How Are Eclipses Predicted So Precisely?

Requirements for a Lunar Eclipse

Learning about eclipses probably was part of subduing the earth of Genesis 1:28, so God likely left it to man to discover and explore eclipses for himself.

Such accuracy has not come easily. We presume that early man had no prior knowledge of eclipses. Learning about eclipses probably was part of subduing the earth of Genesis 1:28, so God likely left it to man to discover and explore eclipses for himself. With some observations of the moon over months, along with some reflection, the cause of lunar phases is clear enough to figure out. The moon is a sphere, with half the moon always lit by the sun. As the moon orbits the earth each month, the amount of the lit half of the moon that we see changes. It is this changing amount of the lit half of the moon that we see throughout the month that causes the phases. However, this nice pattern is occasionally interrupted when the moon is darkened during a lunar eclipse. A lunar eclipse is a relatively rare event, but with time, people eventually learned that lunar eclipses only happen when the moon is full. It is obvious that at full moon, the moon and sun are opposite in the sky, with the earth interposing between the two. Hence, a full moon is the only phase that the earth’s shadow could fall on the moon. Therefore, the cause of lunar eclipses must be the earth’s shadow falling on the moon.

But lunar eclipses don’t happen every full moon. How can that be? As the earth orbits the sun each year, from the earth, the sun appears to move once through the stars. This great circle around the sky is the intersection of the earth’s orbital plane with the sky. At the same time, the moon orbits the earth each month. The moon’s monthly motion through the stars defines its orbital plane. However, the moon’s orbital plane is inclined 5.1 degrees to the earth’s orbital plane. Therefore, these two great circles (the earth’s orbit and the moon’s orbit) intersect in two points called the nodes. If the moon is near a node (and hence near the earth’s orbital plane) when the moon is full, then a lunar eclipse occurs. However, if the moon is not near a node, then the full moon passes above or below the earth’s shadow so that no lunar eclipse occurs. This recognition that the moon must lie near the earth’s orbital plane for a lunar eclipse to occur provided the name for the earth’s orbital plane, the ecliptic.

“Wait,” you may say. “I thought you were talking about solar eclipses.” Indeed, I was. But it is best to start discussion of predicting eclipses with lunar eclipses. Solar eclipses are more common than lunar eclipses, but lunar eclipses are more often seen than solar eclipses. This is because a lunar eclipse can be seen by the entire night side of the earth, plus a little more that rotates into the night side of the earth during the eclipse. On the other hand, only a portion of the sunlit half of the earth experiences a solar eclipse—much of the earth’s dayside is missed by the moon’s shadow. Furthermore, only people in the very narrow path of totality would know for sure that an eclipse happened. Out of that path of totality, most people wouldn’t be aware that an eclipse is going on. The only exception might be locations where a partial solar eclipse occurred near sunrise or sunset, where people might notice the greatly dimmed sun partially eclipsed. For these reasons, most ancient cultures primarily concerned themselves with lunar eclipses.

Knowing the cause of lunar eclipses enabled some ancient cultures to crudely anticipate when future lunar eclipses might happen. By careful observations and recordkeeping over years, some ancient cultures were able to determine the ecliptic. Similarly, the plane of the moon’s orbit and its tilt to the ecliptic were determined. Finally, knowledge of the orbital period(s) of the moon could be obtained. Combining this information allowed the development of algorithms to compute the positions of the sun and moon with some degree of accuracy. As suggested above, there are two requirements for a lunar eclipse:

1. The moon must be full.
2. The moon must be near one of its nodes.

The synodic month is the orbital period of the moon with respect to the sun. Since the phases are caused by the relative geometry of the moon and sun when viewed from the earth, the synodic month is the period over which the moon’s phases repeat. The synodic month is 29.530588 days. Hence, if a full moon occurs, the first requirement for a lunar eclipse, then the moon will next meet that first requirement after one synodic month. What about the second requirement for a lunar eclipse? The draconic, or nodical, month is the orbital period of the moon with respect to its nodes. The draconic month is 27.212220 days. When a lunar eclipse happens, the moon must be near a node, the second requirement for a lunar eclipse. Therefore, the moon will next meet the second requirement for a lunar eclipse after one draconic month. Notice the 2.32-day mismatch between the synodic and draconic months, so a lunar eclipse likely will not happen a month following a lunar eclipse. To crudely predict lunar eclipses, all one need do is compute when full moons will occur (once each synodic month) and when the moon will be near one of its nodes (this will happen twice each draconic month) and then look for times when the two requirements reasonably coincide.

