Rambam - 1 Chapter a Day - Daily Torah Study

1The mean distance traveled by the sun in one day—i.e., in twenty-four hours—is 59 minutes and 8 seconds; in symbols 59’ 8”.1 Thus, in ten days, it travels 9 degrees, 51 minutes and 23 seconds,2 in symbols 9° 51’ 23”. In one hundred days, it travels 98 degrees, 33 minutes and 53 seconds, in symbols 98° 33’ 53”. The remainder of the degrees traveled by the sun over the course of one thousand days—after all the multiples of 360 have been subtracted, as explained3 —is 265 degrees, 38 minutes and 50 seconds, in symbols 265° 38’ 50”. The remainder of the degrees traveled by the sun over the course of ten thousand days is 136 degrees, 28 minutes and 20 seconds, in symbols 136° 28’ 20”.אמַהַלַךְ הַשֶּׁמֶשׁ הָאֶמְצָעִי בְּיוֹם אֶחָד שֶׁהוּא אַרְבַּע וְעֶשְׂרִים שָׁעוֹת, תִּשְׁעָה וַחֲמִשִּׁים חֲלָקִים וּשְׁמוֹנֶה שְׁנִיּוֹת - סִימָנָם נ"ט ח'. נִמְצָא מַהֲלָכָהּ בַּעֲשָׂרָה יָמִים, תֵּשַׁע מַעֲלוֹת וְאֶחָד וַחֲמִשִּׁים חֲלָקִים וְשָׁלוֹשׁ וְעֶשְׂרִים שְׁנִיּוֹת - סִימָנָם ט' נ"א כ"ג. וְנִמְצָא מַהֲלָכָהּ בְּמֵאָה יוֹם, שְׁמוֹנֶה וְתִשְׁעִים מַעֲלוֹת וּשְׁלוֹשָׁה וּשְׁלוֹשִׁים חֲלָקִים וְשָׁלוֹשׁ וַחֲמִשִּׁים שְׁנִיּוֹת - סִימָנָם צ"ח ל"ג נ"ג. וְנִמְצָא שְׁאֵרִית מַהֲלָכָהּ בְּאֶלֶף יוֹם, אַחַר שֶׁתַּשְׁלִיךְ כָּל שְׁלוֹשׁ מֵאוֹת וְשִׁשִּׁים מַעֲלוֹת כְּמוֹ שֶׁבֵּאַרְנוּ, מָאתַיִם וְחָמֵשׁ וְשִׁשִּׁים מַעֲלוֹת וּשְׁמוֹנָה וּשְׁלוֹשִׁים חֲלָקִים וַחֲמִשִּׁים שְׁנִיּוֹת - סִימָנָם רס"ה ל"ח נ'. וְנִמְצָא שְׁאֵרִית מַהֲלָכָהּ בַּעֲשֶׂרֶת אֲלָפִים יוֹם, מֵאָה שֵׁשׁ וּשְׁלוֹשִׁים מַעֲלוֹת וּשְׁמוֹנָה וְעֶשְׂרִים חֲלָקִים וְעֶשְׂרִים שְׁנִיּוֹת - סִימָנָם קל"ו כ"ח כ'.

In this manner, one can multiply the mean distance of a day and calculate the distance traveled by the sun over any number of days. Similarly, if one would like to make pre-calculated figures for the mean distance for two days, for three days, for four days, up to ten days, one may do so. Similarly, if one desires to make pre-calculated figures for the mean distance for twenty days, for thirty days, for forty days, until one hundred days, one may do so. These figures become evident once one knows the mean distance for a single day.וְעַל הַדֶּרֶךְ הַזֶּה תִּכְפֹּל וְתוֹצִיא מַהֲלָכָהּ לְכָל מִנְיָן שֶׁתִּרְצֶה. וְכֵן אִם תִּרְצֶה לַעֲשׂוֹת סִימָנִין יְדוּעִים אֶצְלְךָ לְמַהֲלָכָהּ לִשְׁנֵי יָמִים, וְלִשְׁלוֹשָׁה, וּלְאַרְבָּעָה, עַד עֲשָׂרָה - תַּעֲשֶׂה. וְכֵן אִם תִּרְצֶה לִהְיוֹת לְךָ סִימָנִין יְדוּעִים מוּכָנִין לְמַהֲלָכָהּ לְעֶשְׂרִים יוֹם, וְלִשְׁלוֹשִׁים, וּלאַרְבָּעִים, עַד מֵאָה - תַּעֲשֶׂה. וְדָבָר גָּלוּי הוּא וְיָדוּעַ, מֵאַחַר שֶׁיָּדַעְתָּ מַהַלַךְ יוֹם אֶחָד.

