[7] Astronomical New Moon (Conjunction) and Full Moon

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From the viewpoint of an observer on the earth far away from the north and south poles, the moon has periodically changing appearances. Typical appearances of the moon's cycle may be described as (1) the widening crescent, (2) the moon increasing toward full circle, (3) the full circle, (4) the moon decreasing away from full circle, (5) the narrowing crescent, and (6) invisibility. The astronomical new moon (as recognized by modern astronomers) is the moment in time (or the moon's position) in each cycle of the moon around the earth at which the center of the moon is closest to the straight line between the sun and the earth. The astronomical new moon is also called the conjunction of the sun and the moon as observed from a person on the surface of the earth.

A solar eclipse is the covering of the sun by the moon as seen by an
observer on the earth when the moon comes between the sun and the earth.

Such an eclipse is called total eclipse when the circle of the moon lies inside the circle of the sun. A solar eclipse can only occur during the time of the conjunction. How dark is it during a solar eclipse, and how long does a solar eclipse last? On pages 198-199 of Zirker we read, “During a total eclipse, however, the corona [the sun's disk] is only as bright as the full moon.” On page 30 we read, “The maximum diameter difference is 2'38" and the maximum duration of totality is 7 minutes and 40 seconds for an observer near the equator. The 1973 eclipse in West Africa came very close to this maximum theoretical totality. On the average, a total eclipse only lasts for two or three minutes and seems much shorter.”

Chapter 12 of Zirker's book is titled “The Great Hawaiian Eclipse” where Zirker describes the famous total eclipse over the Hawaiian Islands on July 11, 1991, which is significant because of the world famous observatory on Mauna Kea at 13,700 feet above sea level, which provided superb scientific facilities for observation. This total eclipse lasted 4 minutes 11 seconds (page 197). Page 197 states, “Schoolchildren [on Hawaii] were equipped with dark slides to view the eclipse and preparations were made to bus them to favorable locations.” The reason that they look through special dark slides is so that their eyes are not damaged due to the harmful rays of the sun.

During the 4 minutes 11 seconds of totality of the solar eclipse, one's eyes should not be damaged because the brightness is near that of the full moon, but outside that narrow window of time, one's eyes surely will be damaged when the moon only partially blocks the sun.

The following definitions are relative to a place on the earth significantly away from the north and south poles. The crescent period of the moon's cycle is the time after the three-quarter-size moon and before the following one-quarter-size moon excluding the time during which the moon is invisible and the time at which there may be a solar eclipse. The moon is called a crescent during the crescent period. The old crescent is the moon during the time that it is visible, assuming the atmosphere is clear, on the last day that it is visible prior to the astronomical new moon. The old crescent is
seen looking east in the morning. The new crescent is the moon during the time that it is visible, assuming the atmosphere is clear, on the first day that it is visible after the astronomical new moon. The new crescent is seen looking west in the evening. The new crescent is sometimes called a young crescent.

Bartel Leendert van der Waerden (1903-1996) was an internationally prominent scholar in the fields of mathematics and the history of ancient astronomy. On page 169 of van der Waerden 1960, he wrote: “The difference between the first days of an exact month [month starting with and ending with the conjunction] and an observed lunar month [month starting with and ending with the new crescent] is one or two days, or in exceptional cases three days.”

On page 66 of Beaulieu we find, “In ancient Babylonia the day was reckoned from one sunset to the next. The monthly count was based on lunar phases, with the month beginning after sunset when the new crescent of the moon was seen again in the western horizon. This happened at the earliest one day, and at the latest three days after conjunction.”

At the end of the above sentence is “2” (footnote) which states the following (same page, square bracket comments are in the journal, not from me), “That the moon never disappeared for more than three days following conjunction was evidently known to Assyrian and Babylonian astronomers, as shown in H. Hunger, Astrological Reports to Assyrian Kings (SAA 8, 1992), text 346, a report sent by the scholar Asaredu the younger: ‘On this 30th day [the moon became visible]. The lord of kings will say: “Is [the sign?] not affected?” The moon disappeared on the 27th; the 28th and the 29th it stayed inside the sky, and was seen on the 30th; when else should it have been seen? It should stay in the sky less than 4 days, it never stayed 4 days.’”

On page 87 Beaulieu wrote: “Even after the 6th century B.C., when
Babylonian astronomers developed the mathematical schemes which
enabled them to calculate month-lengths in advance, it is probable that observation remained the sole authoritative way of fixing the beginning of the month.” Page 244 of Britton 1999 indicates that the Babylonian method for predicting the sighting of the new crescent is likely to have originated within the years 457-419 BCE. The Babylonian calculation for the sighting of the new crescent is based upon approximate repeating sequences of data over long periods of time. Existing records of some of the data that are used
in these patterns go back to 568 BCE, which is 18 years after Solomon's temple was destroyed in 586 BCE., and the earliest archaeological source that has all astronomical parameters that are needed for the prediction of the sighting of the new crescent is dated 373 BCE (see page 197 of Hunger and Pingree). Thus the time at which the Babylonians developed methods to approximately determine the day of the new crescent is about 450 BCE.

Perhaps about 400 BCE their method was actively being used. I have not seen any published papers that attempt to quantify how accurately the Babylonian methods predicted the new crescent.
Based upon data showing that one factor of considerable significance to the Babylonians is predicting the time from when the sun sets below the western horizon to the time when the moon sets below the western horizon during the crescent phase (although other time based factors were also sought by the Babylonians), and knowing that this method has some degree of
reliability toward predicting the visibility of the new crescent (but is far from a perfect method), my estimated guess is that their predictions for the new crescent were correct between 80 and 85 percent of the time when the weather was clear.

