) takes an alternate approach, explaining that even though Shimon Kippa was indeed a tzaddik, nevertheless since he was technically a meshumad, and people followed in his ways, he was called a derogatory nickname, ‘Shimon Petter Chamor’, as is the proper custom to do with meshumadim, as fulfillment of the pasuk in Tehillim (Ch. 116, 8) ‘Kemohem Yehiyu Osaihem’.] The second tzaddik’s passing on that day that Rav Teumim - Frankel cites was Rav Yosef HaLevi, son of Rav Shmuel HaNaggid, who was assassinated on the 9th of Teves in 1066, thus ending the Golden Age for Jewry in Spain. He quotes the Raavad’s Sefer HaKabbalah that ‘when Rabboseinu HaKadmonim wrote Megillas Taanis and established a fast on the 9th of Teves, they themselves didn’t know the reason. Later on, after Rav Yosef HaNaggid was assassinated we knew that they foresaw this tragedy with Ruach HaKodesh’. An additional reason for fasting on this day is cited by the Rema in his commentary to Megillas Esther (Mechir Yayin, Ch. 2, 16) that we fast on the 9th of Teves as Esther was forcibly taken to Achashveirosh’s palace in the month of Teves (possibly on this day). Interestingly, some posit [as heard in the name of Rav Moshe Shapiro shlit”a; also found in the Davar B’Ito calendar (9 Teves) and in Netei Gavriel (Hilchos Chanuka, Inyanei Nittel, pg. 416; quoting the Tosafos Chadashim on Megillas Taanis)] that the real reason for fasting is that the 9th of Teves is the true birthday of ‘Oso HaIsh’, in whose name myriads of Jews over the millennia were r”l murdered. The origin of this claim seems to be the 12th century Sefer HaIbur by Rav Avraham bar Chiya (pg. 109). In fact, the Netei Gavriel (ibid.) cites that some say that Nittel, the name used for the Christian December holiday, actually stands for Nolad Y eishu T es L’Teves. [The author wishes to thank his talmid, R’ Yitzchak Goodman, as well as Rabbi Eliezer Brodt, for pointing out several of these invaluable sources.]
 As found throughout Shas - see for example Bava Kama (82a) and Kesuvos (3a).
 Sefer HaToda’ah (vol. 1, Ch. 8, Chodesh Teves, end par. Yom Kasheh).
 Gemara Eiruvin 41a.
 However, even those who advise not to bathe on a regular fast day, nevertheless allow one to do so on a Friday fast L’Kavod Shabbos, with hot water as usual [see Bach (Orach Chaim 550, 3; although cited by both the Ba’er Heitiv and Mishnah Berurah as the source for this rule, nevertheless, this author has been unable to locate where exactly the Bach states an explicit Erev Shabbos exception for bathing), Elya Rabba (ad loc. 2), Ba’er Heitiv (ad loc. 3), Shu”t Ksav Sofer (Orach Chaim 100), Shulchan HaTahor (249, 4), Mishnah Berurah (ad loc. end 6), and Shu”t Siach Yitzchak (247)].
 Although the Gemara (Eruvin 41a; also in Midrash Tanchuma, Bereishis 2) concludes ‘Halacha - Mesaneh U’Mashlim’, even so there are many Rishonim (most notably Tosafos ad loc. 41b s.v. v’hilchasa) who understand that to mean that one may conclude his Erev Shabbos fast at Tzeis HaKochavim, even though it means he will enter Shabbos famished (a situation that is normally disfavored), and not that one must conclude his fast on Friday night at Tzeis HaKochavim. A further complication is that this also may depend on whether one is fasting for personal reasons (Taanis Yachid) or an obligatory public fast (Taanis Tzibbur). The Rema (Orach Chaim 249, 4) concludes that for a Taanis Yachid one may rely upon the lenient opinions and end his fast after he accepted Shabbos, prior to Tzeis HaKochavim (especially if he made such a stipulation before commencing his fast), yet for a Taanis Tzibbur, he rules that we follow the Rishonim who mandate strict interpretation of the Gemara, and we must fast until actual nightfall on Friday night. It is debatable whether the Shulchan Aruch is actually fully agreeing with this approach or not. See explanation of the Mishnah Berurah (ad loc. 21 and Biur Halacha s.v. v’im) at length. This has since become normative halacha. See next footnote.