It would be proper for one to know and have prepared the mean distances traveled by the sun in 29 days, and in 354 days, the latter being the number of days in a lunar year when the months follow a regular pattern. This is called a regular year.4וְרָאוּי הוּא לִהְיוֹת מוּכָן וְיָדוּעַ אֶצְלְךָ, מַהַלָךְ אֶמְצַע הַשֶּׁמֶשׁ לְתִשְׁעָה וְעֶשְׂרִים יוֹם; וְלִשְׁלוֹשׁ מֵאוֹת וְאַרְבָּעָה וַחֲמִשִּׁים יוֹם, שֶׁהֵן יְמֵי שְׁנַת הַלְּבָנָה בִּזְמָן שֶׁחֳדָשֶׁיהָ כְּסִדְרָן - וְהִיא הַנִּקְרֵאת 'שָׁנָה סְדוּרָה'.

When you have these figures prepared, it will be easy to calculate the visibility of the moon. For there are 29 full days from the night when the moon was sighted in one month to the night that it may be sighted in the following month. Similarly, each and every month, there will be a difference of 29 days between the nights on which the moon may be sighted, no more and no less.5 This is what concerns us, for our sole desire in these calculations is to know when the moon will be sighted.6שֶׁבִּזְמָן שֶׁיִּהְיוּ לְךָ אֶמְצָעִיּוֹת אֵלּוּ מוּכָנִין, יִהְיֶה הַחֶשְׁבּוֹן קַל עָלֶיךָ לִרְאִיַּת הַיָּרֵחַ, לְפִי שֶׁתִּשְׁעָה וְעֶשְׂרִים יוֹם גְּמוּרִים מִלֵּיל הָרְאִיָּה עַד לֵיל הָרְאִיָּה שֶׁל חֹדֶשׁ הַבָּא. וְכֵן בְּכָל חֹדֶשׁ וְחֹדֶשׁ אֵין פָּחוֹת מִתִּשְׁעָה וְעֶשְׂרִים יוֹם וְלֹא יָתֵר, שֶׁאֵין חֶפְצֵנוּ בְּכָל אֵלּוּ הַחֶשְׁבּוֹנוֹת אֶלָא לָדַעַת הָרְאִיָּה בִּלְבָד.

Similarly, the difference in the sun’s position between the night when the moon will be sighted in a particular month one year and the night when it will be sighted in that month the following year will be that of a regular year, or that of a regular year plus one day.7וְכֵן מִלֵּיל הָרְאִיָּה שֶׁל חֹדֶשׁ זֶה עַד לֵיל הָרְאִיָּה לְאוֹתוֹ הַחֹדֶשׁ לַשָּׁנָה הַבָּאָה, שָׁנָה סְדוּרָה אוֹ שָׁנָה וְיוֹם אֶחָד. וְכֵן בְּכָל שָׁנָה וְשָׁנָה.

The mean distance traveled by the sun in one month is 28 degrees, 35 minutes and one second, in symbols 28° 35’ 1”. The distance it travels over the course of a regular lunar year is 348 degrees, 55 minutes and 15 seconds, in symbols 348° 55’ 15”.וּמַהְלַךְ הַשֶּׁמֶשׁ הָאֶמְצָעִי לְתִשְׁעָה וְעֶשְׂרִים יוֹם, שְׁמוֹנֶה וְעֶשְׂרִים מַעֲלוֹת וַחֲמִשָּׁה וּשְׁלוֹשִׁים חֲלָקִים וּשְׁנִיָּה אַחַת - סִימָנָן כ"ח ל"ה א'. וּמַהֲלָכָהּ לְשָׁנָה סְדוּרָה, שְׁלוֹשׁ מֵאוֹת וּשְׁמוֹנֶה וְאַרְבָּעִים מַעֲלוֹת וַחֲמִשָּׁה וַחֲמִשִּׁים חֲלָקִים וְחָמֵשׁ עֶשְׂרֵה שְׁנִיּוֹת - סִימָנָן שמ"ח נ"ה ט"ו.

