What is the "New Moon"?

 

Historically, the "new moon" has always referred to the first visible crescent. One need only to check historical works to show that this statement is true. To prove that the "new moon" is the first crescent is another matter. How do we know that "right" (the direction) is "right" and not "left". How do we know that "up" is really "up" and not "down". If I am facing you, my right is your left. As a North American, my "down" is an Australian's "up". But historically, there has never been any debate over left and right, or up and down. Historically, there has never been any question that the "new moon" is not the first visible crescent.

Unless you are an astronomer. Like all scientists, their definitions may not correspond to those commonly used. For instance "north" to an astronomer can mean either "magnetic north" (as in the north pole) or "celestial north" (as in the north star), which are neither equivalent nor fixed, but vary with the earth's movements.

People have looked at the planets and stars since the Creation. After all, it was God who said they were for "signs and for seasons, for days and years" (Gen. 1:14). Archaeology shows, and written history confirms, that people have always been aware of the movement and cycles of the planets and stars. It doesn't take a rocket scientist to recognize that the moon appears "full" approximately every 29 or 30 days. But from observation alone, it is impossible to predict exactly when any phase of the moon will be visible, or invisible if you include the conjunction. It is also impossible from observation to predict exactly how long any particular phase will last as they can vary from 6 to 8 days in length.

And prediction was very important to the official astrologers, magicians, "wise men" or whatever title held by those whose job it was to advise the rulers of nations. So a great amount of time and effort was put into recording observations and attempting to use that data to predict astronomical events, particularly eclipses. And the conjunction of the moon and the sun occurs as an eclipse on a regular basis. But no one figured that out until a Greek astronomer named Meton announced that it was a 19-year cycle at the Olympic Games in 532-533 BC. (It is not known if he received the first gold medal for "cycling" or not. ;-)

This lack of knowledge was partly, or perhaps even largely due to the fact that astronomy was not yet a pure science as we know it today, but was hopelessly intertwined with astrology and superstition until the 8th century BC, which is considered to be the beginning of modern astronomy as a science.

Interestingly enough, in the 8th cent. BC, all the "wise men" of Judah were the unwilling "guests" of the Babylonians. It was the custom, and still is to some extent, that p.o.w.'s who are scientists are put to work for the benefit of their captors. The Allied nations offered jobs to the captured German scientists after WWII. Nebuchadnezzar, king of Babylon, ordered that the Israelite (Jewish) prisoners who were "skilful in all wisdom, and cunning in knowledge, and understanding science, and such as had ability in them to stay in the king's palace" (Dan.1:4) and so we have the story of Daniel and of the three princes who were almost "fired" for not practicing idolatry.
The Jews now had the problem of identifying the day on which the first crescent could be seen in Jerusalem. But they were in Babylon. Learning to do calculations could solve their problem, and give the king advance notice of an eclipse. But forecasting requires accurate information and no one had yet discovered how long the solar year actually is. It would be another 200 years before Meton would discover the "19 year" cycle of the moon (532 BC). And it would be at least 1,000 years after that, before the Jews would discard the Babylonian 8 year cycle for Meton's. (Actually Meton was wrong and Hipparchus improved the number in the 2nd cent. AD, but it still bears Meton's name. You see, the "19 year cycle" isn't exactly 19 years.)

So when the Jews were allowed to return to Jerusalem in the 6th cent. BC, they still used observations. Records from 650 years later, about 70 AD, show that the new moon was still "fixed" by the priests, based on observations. It would be over 700 years after their stay in Babylon, before a set of calculations would become available and even then, they contained errors. The Jewish astronomer Samuel (c. 200-250 AD) working in Babylon, sent a set of calculations for 60 years to the High Priest in Jerusalem. He was the first Jewish astronomer to get the length of the solar year nearly correct, but he still lacked other vital principles to get the calculations correct.
According to Jewish accounts, the calculations, when available, were used only to check the observations until, by one tradition, they were made public in 359 AD. Jewish scholars admit that the current Jewish calculations cannot be dated any earlier than 921 AD.

