013 - הִלְכוֹת קִדּוּשׁ הַחֹדֶשׁ פֵּרֶק יג

Laws of Sanctifying the New Month, Chapter 13

1. If you wish to know the true position of the sun on any day you desire, first determine its mean position for that day in the manner we have explained. Then determine the sun’s elevation, and subtract the sun’s elevation from its mean position. What remains is called the sun’s anomaly.

2. See how many degrees the sun’s anomaly is. If the anomaly is less than one hundred and eighty degrees, subtract the portion of the anomaly from the sun’s mean position. If the anomaly is more than one hundred and eighty degrees, up to three hundred and sixty, add the portion of the anomaly to the sun’s mean position. What results after you add to or subtract from it is the true position.

3. Know that if the anomaly is exactly one hundred and eighty, or exactly three hundred and sixty, it has no portion; rather, the mean position is the true position.

4. What is the portion of the anomaly? If the anomaly is ten degrees, its portion is twenty parts; if it is twenty degrees, its portion is forty parts; if it is thirty degrees, its portion is fifty-eight parts; if it is forty degrees, its portion is one degree and fifteen parts; if it is fifty degrees, its portion is one degree and twenty-nine parts; if it is sixty degrees, its portion is one degree and forty-one parts; if it is seventy degrees, its portion is one degree and fifty-one parts; if it is eighty degrees, its portion is one degree and fifty-seven parts; if it is ninety degrees, its portion is one degree and fifty-nine parts; if it is one hundred degrees, its portion is one degree and fifty-eight parts; if it is one hundred and ten, its portion is one degree and fifty-three parts; if it is one hundred and twenty, its portion is one degree and forty-five parts; if it is one hundred and thirty, its portion is one degree and thirty-three parts; if it is one hundred and forty, its portion is one degree and nineteen parts; if it is one hundred and fifty, its portion is one degree and one part; if it is one hundred and sixty, its portion is two degrees and forty parts; if it is one hundred and seventy, its portion is one degree and twenty parts; and if it is exactly one hundred and eighty, it has no portion as we have explained; rather, the sun’s mean position is its true position.

5. If the anomaly is more than one hundred and eighty degrees, subtract it from three hundred and sixty degrees, and you will know its portion. How so? If the anomaly is two hundred degrees, subtract it from three hundred and sixty, and there remain one hundred and sixty degrees; and we have already stated that the portion for one hundred and sixty degrees is two degrees and forty parts—so too, the portion for two hundred degrees is two degrees and forty parts.

6. Similarly, if the anomaly is three hundred degrees, subtract it from three hundred and sixty, and there remain sixty; and you already know that the portion for sixty degrees is one degree and forty-one parts—so too, this is the portion for three hundred degrees. And so it is for every number.

7. For example, if the anomaly is sixty-five degrees—and we already know that the portion for sixty degrees is one degree and forty-one parts, and the portion for seventy is one degree and fifty-one parts—there is a difference of ten parts between the two portions, and according to the calculation of degrees, each degree is one part. Thus, the portion for an anomaly of sixty-five degrees is one degree and forty-six parts.

Laws of Sanctifying the New Month, Chapter 13

8. Similarly, if the path is sixty-seven, its portion is one degree and forty-eight parts. In this manner, you should proceed with any path whose number is units together with tens, whether in the calculation of the sun or in the other calculations of the moon.

9. How is this done? For example, if we want to know the true position of the sun at the beginning of Friday night, the fourteenth day of the month of Tammuz from this year—first, determine the mean position of the sun for this time, which is indicated by the sign 105, 37, 25, as we have explained. Then, determine the sun’s greatest height for this time, which will be indicated by the sign 26, 45, 23. Subtract the greatest height from the mean position, and you will have the path: eighteen degrees, fifty-two parts, and two seconds—its sign is 18, 52, 2. Do not be particular about the parts in any path; if they are less than thirty, pay them no attention. If they are thirty or more, count them as one degree and add it to the number of degrees of the path. Therefore, this path will be nineteen degrees, and its portion, as we have explained, will be thirty-eight parts.