2There is one point in the orbit of the sun around the Earth—and similarly, in the orbits of the remainder of the seven stars around the Earth—when the sun or that star will be furthest removed from the Earth.8 With the exception of the moon, that point in the orbit of the sun and, similarly, in the orbit of the other planets rotates in a uniform pattern, traveling about one degree in seventy years.9בנְקֻדָּה אַחַת יֵשׁ בְּגַלְגַּל הַשֶּׁמֶשׁ, וְכֵן בִּשְׁאָר גַּלְגַּלֵּי הַשִּׁבְעָה כּוֹכָבִים, בְּעֵת שֶׁיִּהְיֶה הַכּוֹכָב בָּהּ, יִהְיֶה גָּבוֹהַּ מֵעַל הָאָרֶץ כָּל מְאוֹדוֹ. וְאוֹתָהּ הַנְּקֻדָּה שֶׁל גַלְגַּל הַשֶּׁמֶשׁ וּשְׁאָר הַכּוֹכָבִים חוּץ מִן הַיָּרֵחַ, סוֹבֶבֶת בְּשָׁוֶה, וּמַהֲלָכָהּ בְּכָל שִׁבְעִים שָׁנָה בְּקֵרוּב, מַעֲלָה אַחַת.

This point is referred to as the apogee.וּנְקֻדָּה זוֹ הִיא הַנִּקְרֵאת 'גֹּבַהּ'.

Accordingly, in ten days, the apogee of the sun travels one and a half seconds—i.e., a second and thirty thirds. Thus, in one hundred days, the apogee travels fifteen seconds. In one thousand days, it travels two minutes and thirty seconds, and in ten thousand days, 25 minutes. In twenty-nine days, it travels four seconds and a fraction. In a regular year, it travels 53 seconds.גֹּבַהּ הַשֶּׁמֶשׁ - מַהַלָכוֹ בְּכָל עֲשָׂרָה יָמִים, שְׁנִיָּה אַחַת וַחֲצִי שְׁנִיָּה, שֶׁהִיא שְׁלוֹשִׁים שְׁלִישִׁיּוֹת; נִמְצָא מַהַלָכוֹ בְּמֵאָה יוֹם, חָמֵשׁ עֶשְׂרֵה שְׁנִיּוֹת, וּמַהַלָכוֹ בְּאֶלֶף יוֹם, שְׁנֵי חֲלָקִים וּשְׁלוֹשִׁים שְׁנִיּוֹת; וּמַהַלָכוֹ בַּעֲשֶׂרֶת אֲלָפִים יוֹם, חֲמִשָּׁה וְעֶשְׂרִים חֲלָקִים. וְנִמְצָא מַהַלָכוֹ לְתִשְׁעָה וְעֶשְׂרִים יוֹם, אַרְבַּע שְׁנִיּוֹת; וּמַהַלָכוֹ בְּשָׁנָה סְדוּרָה, שָׁלוֹשׁ וַחֲמִשִּׁים שְׁנִיּוֹת.

As mentioned, the starting point for all our calculations is the eve of Thursday, the third of Nisan, 4938 years after creation. The position of the sun in terms of its mean distance on this date was 7 degrees, 3 minutes and 32 seconds in the constellation of Aries, in symbols 7° 3’ 32”. The apogee of the sun at this starting point was 26 degrees, 45 minutes and 8 seconds in the constellation of Gemini, in symbols 26° 45’ 8”.10כְּבָר אָמַרְנוּ שֶׁהָעִיקָר שֶׁמִּמֶּנּוּ הַהַתְחָלָה בְּחֶשְׁבּוֹן זֶה, הוּא מִתְּחִלַּת לֵיל חֲמִישִׁי שֶׁיּוֹמוֹ שְׁלִישִׁי לְחֹדֶשׁ נִיסָן מִשְּׁנַת שְׁמוֹנֶה וּשְׁלוֹשִׁים וּתְשַׁע מֵאוֹת וְאַרְבַּעַת אֲלָפִים לַיְּצִירָה. וּמָקוֹם הַשֶּׁמֶשׁ בְּמַהֲלָכָהּ הָאֶמְצָעִי הָיָה בָּעִיקָר הַזֶּה, בְּשֶׁבַע מַעֲלוֹת וּשְׁלוֹשָׁה חֲלָקִים וּשְׁתַּיִם וּשְׁלוֹשִׁים שְׁנִיּוֹת מִמַּזַּל טָלֶה - סִימָנָן ז' ג' ל"ב. וּמָקוֹם גֹּבַהּ הַשֶּׁמֶשׁ הָיָה בְּעִיקָר זֶה, בְּשֵׁשׁ וְעֶשְׂרִים מַעֲלוֹת וַחֲמִשָּׁה וְאַרְבָּעִים חֲלָקִים וּשְׁמוֹנֶה שְׁנִיּוֹת מִמַּזַּל תְּאוֹמִים - סִימָנָם כ"ו מ"ה ח'.