But even after they began to use calculations, it was important that the first day coincide with the first visible crescent. Hence, we still see the "postponement" rule that says if the "molad of Tishrei" occurs after 12:00 noon, Rosh HaShana (Festival of Trumpets) is postponed until the next day "because the moon would not become visible until the next day."
Astronomically, this assumes two things, both of which are incorrect, but they either didn't realize this when they began using the calculations or, with the increasing oppression of Roman occupation of Palestine, they simply ran out of time to figure out a solution.
The Jewish calculations assume 1) that the molad (or at least the molad of Tishrei) always occurs directly over Jerusalem and 2) that a visible first crescent would always be visible (also in Jerusalem) either on the day of conjunction or the day following.
In the real universe, as opposed to the theoretical, the conjunction of the moon and sun occurs over a different meridian every month and may never have occurred directly over Jerusalem. From the astronomical conjunction, the first illumination of the crescent may not be visible anywhere for up to two days. When using a "mean" conjunction, the first visible crescent can actually occur prior to the Jewish calculated "molad" or up to two days afterward.

 

A "Definable" Starting Point

A major problem for all star-gazers, as they were sometimes called, was that neither the solar year nor the moon have cycles that can be measured in whole numbers. There are many variables, the moon alone has nearly 1,500, over 500 of which are necessary to determine its position at any one time. And some stars actually appear to move backwards during their cycles.
Another obstacle to understanding the celestial universe was the concept that the earth was the center of all movement. Even scripture speaks of the sun as "rising" and "going down" (Gen. 15:17, 2 Sam. 23:4, Mat. 5:45, Mk. 1:32). When Copernicus published his "On The Revolutions" in 1543, his idea of the earth orbiting the sun had been public for 30 years. The book contained an anonymous preface by the publisher which called his concept a "hypothesis for computation only" and so its publication did not cause any noticeable reaction. But when Galileo began to actively promote the idea as fact and published his own "Dialogue" in 1632, the Catholic Church, by the authority of the Inquisition, sentenced Galileo to life in prison for promoting heresy and both books were banned by the Church for the next 200 years, until 1835. It wasn't until the 1990s that the Catholic church publically acknowledged that "there was room for more than one viewpoint". In effect, they still maintain that everything in space, including the sun, orbits the earth.

Even after astronomers adjusted their thinking to the fact that our planets are moving around the sun, the problem of actual measurement still remained. The planets went in circles, or more correctly, flattened circles called ellipses.
To look into space and realize that everything (actually including the sun) is moving, and to attempt to measure those movements requires more than ordinary arithmetic. Geometry basically began with the Greek, Archimedes in the 3rd cent. BC. The first publication of algebraic formulas was by an Egyptian in the 3rd cent. AD. Trigonometry is credited to Hipparchus, a Greek living in 140 BC, with contributions by Menelaus, a Greek, c. 100 AD, and Ptolemy, a Greco-Egyptian, c. 87-150 AD. Calculus was developed in the late 1500's to mid 1600's by Kepler, Cavalieri, Fermat, and Leibniz but is usually credited to Sir Isaac Newton.
(See also Footnote 1).

Theoretical models of planetary movements could only be constructed as the math was developed to describe the theories. And the theories were only as good as the math being used at the time. The Julian calendar of the 1st cent. AD was based on a solar year that was still incorrect by 11 minutes, 14 seconds. This difference amounted to a day and a half in two centuries and 7 days in 1,000 years. The matter was often brought before (Catholic) "church" councils, but "the astronomers consulted doubted whether enough precise information was available for a really accurate value of the tropical year to be obtained." ("calendar", http://britannica.com)
By 1542, the vernal equinox, which was used to determine Easter, was 10 days out of place with the calendar. Neither Pope Paul III nor his successors could obtain any workable solutions until 1572. Finally in 1582, Pope Gregory XIII issued a bull, based on the recommendations of an Italian astronomer and approved by a Jesuit astronomer, omitting 10 days from the calendar, authorizing a new length for the tropical year, and requiring one extra day be added every fourth year, except in certain years. In English speaking countries, and in many others, this is the calendar on your wall.