10. And since this path was less than one hundred and eighty, subtract the portion, which is thirty-eight parts, from the mean position of the sun. What remains is one hundred and four degrees, fifty-nine parts, and twenty-five seconds—its sign is 104, 59, 25. Thus, the true position of the sun at the beginning of this night is in the constellation Cancer, at fifteen degrees within it, minus seconds. Do not pay attention to the seconds at all, neither in the position of the sun, nor in the position of the moon, nor in the other calculations of the sighting—rather, consider only the parts. If the seconds are close to thirty, make them into a part and add it to the parts.

11. Once you know the position of the sun at any time you wish, you can determine the true day of the season for any season you wish, whether for seasons that follow after this principal one from which we began, or for seasons that have passed from previous years.

Laws of Sanctifying the New Month, Chapter 13

In this chapter, the Rambam comes to explain how to determine the true position of the sun. After, in this chapter, we reach the true position of the sun, we will then be able to compare it with the true position of the moon in order to know whether the witnesses could see the moon on the thirtieth night.

The true position of the sun is the place within the circle of the constellations where the sun is found at that time, as we, standing on earth, see it. Since the sun moves every day until it completes a full circuit, it follows that each day it is in a different place within the circle of the constellations. However, from our perspective, the sun’s movement is not uniform and at the same rate each day, so it is not possible to know exactly in which place (degree) within the circle the sun is on the day we want to determine its position.

This lack of uniform movement of the sun is only from our perspective, as we are at the center of the circle of the spheres, but we are not at the center of the sun’s orbit. Therefore, from our viewpoint on the circle of the constellations, the change from day to day is not uniform; sometimes it appears that the sun moves (in the degrees of the constellations) more slowly, and sometimes more quickly, and we cannot know the position each day, where the sun will be in the circle of the constellations. How can we know this?

This comes from the mean movement of the sun, for in truth, the sun revolves at a uniform rate every day, and from the viewpoint of the center of the sun in relation to the circle of the constellations, its position changes uniformly from day to day. This is called the mean movement of the sun.

In chapter 12, the Rambam gave the calculation for how it is possible to know exactly the position of the sun in the circle of the constellations each day from the sun’s perspective, the mean movement, since this is at a constant rate, and it is possible to calculate exactly how many degrees the sun moves each day. In this chapter, the Rambam wants to arrive at the position of the sun as it appears from our perspective, which is the main point, since we want to determine the position of the sun together with the position of the moon as it appears to our eyes. This, however, does not move at a uniform rate, so how do we calculate the position of the sun in its true movement (as we see the sun within the circle of the constellations, which is the position we need for the moon’s position from the mean movement of the sun)?

For this, the Rambam gave the calculation in chapter 12 regarding the sun’s apogee, meaning the place in the circle of the constellations where, when the sun passes there in its circuit, it is at the farthest distance from the earth, that is, the sun’s apogee. If the sun’s orbit revolved around us and we were at the center of the orbit, then the sun’s distance from the earth would be uniform as it revolves around the center. But since in the sun’s orbit we are not at the center, there are times when the sun is farthest from us and times when it is closest to us.

Now, it is not possible to fix the sun’s apogee in the constellations and say that on this day of the year the sun is at its greatest distance from us, because, as the Rambam explained, the apogee is not fixed but changes gradually. The Rambam gave the method for determining the position of the sun’s apogee on any day you wish, meaning on which day of the year the sun is at its farthest from us.

Now the Rambam will explain that in order to know the true position of the sun on any given day, you must: 1) first know what the sun’s apogee is on that day (in the circle of the constellations), and 2) what the position of the sun is in its mean movement on that day (in the circle of the constellations). You must see how much of the sun’s circuit has been completed from the place of the sun’s apogee to the place of the sun in the circle of the constellations on that day, meaning how many degrees the sun has moved from the apogee to that day as it is in the mean movement.