Today we speak of the conjunction and we define it in terms of the three dimensional geometry of the sun-earth-moon system and the language of orbits. But ancient people did not have our modern concept of a sun centered solar system (except for two known ancient astronomers who were ridiculed), and to the best of our knowledge today, ancient people did not have our three dimensional model of the sun-earth-moon system. We must realize that the ancient concept of the conjunction and our modern concept are different. They could see a solar eclipse, and whenever there was a solar eclipse, there was necessarily a conjunction also. But that was the only kind of conjunction they could see. What concept could they have for the conjunction generally if they could not see it? Page 110 of Koch-Westenholz states, “The Babylonians seem never to have given an astronomical explanation of eclipses.” Page 101 of Koch-Westenholz states, “I know of no Babylonian astronomical explanation of the phases of the moon, ...” The Babylonians did notice the obvious fact that when the full moon occurs the moon and sun are at opposite ends of the sky, and during the symmetrically opposite time of the lunar cycle the moon and sun are traveling along side by side. A translation of an ancient Babylonian text that discusses the moon's cycle of disappearance is on page 101 of Koch-Westenholz, where “you” refers to the moon: “On the day of disappearance, approach the path of the sun so that [on the thirtieth day (?)], you shall be in conjunction, you shall be the sun's companion.” Here the author's translation “conjunction” does not require that it refer to an instant in time. It is merely the time that the sun and moon are companions, traveling together.

With clear weather the Babylonians knew there could be one, two, or three nights of invisibility of the moon (as mentioned above from van der Waerden and from Beaulieu). At the moment of true conjunction the moon and sun can be at most 5.2 degrees apart from a point on the earth's surface.

At this narrow an angle if the sun is in view or very near the horizon, the light from the sun will be too brilliant for the moon to be seen directly or even indirectly (the latter is called earthshine). Earthshine is the light from the sun to the earth, which then reflects back to the moon and then reflects to the observer on earth. Thus earthshine is the light seen from a double reflection. It is usually easy to see earthshine as the completion of the moon's circle as a faint grayish blue with the crescent at one edge on the
second day old crescent. Often earthshine may be seen on the day of the new crescent if it is not a very narrow crescent. Neither modern nor ancient people could see earthshine at the time of conjunction because the sun's brilliance is too close to the moon, and this has nothing to do with air pollution.

When the conjunction occurs, the moon is invisible except during a rare solar eclipse when the moon covers the sun from view from observers in a certain region on the earth for at most 7 minutes and 40 seconds (see the quote from Zirker above). Without knowledgeable calculations, it is not possible to accurately determine the time of the conjunction. Because the conjunction is not visible except during a rare solar eclipse, ancient people who did manage to arrive at some mental concept of the conjunction (such as the time period when the sun and moon are traveling together) and who also desired to achieve a mathematical computation to predict the time of the conjunction, would only be able to check the accuracy of their mathematical prediction during the rare occasion of a solar eclipse where they were located. The strong desire of certain ancient peoples, specifically the Chinese, the Babylonians, and the Greeks, to be able to predict solar eclipses, along with a knowledge of the mathematics that enabled then to make this approximation led to their interest in the conjunction as the approximate time when the sun and moon were traveling together.

Historical records of eclipses over a long period of time will suggest cycles of repetition of eclipses, and this may be simply described as a “bookkeeping” method to predict eclipses. In the book on ancient eclipse predictions by John Steele 2000, he discusses Chinese eclipse predictions on pages 175-215. On page 177 in the context of China, Steele wrote, “Although there are many steps in this process – and many potential places for mistakes – it has the advantage that eclipse prediction is reduced merely to bookkeeping, and yet the method still predicts most visible eclipses over the course of a hundred years or so. Furthermore, the calendar tends to predict too many, rather than too few, eclipses.” Later on this page we find, “The first mathematical treatment of eclipse calculation [in China] without reference to an eclipse cycle is found in the Ch’ing-ch’u-li from the third century AD.” Steele’s description of these methods reveals a computation to repeat an eclipse rather than a mathematical geometrical model of where the
heavenly bodies will be in the future. The purpose of including this piece of history is to remove some of the exotic imagined ideas that some laymen possess concerning the abilities of ancient peoples.

The full moon is the moment in time (or the moon's position) in each cycle of the moon around the earth in which the center of the earth is closest to the straight line between the sun and moon. The full moon is also called the opposition. When the full moon occurs, it looks like a full circle. However, the time of the moon's appearance as a full circle lasts at least two nights and it looks quite circular for several nights, so without knowledgeable calculations, it is not possible to accurately determine the time of the full moon by observing the circularity of the moon. On the other hand, it is possible to use a different observational method to make a judgment of the day after the moment of full moon as follows. During the several days near the time of the full moon the following two statements are true. Before the moment of the full moon, the moon rises in the east before the sun sets in the west. After the moment of the full moon, the moon rises in the east after the sun sets in the west. Using these principles one can use the rule that the first evening in which the moon rises in the east after the sun sets in the west begins the day after the moment of the full moon. One drawback of using this observational method is that it requires a straight horizontal unobstructed view of both the eastern horizon and the western horizon, and both of these horizons must be at the same altitude above sea level. Hills and trees will hinder accuracy. Besides this, if two observers perform this activity from different locations that have opposing horizons, which differ in their altitude above sea level, it is possible that their conclusions will differ in a near borderline case.