But beyond the continuing problem of improving the math to improve the models, were other, as yet undiscovered variables including the fact that the earth is slowing down and the moon is speeding up.
As late as the 20th century, models still quickly became obsolete. The theories for the moon and other planets, developed by the U.S. Naval Observatory between 1877 and 1900 could not be used past 1960. Their theories for the earth were good only until 1984.
On their web pages, the USNO Astronomical Applications Department mention that they frequently receive requests for the formulas or algorithims used to compute astronomical phemomena for the sun and moon. Their response is, "Unfortunately there is no single formula that can be used to accurately predict times of these phenomena over an acceptably wide range of dates and places." Among the resources to which they refer readers is an algorithm published in 1996 that is valid only until 2050.

A logical starting place to begin to measure the moon's orbit was when it passed something and, as viewed from earth, it appears to "pass" the sun every month. The moment when the center of the moon's disc passes the center of the sun's disc was, although invisible, at least a definable point from which to start. Thus the "conjunction" of the center points of the two discs, even though no one could see it, became the astronomical border between the "old moon" and the "new moon" but only for the purpose of trying to measure the cycles.
Almanacs, or diaries of the planet's positions, are produced by astronomers. Wall calendars are produced by printers who refer to astronomical almanacs. To an astronomer, the "new moon" is the theoretically calculated moment of conjunction. In a scientific discussion, the "new moon" does not include the moment after conjunction nor the days nor phases after conjunction. That would only allow room for confusion, and the purpose of adapting, what to astronomers and scientists was an archaic term, and assigning it to a definable moment of event, was to eliminate confusion within their work.

Confusion among non-astronomers still arises however due to several factors. The term "new moon" has two specific meanings just as "north" can mean either magnetic north or celestial north, neither of which are critical to the average person who is oriented by the average sunrise and sunset.

Dictionaries often give more than a single definition for words or terms, because of common usage, slang, or specialized meaning according to a profession, trade, scientific or artistic usage. Hence, under "new moon" we see two definitions, one describing a conjunction of the moon and sun, and another describing, "the moon shortly after this phase when it is visible as a crescent."
The second definition is the historical and the common usage, or at least common prior to everyone having a preprinted calendar on their wall. The first definition reflects the astronomers' scientific usage in their efforts to measure movements and cycles.
Confusion can arise when the average person who has no background in astronomy sees the theoretically calculated "new moon" on a pre-printed wall calendar and yet, may or may not see a visible first crescent (the historic or common "new moon") on that night.

Confusion in the use of the term "new moon" also arises from the use of the Jewish calculated calendar which was invented to determine, from locations outside Palestine, the first visible crescent over Jerusalem. Because a "mean" conjunction is used and because certain postponements are applied to prevent certain feast days from conflicting with the Friday and pre-Atonement preparation rituals, God's feast days of Lev. 23 are not always observed on or in relation to the first visible crescent. The second rule of the Jewish postponements was to insure that the first day of the month is the first day that a visible crescent can be seen. But because the Jewish calculations depart from astronomical reality, that will only be true occasionally. In spite of the variations between the theoretically calculated, astronomical "new moon", the "mean new moon" (or "molad") used in Jewish calculations, and the historic "new moon" (or visible first crescent), all of these terms are often used interchangeably by some who write articles on the subject of observing God's feast days.

 

"Birth" or "Baby"?

According to Jewish scholars, the "new moon" always was and still is the first visible crescent. However, for purposes of their calculated calendar they use the Hebrew word "molad" to refer to the day (and more specifically, the moment) of conjunction. "Molad" means "birth".
In the OT, every reference to "new moon" uses the Hebrew word "chodesh", which literally means the "newness" of the lunar crescent. It comes from the root "chadash" meaning to "be new" or to "rebuild". The Hebrew word for month is "yerah" which means "month or moon" and refers to a complete lunar cycle. The word "chodesh" can mean "month'' but only by "implication" (Strong's 3391, 2320). The difference is illustrated by their usage in 1 Kings.

1 Kings 6:38, ". . . in the month (yerah, lunation) Bul, which is the eighth month (chodesh, newness)"

1 Kings 8:2, ". . . in the month (yerah, lunation) Ethanim, which is the seventh month (chodesh, newness)."

Each month the moon is invisible for 1.5 to 3.5 days. Because it was seen "anew" after a period of invisibility, the ancients called it a "new moon" or (c)hodesh from (c)hadash meaning "new".