Accordingly, if you desire to know the position of the sun according to its mean distance at any given time, you should calculate the number of days from the starting point mentioned until the particular day you desire, and determine the mean distance it traveled during these days according to the figures given previously, add the entire sum together, accumulating each unit of measure separately. The result is the mean position of the sun on that particular day.כִּשְׁתִּרְצֶה לֵידַע מָקוֹם הַשֶּׁמֶשׁ בְּמַהֲלָכָהּ הָאֶמְצָעִי בְּכָל זְמָן שֶׁתִּרְצֶה, תִּקַּח מִנְיַן הַיָּמִים שֶׁמִּתְּחִלַּת יוֹם הָעִיקָר עַד הַיּוֹם שֶׁתִּרְצֶה, וְתוֹצִיא מַהֲלָכָהּ הָאֶמְצָעִי בְּאוֹתָן הַיָּמִים מִן הַסִּימָנִין שֶׁהוֹדַעְנוּ; וְתוֹסִיף הַכֹּל עַל הָעִיקָר, וּתְקַבֵּץ כָּל מִין עִם מִינוֹ. וְהַיוֹצֵא, הוּא מָקוֹם הַשֶּׁמֶשׁ בְּמַהֲלָכָהּ הָאֶמְצָעִי לְאוֹתוֹ הַיּוֹם.

For example, if we desired to determine the mean position of the sun at the beginning of the eve of the Sabbath on the fourteenth of the month of Tammuz of the present year, the starting point for these calculations, we should do the following: Calculate the number of days from the starting point until the date on which you desire to know the position of the sun. In this instance, it is one hundred days. The mean distance the sun travels in one hundred days is 98° 33’ 53”. We then add that to the starting point, which is 7° 3’ 32”, and arrive at a total of 105 degrees, 37 minutes and 25 seconds, in symbols 105° 37’ 25”.כֵּיצַד? הֲרֵי שֶׁרָצִינוּ לֵידַע מָקוֹם הַשֶּׁמֶשׁ הָאֶמְצָעִי בִּתְחִלַּת לֵיל הַשַּׁבָּת שֶׁיּוֹמוֹ אַרְבָּעָה עָשָׂר יוֹם לְחֹדֶשׁ תַּמּוּז מִשָּׁנָה זוֹ, שֶׁהִיא שְׁנַת הָעִיקָר - מָצִינוּ מִנְיַן הַיָּמִים מִיּוֹם הָעִיקָר עַד תְּחִלַּת יוֹם זֶה שֶׁאָנוּ רוֹצִים לֵידַע מָקוֹם הַשֶּׁמֶשׁ בּוֹ, מֵאָה יוֹם; לָקַחְנוּ אֶמְצַע מַהֲלָכָהּ לְמֵאָה יוֹם, שֶׁהוּא צ"ח ל"ג נ"ג, וְהוֹסַפְנוּ עַל הָעִיקָר, שֶׁהוּא ז' ג' ל"ב. יָצָא מִן הַחֶשְׁבּוֹן, מֵאָה וְחָמֵשׁ מַעֲלוֹת וְשִׁבְעָה וּשְׁלוֹשִׁים חֲלָקִים וְחָמֵשׁ וְעֶשְׂרִים שְׁנִיּוֹת - סִימָנָן ק"ה ל"ז כ"ה.

