Rambam - 3 Chapters a Day

Shemuel (Eruvin 56a).

Rav Ada (Ibid.). His opinion is discussed in the following chapter.

Ptolemy and Albatani, astronomers whose opinions were valued by the Rambam, from Greece and Arabia respectively, both maintain that the length of a solar year is less than 365 days and six hours. There is, however, a difference between the figures each of them suggests. According to contemporary science, the length of a tropical solar year is 365 days, 5 hours, 48 minutes and 45 1/2 seconds. It is decreasing at the rate of 0.530 second per century.

Chapter 6, Halachah 10.

This figure is based on the following principles: The times of the seasons are calculated according to the opinion of Rabbi Yehoshua, who maintains that the world was created in Nisan. Although the lunar calendar is calculated according to the opinion of Rabbi Eliezer, who maintains that the world was created in Tishrei, our Sages did not see a contradiction in interrelating the two conceptions, as we will continue to explain. The conjunction of the month of Tishrei is the hour of man’s creation, the fourteenth hour of Friday, the sixth day of creation. Based on this figure, by subtracting six times 1 day, 12 hours, and 793 units (the remainder of a lunar month), we can calculate that the conjunction of the month of Nisan—six months before creation—took place on Thursday, nine hours and 642 units after nightfall. The vernal equinox is calculated according to the conception that the world was created in Nisan. The sun was created in the first hour of the fourth day of creation. This is considered the first vernal equinox. Thus, the autumnal equinox (half a year later) took place on Wednesday, three hours after daybreak, one day and twenty-three hours before the conjunction of Tishrei. Since there is a difference of five days, ten hours, and 642 units between six months according to the lunar calendar, and half a year according to the solar calendar, it follows that the conjunction of Nisan was seven days, nine hours, and 642 units after the vernal equinox (Perush).

For the calculations will be based on Rosh Chodesh Nisan, which took place this amount of time after the vernal equinox.

A significant point arises from these statements, when one calculates the progression of the date and time of the vernal equinox by adding one hour and 485 units for each nineteen-year cycle. It follows that within the entire six millennia of the world’s existence, the vernal equinox will have advanced approximately fifteen days. Thus, from the standpoint of the solar calendar, it will always be possible for Pesach, the fifteenth of Nisan, to occur in the spring.

The difference between a lunar year and a solar year, as stated in Chapter 6, Halachah 4.

I.e., calculate every group of 1080 units as an hour, and every group of 24 hours as a day.

By making this subtraction, one bases the calculation on the conjunction of the month of Nisan, and not on the time of the first vernal equinox, which preceded that conjunction by this number of days and hours.

Until this point in the calculation, the Rambam has not taken into consideration the existence of leap years. He does this now by grouping the remainder into months and subtracting the complete months. The number of complete months subtracted represents the number of leap years that have passed in the nineteen-year cycle.

There are 30 hours between the time of the equinox (or solstice) of one year and the next. Since the first vernal equinox took place at nightfall between Tuesday and Wednesday, the second vernal equinox took place at midnight between Wednesday and Thursday, the third at daybreak on Friday, and the fourth at noon on the Sabbath. Similarly, in subsequent years, the time of the equinox will continue to advance in six (i.e., 30) hour intervals according to such a pattern.

There is a difference of seven and a half hours between the time of the vernal equinox and the time of the summer solstice. Since the first vernal equinox took place at nightfall, the first summer solstice took place at 1:30 AM. Afterwards, the time of the summer solstice advances in six- (i.e., 30-) hour intervals every year.

The first autumnal equinox took place at 9 AM.

The first winter solstice took place at 4:30 PM.

This number is chosen because after twenty-eight years, the equinox takes place on the same day of the week and the same hour as it did originally. This figure can be calculated as follows: 1 and 1/4 days (the difference between the time of the equinox in two successive years) times 28 equals 35 days. Thirty-five days are five full weeks. Based on this calculation, it is each twenty-eight years that the sun returns to its original position at the time of creation. To commemorate this occurrence, a special blessing, Birkat HaChamah, is recited. (See Hilchot Berachot 10:18.)

The difference in the time of the equinox from one year to the next.

I.e., the night between the Sabbath and Sunday.

I.e., the night between Tuesday and Wednesday. By making this addition, it is possible for these calculations to start from the beginning of the week.

The commentaries understand this as an indication that this portion of the Mishneh Torah was composed during that year.

The date of the equinox also can be determined by the calculations mentioned in Halachah 4. In this and the following halachot, however, the Rambam offers a simpler calculation, which uses approximations, but ultimately enables one to arrive at the same result.

The Rambam is using an approximation. The difference between a lunar year and a solar year is ten days, twenty-one hours, and 204 units. However, to simplify the calculation, the Rambam rounds off the figure to eleven days.

I.e., in the Rambam’s time. The figure of seven days is reached as follows: In the year 4930, 259 nineteen-year cycles had passed. When an hour and 485 units are added for every nineteen-year cycle, a total of 15 days, 15 hours, and 335 units is obtained. Since the first equinox took place more than seven days before the conjunction of Nisan, eight days are subtracted from this figure, leaving a remainder of approximately seven days.

To account for any leap years. Here, too, the Rambam is rounding off the figure; the length of a lunar month is slightly less.

Since the calculation suggested by the Rambam contains several approximations, it may not be exact, and days may have to be added to reconcile the discrepancy.