 See Shulchan Aruch and Rema (Orach Chaim 249, 4), based on the Rosh (Taanis Ch. 2, 4) and Maharil (Shu”t 33); Magen Avraham (ad loc. 8), Bach (ad loc. end 6), Ba’er Heitiv (ad loc. 7), Elya Rabba (ad loc. 10), Korban Nesanel (Taanis, end Ch. 2, 60), Shulchan Aruch HaRav (ad loc. 12), Kitzur Shulchan Aruch (121, 6), Ben Ish Chai (Year 2, Parshas Lech Lecha 23), Aruch Hashulchan (ad loc. 10), Mishna Berura (ad loc. 21 and Biur Hal acha s.v. v’im), Kaf Hachaim (ad loc. 29 & 31), Shu”t Yabea Omer (vol. 6, Orach Chaim 31), Shu”t Yechaveh Daas (vol. 1, 80), Netei Gavriel (Hilchos Chanuka, Shu”t 14), Yalkut Yosef (Kitzur Shulchan Aruch, Orach Chaim. 249, 7 & 559, 25), and Rav Mordechai Eliyahu’s Darchei Halacha glosses to the Kitzur Shulchan Aruch (121, 5). The Netei Gavriel adds that B’shaas Hadchak and l’tzorech gadol one may be mekabel Shabbos early and rely on the lenient opinions, as long it is after nightfall according to several opinions (meaning, a much earlier zeman of Tzeis HaKochavim than the faster would usually observe).
 See Shulchan HaTahor (Orach Chaim 249, 13) who writes that usually it is assur to complete a Friday fast until Tzeis HaKochavim, even an obligatory fast, as it is an affront to Kedushas Shabbos; rather, he maintains that one should be mekabel Shabbos early and have his seudah before nightfall. Yet, in his explanations (Zer Zahav ad loc. 4) he maintains that regarding Asarah B’Teves on Friday, since we are beholden to follow the ruling of the Rema, one should still be mekabel Shabbos early, and daven earlier than usual, to enable us to end the fast with making Kiddush at the exact zeman of Tzeis HaKochavim.
 AbuDraham (Hilchos Taanis), cited with some skepticism by the Beis Yosef (Orach Chaim end 550). Rashi (Megillah 5a s.v aval) and the Rambam (Hilchos Taaniyos Ch. 5, 5) both explicitly state that if Asarah B’Teves falls out on Shabbos then it gets pushed off. Similarly, the Ibn Ezra, in his famous Shabbos Zemer ‘Ki Eshmera Shabbos’ explicitly states that Yom Kippur is the only fast that can override Shabbos. This is how the Shulchan Aruch (Orach Chaim 550, 3), as well as later poskim [see, for example, Shu”t Shoel U’Meishiv (Mahadura Kama vol. 3, 179), Shu”t Maharam Brisk (vol. 3, 99), and Aruch Hashulchan, Orach Chaim 549, end 2], rule as well. However, there are many who do defend the AbuDraham’s statement based on the verse “B’Etzem HaYom HaZeh”. [In fact, there is even a minority opinion (see Toras Chaim - 550, 4) who is choshesh for the Abudraham and therefore holds that one should not treat Asarah B’Teves as a minor fast, but rather with similar restrictions as the major fasts.] The Minchas Chinuch (Parshas Emor, Mitzva 301, 7), explaining why nowadays we do not observe fast days for two days (as opposed to other Yomim Tovim, due to the safek yom), writes that the Neviim established fast days in specific months, but did not set the actual day it must be observed, hence the ambiguity in the Gemara which days to observe them. Since they were never established as being mandated on one specific day, they are unaffected by the safek yom, and nowadays only one day must be observed. A similar assessment regarding the establishment of fast days was actually expressed by several Rishonim, including the Ritva (Rosh Hashana 18b s.v. v’ha) and Tashbatz (Shu”t vol. 2, 271). Rav Chaim Soloveitchik of Brisk (Chiddushei HaGra”ch V’HaGri”z al Shas, ‘Stencils’, pg. 27, 44) takes this a step further to explain the AbuDraham’s statement (although quite curiously, he inexplicably credits the BeHa”G with this statement, who in fact makes no mention of this; and does not mention the AbuDraham). He asserts that Asarah B’Teves is the exception to this rule of the Neviim’s ambiguity of exact day, since it is stated about it that it must be observed “B’Etzem HaYom HaZeh”, and therefore would be fasted upon even if it fell on Shabbos. Similarly, the Ohr Somayach (Hilchos Taaniyos Ch. 5, 6 s.v. v’hinei, in the brackets) defends the AbuDraham’s statement, based on a diyuk in the Gemara’s (Eruvin ibid.) choice of question about a Taanis Yachid on Friday, with no mention of a Taanis Tzibur. He posits that the reason the Gemara did not cite such a case is that Asarah B’Teves is the only Taanis Tzibur that can fall out on Friday, and if it can override Shabbos due to “B’Etzem HaYom HaZeh”, then certainly one would be required to fast the whole Friday for it! For more on this fascinating topic see Minchas Asher (Moadim vol. 2, Tzomos, 43).