Thus, the sun’s mean position at the beginning of this night will be 15 degrees and 37 minutes of the sixteenth degree in the constellation of Cancer.וְנִמְצָא מְקוֹמָהּ בְּמַהַלָךְ אֶמְצָעִי בִּתְחִלַּת לֵיל זֶה, בְּמַזַּל סַרְטָן בְּחָמֵשׁ עֶשְׂרֵה מַעֲלוֹת בּוֹ וְשִׁבְעָה וּשְׁלוֹשִׁים חֲלָקִים מִמַּעֲלַת שֵׁשׁ עֶשְׂרֵה.

At times, the sun will be located in the mean position that can be determined using the above methods of calculation at the beginning of the night, and at times an hour before the setting of the sun, or an hour afterwards.11וְהָאֶמְצָע שֶׁיֵּצֵא בְּחֶשְׁבּוֹן זֶה, פְּעָמִים יִהְיֶה בִּתְחִלַּת הַלַּיְלָה בְּשָׁוֶה, אוֹ קֹדֶם שְׁקִיעַת הַחַמָּה בְּשָׁעָה, אוֹ אַחַר שְׁקִיעַת הַחַמָּה בְּשָׁעָה.

This lack of definition concerning the sun’s position will not be of consequence with regard to calculating the visibility of the moon, for we will compensate for this approximation when calculating the mean position of the moon.12וְדָבָר זֶה לֹא תָחוּשׁ לוֹ בַּשֶּׁמֶשׁ בְּחֶשְׁבּוֹן הָרְאִיָּה, שֶׁהֲרֵי אָנוּ מַשְׁלִימִים קֵרוּב זֶה כְּשֶׁנְּחַשֵּׁב לְאֶמְצַע הַיָּרֵחַ.

One should follow the same procedure at all times—for any date one desires, even if it is one thousand years in the future. When the mean distance traveled by the sun is calculated and the remainder after all the multiples of 360 have been subtracted is added to the figures of the starting point, you will arrive at the mean position.וְעַל הַדֶּרֶךְ הַזֹּאת תַּעֲשֶׂה תָּמִיד לְכָל עֵת שֶׁתִּרְצֶה, וַאֲפִלּוּ אַחַר אֶלֶף שָׁנִים - שֶׁתְּקַבֵּץ כָּל הַשְּׁאֵרִית וְתוֹסִיף עַל הָעִיקָר, יֵצֵא לְךָ הַמָּקוֹם הָאֶמְצָעִי.

The same principles apply regarding the mean position of the moon, or the mean position of any other planet. Once you know the distance it travels in a single day, and you know the starting point from which to begin calculations, total up the distance it travels throughout as many years or days as you desire, add that to the starting point, and you will arrive at its position according to its mean distance.וְכֵן תַּעֲשֶׂה בְּאֶמְצַע הַיָּרֵחַ, וּבְאֶמְצַע כָּל כּוֹכָב וְכוֹכָב - מֵאַחַר שֶׁתֵּדַע מַהַלָכוֹ בְּיוֹם אֶחָד כַּמָּה הוּא, וְתֵדַע הָעִיקָר שֶׁמִּמֶּנּוּ תַּתְחִיל, וּתְקַבֵּץ מַהַלָכוֹ לְכָל הַשָּׁנִים וְהַיָּמִים שֶׁתִּרְצֶה וְתוֹסִיף עַל הָעִיקָר, וְיֵצֵא לְךָ מְקוֹמוֹ בְּמַהַלָךְ אֶמְצָעִי.

The same concepts apply regarding the apogee of the sun. Add to the starting point the distance it travels over the course of days or years, and you will know the position of the apogee of the sun for the day you desire.וְכֵן תַּעֲשֶׂה בְּגֹבַהּ הַשֶּׁמֶשׁ - תּוֹסִיף מַהַלָכוֹ בְּאוֹתָם הַיָּמִים אוֹ הַשָּׁנִים עַל הָעִיקָר, יֵצֵא לְךָ מָקוֹם גֹּבַהּ הַשֶּׁמֶשׁ לְאוֹתוֹ הַיּוֹם שֶׁתִּרְצֶה.