There will be more than thirty days remaining. Therefore, the reckoning should be made from Rosh Chodesh Adar.

Further calculations are necessary, for in this instance, it is impossible that the equinox will take place on the first of the month, the eighth, or the fifteenth.

I.e., although the calculation mentioned by the Rambam operates using approximations, the difference between these approximations and the actual data will hardly ever exceed three days.

The maximum difference between the approximations employed by the Rambam and the actual data is three and one half days. Thus, it is possible, but highly improbable, that there be a four-day difference.

This differs from the figure given in Chapter 9, Halachah 3. The reason for this difference is that Rav Ada’s calculations (the figures mentioned in this chapter) follow Rabbi Yehoshua’s view, which maintains that the world was created in Nisan. In contrast, Shemuel’s calculations (those mentioned in Chapter 9) depend more on the view of Rabbi Eliezer, who maintains that the world was created in Tishrei.

So that the calculation will begin from the day of the conjunction of Nisan.

Thus accounting for all the leap years that have passed within the nineteen-year cycle.

As mentioned previously, and as is explained in the subsequent chapters, the mean position or the mean rate of progress of a body in the celestial sphere refers to the average of its monthly or yearly cycle. In actual fact, there are slight inconsistencies between the position of any of these bodies according to these calculations and its actual position as observed in the celestial sphere. Until this point, the Rambam has relied on the mean rate of progress of the celestial bodies for his calculations. In the subsequent chapters, he explains how their exact position in the celestial sphere can be determined.

E.g., Chapter 1, Halachah 6; Chapter 2, Halachah 4; Chapter 6, Halachah 1.

This concept, the calculation of the place and position of the new moon, and the determination of when it will be visible, is the subject of this and the following eight chapters. In the present chapter, the Rambam outlines the general principles and ground rules governing his calculations.

See Chapter 17, Halachah 24, where the Rambam states that in this text he refers to the works of Greek scientists, because the books written by the Sages of Israel on the subject were not available to him. In the following halachah, however, he mentions having accepted traditions from the Rabbis.

The poetic wording is borrowed, out of context, from Bava Kama 91a.

The latter phrase is borrowed, also out of context, from Exodus 36:2.

I.e., to receive this knowledge, one had to have received semichah as described in Hilchot Sanhedrin, Chapter 4. Nevertheless, not all the Sages who received semichah were privileged to this knowledge.

This term is used, because from man’s perspective, the earth appears flat and the heavens appear as a sphere that revolves around him, only half of which is visible at any given time.

The number 360 was chosen because it can be divided by all the cardinal integers except for seven (Perush).

One corresponding roughly to each of the months of the year.

For the year begins in spring, and during the spring the sun is located in the constellation of Aries.

See Hilchot Yesodei HaTorah 3:7, which states that these constellations appeared in these forms at the time of the flood, and then they were given these names. At present, the stars have changed position somewhat, and some creativity is required to perceive how the images suggested by these names are appropriate for these constellations.

The Rambam appears to be referring to his statements in Hilchot Yesodei HaTorah 3:1, which relate that there are nine spheres in which the stars revolve: The moon revolves in the first, then Mercury, Venus, the Sun, Mars, Jupiter, and then Saturn. In the eighth sphere revolve all the stars that are visible, and the ninth sphere includes and encircles all existence.

The Rambam is following the theory of an earth-centered universe. The term “center” must, however, be understood loosely, because the earth does not lie at the exact center of all these spheres.

The early astronomers realized that at some given times, the sun appears to travel faster or slower than at others—i.e., the pace at which it appears to proceed in the heavens varies between approximately 1 1/2 degrees per day and 58 1/2 minutes per day. Similarly, they saw that at different times of the year, the sun appears larger or smaller. By postulating that the earth was not the center of the sun’s orbit, they were able to resolve these anomalies.

Were the earth to lie at the center of all the planets’ orbits, the speed at which the planets progress would not only be uniform, it would appear uniform. Since the earth is not in the center, although the planets are proceeding at a uniform pace, this does not always appear to be the case.

See the notes on Chapter 6, Halachah 1.

I.e., the angular location in the heavenly sphere at which the sun can be found. The stars cannot be seen during the daytime. Hence, we cannot actually see the constellations in which the sun is located. Throughout this text, the term “the position of the sun” generally refers to the angular position of the celestial sphere that is just below the horizon when the sun sets.

The place of the moon in the heavenly sphere can be seen at night. It is possible for us to determine its angular position in comparison to the constellations of the Zodiac.

I.e., Wednesday night.

This year corresponds to 1178 C.E. There are several other dates cited within the Mishneh Torah with regard to the composition of that text.

In Talmudic times, legal contracts were dated from the year when Alexander the Great ascended to the throne.

For the New Moon can be sanctified only in Eretz Yisrael, as stated in Chapter 1, Halachah 8.

The value of testimony from locales of more than a day’s journey is mentioned in Chapter 3, Halachot 15-18.

More precisely, Jerusalem is 31° 47’ north of the equator.

The populated area refers to the land mass of Europe and Asia, for at the time the Rambam wrote his text, America had not been discovered. The center of the populated area refers to a line approximately 90° east of Greenwich. Thus, Jerusalem, which is 66° east of Greenwich, is 24° west of this line. The significance of the latitude and longitude of Jerusalem with regard to these calculations is mentioned in Chapter 17.