 According to our calendar Asarah B’Teves cannot fall out on Shabbos. The AbuDraham (Hilchos Taanis) himself mentions this, as does the Magen Avraham (Orach Chaim 550, 4 & 5), Ba’er Heitiv (ad loc. 3), Aruch Hashulchan (ad loc. 2), and Mishnah Berurah (ad loc. 8). Everyone can easily make this calculation themselves. See Shul chan Aruch (Orach Chaim 128, 2) regarding which days various Roshei Chodesh can fall out on. For the month of Teves, Rosh Chodesh cannot fall out on a Thursday. That means Asarah B’Teves, ten days later, cannot fall out on Shabbos!
 Ya’aros Dvash (Vol. 1, Drush 2 for 9 Teves, 32 - 33; see also vol. 2, 191 - 193 s.v. v’hinei yadua), Bnei Yisaschar (Maamrei Chodesh Kislev / Teves 14, 1), and Shu”t Shoel U’Meishiv (Mahadura Kama vol. 3, 179); see also Shu”t Maharam Brisk (vol. 3, 99). The Chasam Sofer (Toras Moshe, Parshas Vayigash pg. 40b s.v. vad”z) also cites this reason and explains that it is only at the end of a tragedy when salvation has a chance to sprout. We see this from the famous Gemara at the end of Makkos (24a - b) with Rabbi Akiva, who laughed when he saw foxes wandering through the ruins of the Beis HaMikdash. Only when a tragedy is complete can there be a glimmer of hope for the future redemption. See also sefer Siach Yitzchak (pg. 293) and R’ Moshe Chaim Leitner’s sefer Tzom Ha’Asiri at length. Rav Yonason Eibeschutz adds that according to his calculations, Nevuchadnetzar’s actual siege on that first Asarah B’Teves commenced on Shabbos; meaning that that Asarah B’Teves that Yechezkel wrote “B’Etzem HaYom HaZeh” about was actually Shabbos. The Chasam Sofer (Toras Moshe, Parshas Vayechi, Drush for 8 Teves 5599, s.v. ksiv) agrees with this assessment and offers a variation, that the reason Nevuchadnetzar was successful in his conquest of Yerushalayim, as opposed to Sancheirev, was due to lack of Shemiras Shabbos among its inhabitants!
 Midrash Tanchuma (Tazria 9). However, see Midrash Tanchuma (Bereishis 2 & 3), who actually takes a very strong stance against fasting on Shabbos, as ‘Kavod Shabbos is adif than one thousand fasts’!
 Toras Moshe (vol. 2, Parshas Vayikra, Drush for 7 Adar, pg. 9b - 10a, s.v. kasuv).
 Yerushalmi Yoma (Ch. 1, 1, 6a).
 Rambam (Hilchos Taaniyos Ch. 5, 1); see also Mishnah Berurah (549, 1).
 Zecharia (Ch. 8, verse 19).
Disclaimer: This is not a comprehensive guide, rather a brief summary to raise awareness of the issues. In any real case one should ask a competent Halachic authority.
L'iluy Nishmas the Rosh HaYeshiva - Rav Chonoh Menachem Mendel ben R' Yechezkel Shraga, Rav Yaakov Yeshaya ben R' Boruch Yehuda, and l'zchus for Shira Yaffa bas Rochel Miriam and her children for a yeshua teikef u'miyad!