Similarly, if you desire to establish another date as the starting point instead of the date which we have chosen to begin in this year, choosing a year that will be the beginning of a particular nineteen-year cycle, or that will be the beginning of a new century, you may. Similarly, if you would like to use as a starting point a date in the past, before the date given above, or a date many years in the future, the path to arrive at such a starting point is well known.וְכֵן אִם תִּרְצֶה לַעֲשׂוֹת לְךָ עִיקָר אַחֵר שֶׁתַּתְחִיל מִמֶּנּוּ חוּץ מֵעִיקָר זֶה שֶׁהִתְחַלְנוּ מִמֶּנּוּ בְּשָׁנָה זוֹ, כְּדֵי שֶׁיִּהְיֶה אוֹתוֹ עִיקָר בִּתְחִלַּת שְׁנַת מַחְזוֹר יָדוּעַ, אוֹ בִּתְחִלַּת מֵאָה מִן הַמֵּאוֹת - הָרְשׁוּת בְּיָדְךָ. וְאִם תִּרְצֶה לִהְיוֹת הָעִיקָר שֶׁתַּתְחִיל מִמֶּנּוּ מִשָּׁנִים שֶׁעָבְרוּ קֹדֶם עִיקָר זֶה, אוֹ לְאַחַר כַּמָּה שָׁנִים מֵעִיקָר זֶה - הַדֶּרֶךְ יְדוּעָה.

How is this figure to be calculated? We have already established the mean distance traveled by the sun in a regular year, in twenty- nine days, and in a single day. It is known that a year whose months13 are full is one day longer than a regular year. Similarly, a year whose months are lacking is one day shorter than a regular year.כֵּיצַד הִיא הַדֶּרֶךְ? כְּבָר יָדַעְתָּ מַהַלַךְ הַשֶּׁמֶשׁ לְשָׁנָה סְדוּרָה, וּמַהֲלָכָהּ לְתִשְׁעָה וְעֶשְׂרִים יוֹם, וּמַהֲלָכָהּ לְיוֹם אֶחָד. וְדָבָר יָדוּעַ שֶׁהַשָּׁנָה שֶׁחֳדָשֶׁיהָ שְׁלֵמִים - הִיא יְתֵרָה עַל הַסְּדוּרָה יוֹם אֶחָד, וְהַשָּׁנָה שֶׁחֳדָשֶׁיהָ חֲסֵרִין - הִיא חֲסֵרָה מִן הַסְּדוּרָה יוֹם אֶחָד.

With regard to a leap year,14 if its months are regular, it will be thirty days longer than a regular year. If its months are full, it will be thirty-one days longer than a regular year. If its months are lacking, it will be twenty-nine days longer than a regular year.וְהַשָּׁנָה הַמְּעֻבֶּרֶת, אִם הָיוּ חֳדָשֶׁיהָ כְּסִדְרָן - תִּהְיֶה יְתֵרָה עַל הַשָּׁנָה הַסְּדוּרָה שְׁלוֹשִׁים יוֹם, וְאִם הָיוּ חֳדָשֶׁיהָ שְׁלֵמִים - הִיא יְתֵרָה עַל הַסְּדוּרָה אֶחָד וּשְׁלוֹשִׁים יוֹם, וְאִם הָיוּ חֳדָשֶׁיהָ חֲסֵרִין - הִיא יְתֵרָה עַל הַסְּדוּרָה תִּשְׁעָה וְעֶשְׂרִים יוֹם.