The term "new moon" is used only once in the NT, where it is translated from the Greek, "noumenia", meaning "the festival of the new moon". It is a combination of "neos" meaning "new, fresh, or (fig.) regenerate", and "men" meaning "month".

To equate "molad" with "chodesh" is equivalent to saying that the "moment of birth" or the "day of birth" of your child is your "newborn". The two terms are related but not equal. The birth is not the baby.
Ancient Israelites looked for a "chodesh", the "newness" of the lunar crescent, not for a "molad" or birth. The moon is not visible at conjunction unless there is an eclipse. Even then it may be seen by only a few people or by none at all if it occurs over an ocean. An illuminated moon, will sometimes not occur until two days after the astronomical conjunction because illumination is more a matter of angle of distance from the sun, as viewed from the earth, than a matter of time from the astronomical conjunction.

In Isa. 24:23 and 30:26, the Hebrew word translated as moon is lebanah which means the "white".
In Genesis 1:14-18, God ordained the sun and moon saying, "Let there be lights . . . to divide the day from the night: and let them be for signs, and for seasons, and for days, and years:
And let them be for lights . . . to give light upon the earth: . . .
. . . the greater light to rule the day, and the lesser light to rule the night: he made the stars also.
. . . to give light upon the earth,
And to rule over the day and over the night, and to divide the light from the darkness: . ."

Light or lights is used seven times in the passages above. This is translated from the Hebrew words 'ore and ma'ore which come from the same root and both of which mean "illumination, luminary, luminous, light, and brightness".

The dark phase of the moon is the period when it described as being withdrawn .
"Thy sun shall no more go down; neither shall thy moon withdraw itself: . . . "(Isa. 60:20).
The word withdraw is from the Heb. acaph. Strong's 622. "acaph, a prim. root; to gather for any purpose; hence to receive, take away, i.e. remove, utterly take away".

"So David hid himself in the field: and when the new moon was come (Heb. hayah), the king sat him down to eat meat." (1 Sam. 20:24).
Strong's 1961. "hayah, to exist, to be or become, come to pass: --beacon, be."
[Also a name of God, the "I AM" of Ex. 3:14.]
"And it came to pass on the morrow, which was the second day of the month, . . . " (1 Sam. 20:27).
The "new moon" is described as something which "comes". The "morrow" was the "second day", hence the "new moon" was, and is, the "first" day of the month.

Summary

What is a "new moon"? It depends upon whom you ask. If you ask the average person on the street or a non-observant Jew, an Orthodox Jew, a professional astronomer or meteorologist, a publisher of wall calendars, a secular historian, or a Catholic scholar, you could get five or possibly six different answers, any of which could be "correct" depending upon the context of the question.

The "ecclesiastical new moon" is subject to "ecclesiastical [church] calendars" which are based on cycles of "movable" and "immovable" feasts and is determined by tables built on the Metonic cycle. It is not the same as the astronomical new moon.

"In the Gregorian calendar, the date of Easter is defined to occur on the Sunday following the 'ecclesiastical full moon' that falls on or next after March 21.", (which may or may not be the vernal equinox). The "ecclesiastical full moon" being the 14th day after the "ecclesiastical new moon".
("Calendars" by L.E. Doggett, Calendars and their History, http://charon.nmsu.edu)

If this sounds strange, it should be pointed out that the Catholics were trying to imitate the Jewish calendar without imitating the Jews, and ended up imitating the error in the Jewish calendar which causes it to drift away from the spring equinox.
(Catholic Encyclopedia, "Christian Calendar", http://www.newadvent.org/)

Historically the term "new moon" has always, and still does, in common usage, refer to the first visible crescent. This includes both Jewish history and tradition as the Jews and Israelites, prior to 70 AD used the first visible crescent. Their calculated calendar is a temporary institution which they plan to abandon just as soon as a new sanhedrin can be established in Jerusalem, after which they plan to once again use visual observation, although they may use updated and corrected astronomical data for checking in case visual observation is hindered. But they will be using the illuminated moon for observation and not the darkened conjunction.
"The first appearance of the new moon determines the beginning of the month. At first a small and faint arc, like a sickle, can be seen by those endowed with good sight, from spots favorable for such an observation."
("Calendar, History of:", The Jewish Encyclopedia, p. 502, Funk and Wagnalls, 1903).

Most, if not all, non-Jewish ministers who teach observance of the Feast Days of Lev. 23, fail to point out the differences between a "mean molad", an astronomical "new moon", and the calculated Rosh HaShanah of the Orthodox Jews.

Reference to the theoretically calculated, astronomical conjunction as the "new moon" is the result of the adoption, of a pre-existing term, which occurred no earlier than the fourth millennium after Creation. It is useful to astronomers and scientists as a definable point from which to measure movements, but its calculation is still referred to as being among the "theories of movements" which must be periodically revised as they become obsolete through variations and changes in actual movements and cycles of the planets and stars.

The symbolism in scripture regarding light, truth and God himself, is too large a subject to address here and so, shall be addressed in a separate article. But it seems incongruous that with all the scriptural emphasis and analogies regarding light versus darkness, and sight versus blindness and light equated with truth and with "the (right) way" of life, that God would institute an "invisible" sign of the "dark" of the moon, which can only be theoretically calculated in advance and which could not be calculated to a rough degree of accuracy until some 3,000 years after the sign-dependent Feast Days of Lev 23 were given. Christ said he came to, among other things, to figuratively and literally give sight to the blind (Lk. 4:18). It would seem symbolically incongruous, as well as a cruel joke, to establish a physical "sign", the literal use of which would lead to physical blindness, when the expressed purpose of the knowledge of God to give us spiritual "sight".
The greatest single symbolism in scripture is Israel's coming out of Egypt after the first Passover, which was accomplished "by night" and "in the 15th day of the (lunar) month" which indicates they were traveling under a fully illuminated moon (Deu. 16:1; Ex. 12:2-8, 12, 29-31, 37-42; Num. 33:3). This was after a recent plague in which all Egypt was in total and absolute "darkness" (blindness) for three days, while the homes of the Israelites had "light" (Ex. 10:21-23).

As man's knowledge increases, especially as we approach the "time of the end" (Dan. 12:4), the "theoretical models" used to determine the moon's astronomical conjunction should become more accurate and more easily adjusted to reflect actual cycles. But by the same token, approaching "the end" means approaching the "one world government" (or "beast") of Revelation 13-20 which shall control all buying and selling (in effect all aspects of human life).
In Amos 8, the prophet Amos relates a vision of "the end" (verse 2). In verse 5, people are prophesied to say, "When will the new moon be gone, that we may sell corn? and the sabbath, that we may set forth wheat, . . .?"
In Rev. 13, a "beast" is described as an individual (v. 11-15) who rules over "a world government" (v.1-2) which issues a permit, or proclaims a law, or somehow regulates all buying and selling. Historically, the Roman Empire and the Catholic Church have been the only organizations large enough to have fulfilled these prophecies. Historically, the Catholic Church has regulated the calendar and enforced prohibition of "buying and selling" on Sunday. The residue of this is still seen today in some parts of the U.S. where certain types of businesses can only be open during certain hours on Sunday and others cannot open at all.
Historically, the pagan "pontiffs" of earliest Rome held absolute rule over all astronomy and calendars for over 1,000 years before they became "Christian" with the conversion of Constantine in the 4th century AD. After this they still held absolute power until the Reformation, and their influence is still seen in the calendar on your wall.
Today, your wall calendar is calculated by offices of the U.S and British Navies under the authority of two world organizations based in France, a predominately Catholic country, in which the wall calendars already show Sunday as the seventh day (or Sabbath) of the week. France is a dedicated member of the European Union, the most likely organization to fulfill the prophecies of Revelation which lead to a single world government.
Dan. 7:23 is a prophecy about a future world government that controls the entire world and will seek to "change time and laws" (v.25).