Since these principles are already established, it is possible to calculate the mean distance traveled by the sun for as many years or as many days as you desire, and add it to the mean position of the sun on the date established previously as the starting point, and you will be able to determine the mean position of the sun for any future date. Afterwards, you can use that date as a starting point. Conversely, you may subtract the mean distance traveled by the sun over the course of a particular period from the mean position of the sun on the date established previously as the starting point, and you will be able to determine the mean position of the sun for any past date. Afterwards, you can use that date as a starting point. The same principles also apply with regard to the mean position of the moon or any of the other planets, if their mean positions on any particular date are known to you. It also should be apparent that just as it is possible to determine the mean position of the sun for any future date, so too, it is possible to determine its mean position for any previous date.וּמֵאַחַר שֶׁכָּל הַדְּבָרִים הָאֵלּוּ יְדוּעִים, תּוֹצִיא מַהַלַךְ אֶמְצַע הַשֶּׁמֶשׁ לְכָל הַשָּׁנִים וְהַיָּמִים שֶׁתִּרְצֶה, וְתוֹסִיף עַל הָעִיקָר שֶׁעָשִׂינוּ - יֵצֵא לְךָ אֶמְצָעָהּ לְיוֹם שֶׁתִּרְצֶה מִשָּׁנִים הַבָּאוֹת, וְתַעֲשֶׂה אוֹתוֹ הַיּוֹם עִיקָר; אוֹ תִּגְרַע הָאֶמְצָע שֶׁהוֹצֵאתָ מִן הָעִיקָר שֶׁעָשִׂינוּ, וְיֵצֵא לְךָ הָעִיקָר לְיוֹם שֶׁתִּרְצֶה מִשָּׁנִים שֶׁעָבְרוּ, וְתַעֲשֶׂה אוֹתוֹ אֶמְצָע עִיקָר. וּכְזֶה תַּעֲשֶׂה בְּאֶמְצַע הַיָּרֵחַ וּשְׁאָר הַכּוֹכָבִים, אִם יִהְיוּ יְדוּעִים לְךָ. וּכְבָר נִתְבָּאֵר לְךָ מִכְּלָל דְּבָרֵינוּ, שֶׁכְּשֵׁם שֶׁתֵּדַע אֶמְצַע הַשֶּׁמֶשׁ לְכָל יוֹם שֶׁתִּרְצֶה מִיָּמִים הַבָּאִים, כָּךְ תֵּדַע אֶמְצָעָהּ לְכָל יוֹם שֶׁתִּרְצֶה מִיָּמִים שֶׁעָבְרוּ.

Footnotes

Since the sun travels throughout the entire 360° sphere over the course of a solar year, and a year is slightly longer than 365 days, the daily distance the sun travels is slightly less than one degree—more precisely, 59 minutes, 8 seconds and 19.8 thirds. Although the Rambam does not mention the thirds in this figure, he includes them in his subsequent calculations.

When performing simple multiplication, the sum appears to be three seconds less. These three seconds have been added because of the inclusion of the multiples of the thirds, as mentioned in the previous note. Similarly, in subsequent calculations the Rambam also adds the multiples of the thirds.

See Chapter 11, Halachah 10.

See Chapter 8, Halachah 6, which explains that a year in which all the months follow in order, one full and one lacking, is referred to as a regular year.

A lunar month is slightly longer than 29 days. Therefore, potential witnesses endeavor to sight the moon in the heavens on the night between the twenty-ninth and thirtieth days.

Indeed, many of the subsequent calculations mentioned by the Rambam may be accurate only on the first night of the month and may not be accurate on the subsequent nights.

The one day is added when both the months of Marcheshvan and Kislev are full. The commentaries raise the question why the Rambam does not mention the possibility of the year being lacking a day, as occurs when Marcheshvan and Kislev are both lacking.

As stated in Chapter 11, Halachah 13, the Earth is not in the exact center of the orbits of the sun, the moon, or the other five planets. Therefore, there is one point in their orbits where they are furthest removed from the Earth. The knowledge of the location of this point is significant in calculating the true position of the sun, as will be explained in the following chapter.

As the Rambam mentions in Hilchot Yesodei HaTorah 3:3, not only do the sun and the stars move in their orbits, the orbits themselves move in the heavens. This movement can be seen most clearly by charting the movement of the apogee, the point in the orbit furthest from the Earth. The movement of the sun’s orbit and similarly, that of the other stars, is relatively slow. The moon’s orbit, by contrast, is moving at a much faster pace, as mentioned in the notes on Chapter 14, Halachah 1.

10.

Since more than 800 years have passed since the composition of the Mishneh Torah, the apogee of the sun has moved approximately twelve degrees and is presently located in the constellation of Cancer.

11.

Since, as explained in the previous chapter, the mean distance does not represent the place where the sun can actually be seen in the sky, there will be a slight discrepancy. The mean position represents the sun’s position at 6 PM. During the summer months, the sun will reach that position before sunset, and during the winter months, it will reach that position after sunset.

12.

See the conclusion of Chapter 14.

13.

I.e., both Marcheshvan and Kislev.

14.

See Chapter 6, Halachah 11, which relates that seven of the years in a nineteen-year cycle are leap years, and states which of these years will be leap years.

Rambam - 1 Chapter a Day

Kiddush HaChodesh - Chapter 12

Kiddush HaChodesh - Chapter 12

Test Yourself on Kiddush HaChodesh Chapter 12