Unless you have a professional knowledge of astronomy and the skills of an astronomer, possess the most recent observational data, have knowledge of calculus and the algorithms (2) to perform the calculations, and understand the most recent theoretical models of planetary movements you cannot determine the moment of astronomical conjunction.
You can try to determine it by counting from what appears to be a full moon, and will probably be correct within one or two days but may occasionally be in error by three days. For instance, the astronomical full moon for February 8, 2001, is at 12 midnight UT (Greenwich, England). Our location is 6 hours earlier than Greenwich and sunset on Feb. 8, is 6:01 local time. This means that the full moon is on the Hebrew day (sunset to sunset) of Feb.9.
Had the astronomical full moon occurred two minutes earlier, it would have been on Feb. 8 by the Hebrew reckoning. Had it occurred one minute later, it would have been shown on our commercially printed calendar as being on Feb. 9th. and would have been on the Hebrew day of Feb. 9th.
The astronomically calculated time of sunset for any location assumes a level earth surface, allows for the refraction at horizon (we actually see the sun before it rises and after it sets), and is based on the highest edge of the sun's disk. Because of geographic features (mountains, valleys), and climatic conditions (clouds, dust, pollution) actual sunset for us may vary from the time given.
On Feb. 8, 2001, variations in sunset of one or two minutes will make one day's difference in counting.

By astronomical calculations the moon will have 0% illumination on both January 24th and 25th, 2001. Which day is the new moon? It will have 100% illumination on both October 2nd and 3rd, 2001. Which day is the full moon?

Prior to the Industrial Revolution of the mid-1800's, all of the earth's nations were agriculturally- based societies. When your immediate, short term and long term survival are all directly dependent upon agriculture, you must be acutely attuned to the weather, to the daytime sky and the early morning and late evening sky. This was true for all humanity for the first 5,800 years of its existence. It is still true for some Third World nations, but in industrialized nations it is true for only about 1% of the population.
Most have become disconnected from the "signs" God gave us for "signs, seasons, days and years". Most could not define the words "equinox", much less recognize it by the shadows in their own yard or through a window. We all tell time by a watch, not by the sun (12:00 noon will only occasionally correspond to the sun being at its highest point in the sky). If we want to know about sunrise or sunset, we look at a television. Day and night don't matter much since we have electric lights and access to work, education or entertainment all night long. We have literally insulated ourselves from summer and winter, so that our lives continue year round as if there were almost no difference. We all enjoy the comforts produced by industrialization and technology. We can make positive use of most of the products and services of industrialization.

What happens when the electricity goes off? What happens when the astronomers cannot move their electrically powered telescopes, or operate their electric calculators or boot up their computers to access their theoretical models, their database for computations, or their software for calculations? What happens when your power goes off and your television doesn't work? When the television station doesn't have power to broadcast? When the printer can't print a new calendar? When the battery in your watch dies?
Even if you were an astronomer and understood the celestial system, your options would be limited to "wysiwyg", a computer term for "what you see is what you get". Would you look at the visible moon and mentally calculate the number of days until the mid-point of its time of invisibility, so that you could count from that to determine the next mid-point of invisibility?
Even if you could successfully accomplish this, how would you answer your children when they ask why the visible first crescent and the visible full moon don't correspond to your count of days? How would you explain that the "signs" of Gen. 1:14 have little or nothing to do with the day of the month? How would you explain to your child "how they did it in the old days", before electricity, before astronomy was a science, before a reasonably correct length of the year was known, before anyone could calculate something which you still cannot see?

The more one understands God's creation through astronomy, the more sense it makes that the ancient Israelites used observation and the Jews also, who say that observation alone was used until after the time of Christ.

These are all things to keep in mind if one chooses to use the astronomical conjunction as the beginning of the month or uses it to roughly determine when the first visible crescent might appear.

 

Separation of Church and Science

When any science, such as astronomy, is under the control of an organization that manipulates or changes the product in order to conform to or to support human traditions or opinions, then that product or information is not just useless but dangerous in that it will cause confusion. A classic example is the reaction of the Catholic Church to Galileo and his true understanding of our universe. Paul wrote about those who "changed the truth of God into a lie" (Rom. 1:25).

When any science, such as astronomy, is not manipulated to vary from reality, then it merely is a description of what God has created.

God controls how much knowledge man can access. At the tower of Babel, he confused the languages to prevent a single world government which would have bought about the events of Revelation too soon (Gen. 11:1-10, esp. v. 6). He revealed through Daniel that man would have access to more knowledge as we approach the time of the end of the world (Dan. 12:2).

Can we use any of this increased knowledge in "watching" the "signs" which God gave us to find his feast days? As long as the information is true and accurate, it is simply a measurement of what God has created. God never condemns knowledge, rather he encourages us to seek it (Pro.1:7, 22; 2:1-6; 3:19-20; 8:10-12).

With that in mind, we come back to the question of, "what is the new moon?". To an astronomer it is the moment of conjunction and that serves their purposes of measuring. To one who is seeking an approximately 24 hour period as the first true day of the lunar month it would be something after that event. Since the conjunction, by definition, occurs at high noon, and God's definition of a day begins at sunset, the earliest it could be is the period beginning at the next sunset, at least 6 hours east of the point of conjunction, and usually further.

If the first visible crescent were always seen just after that sunset, there would be no question as to the "first" day. But because the illumination is more dependent upon its angle from the sun as seen from earth, than it is upon time elapsed from the moment of conjunction, we will not always see a crescent with the first sunset after conjunction. It may be one or two days later before we will see a crescent. Other factors include the distance from the meridian of conjunction to our location, the time of year, the viewing conditions at our location, the condition of our eyesight, and our looking in the right part of the sky at the right moment.

If we don't see the first crescent, but it is a day after the conjunction, does it still count as the first day? We could give several examples of things not seen, but which are still in effect. For instance if it is cloudy during the first half of Abib, we must still count 14 days from some point, to find Passover. If we are physically blind or have difficulty seeing, we may have to depend on someone else to tell us about sighting the first crescent. Is there any difference between that and depending upon astronomers to tell us of the conjunction and the degree of illumination?

In most cases, according to the calculations of astronomers, there will be some degree of illumination on the Hebrew day (sunset to sunset) following the noon conjunction. Whether it can be seen at all, or whether you can see it from your location is subject to various factors as mentioned above. Whether you see it or not, it still exists, if the astronomers are accurate in their calculations. If it exists, it is by God's design, not by human invention. If it exists, then it can be counted.
The U.S. Naval Observatory web site gives the time of conjunction to the nearest minute. It also gives tables of the degree of illumination for every day of the year. Tables of times for sunrise and sunset are given and for equinoxes and solstices. Using this information, it is easy to determine the first month of the year, and the first day of the month.
If it ever happens that this information is not available, or that it becomes unreliable, then we will still have the visible "signs" that God gave us.

***

Footnotes:

(1) The History of Math

Algebra; Arabic al-jabr, "the putting together of broken things", The reduction of fractions to whole numbers. The system of math in which signs and letters are used to represent operations and quantities. Its earliest simple form found in a papyrus of 1650 BC. First publication of algebraic principles by Diophantus of Alexandria in 3rd cent. AD.

Geometry: Gk. "earth + measure", a system involving the properties, relationships, and measurements of points, lines, angles, surfaces and solids. Example mentioned in 2K. 7:23 of pi =3 (sic) (c. 1075-975 BC). Basically began with the Greek, Archimedes, 287-212 BC.

Trigonometry: Gk. "triangle + measurement" or the "study of triangles". The system of math dealing with relations between the sides and angles of a plane or spherical triangles and their calculations. It was developed to measure distances that could not be measured by hand. The Greek Hipparchus (c. 140 BC) is called the "founder of trigonometry".

Calculus: L. calculi, for pebble or stone used in counting. The study of variations of functions, using a specialized set of algebraic symbols and a systematic method of computation, usually subdivided into calculus of variations, differential and integral calculus.
The development of calculus is credited mainly to the works of Kepler, Cavalieri, Fermat, Leibniz, and Newton from the late 1500's to the late 1600's. Many others contributed to the effort, but Issac Newton (1642-1727) is considered the "father of calculus".

In the scientific communities, it is understood that modern astronomy could not have been developed or exist without the development of calculus.

(2) algorithms, (Math.) a number of rules, which are to be followed in a prescribed order, for solving a specific type of problem.

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