Because there are two eclipse seasons per year, there must be at least two lunar eclipses each year.

Note that while the first requirement must be strictly met, there is some leeway in the second requirement. It’s like horseshoes and hand grenades—close is good enough. But how close? There are eclipse limits along the nodes, extending a little more than 30 degrees along the ecliptic. Since a lunar eclipse can happen only at full moon, which happens when the sun, earth, and moon line up (what we call a syzygy), a lunar eclipse can happen only when the line of nodes points generally toward the sun. There are two times per year when this happens, defining eclipse seasons nearly six months apart. Since it takes the earth a little more than a synodic month to travel through the eclipse limits, there must be at least one full moon, and hence at least one lunar eclipse, every eclipse season. Because there are two eclipse seasons per year, there must be at least two lunar eclipses each year. Gravitational effects tug on the moon’s orbit so that the nodes precess, or slip, around the ecliptic over an 18.6-year period. Consequently, the eclipse seasons are about 20 days earlier each year.

The Saros Cycle

Are you confused yet? You probably aren’t alone because predicting eclipses is not a simple matter. However, there are some shortcuts that one can find. Suppose that a lunar eclipse were to occur tonight. That would mean that both requirements for a lunar eclipse were met at the same time. After each successive synodic month, the first requirement will be met again, but what about the second requirement? The second requirement will be met again each successive draconic month. Since there is a difference of more than two days between the two types of months, the two requirements for a lunar eclipse generally will not be fulfilled a month after the eclipse. Nor will the two requirements be met the following month . When will these two requirements be met simultaneously again? There are 6,585.32 days in 223 synodic months. This is nearly equal to 6,585.36 days, which is 242 draconic months. That is, after 18 years and 11 1/3 days, the two requirements for a lunar eclipse will be met once again. Astronomers call this period over which nearly identical eclipses occur the saros cycle. When hearing about the saros cycle for the first time, it is easy to get the impression that it must be 18 years between eclipses, so you may wonder how there can be more than one eclipse in a year. More on that in a moment.

The difference between 223 synodic months and 242 draconic months is only 52 minutes. This means that once a lunar eclipse occurs, a nearly identical (similar depth and duration) lunar eclipse will happen 18 years and 11 1/3 days later . The one-third day means that after a saros cycle, a very similar lunar eclipse will occur, but the portion of the earth that will see the eclipse will be shifted about 1/3 away around the globe. Therefore, after three saros cycles (54 years and 34 days), a similar lunar eclipse will happen near where the first lunar eclipse was seen. For instance, I saw my first lunar eclipse on the night of April 12–13, 1968. Fifty-four years later (three saros cycles later), there was a similar eclipse on the night of May 15–16, 2022. Unfortunately, it was cloudy where I lived that night, so I couldn’t see that eclipse.

Saros Cycle for Solar Eclipses

What are the requirements for a solar eclipse? They are:

1. The moon must be new.
2. The moon must be near one of its nodes.

Since the requirements for a solar eclipse and the requirements for a lunar eclipse are so similar (the only difference is the phase of the moon), the same periodicities can be used to roughly compute when a solar eclipse may occur. So, the saros cycle also applies to solar eclipses as well. For instance, my first solar eclipse was on March 7, 1970. Where I grew up in Fairborn, Ohio, the eclipse was only partial (totality was a few hundred miles to the east and south). I set up my telescope in the front yard, where I projected the image of the partially eclipsed sun for everyone present to see at the same time. Back then, I lacked the equipment to take astrophotos properly. I did the best that I could by using a Kodak instamatic camera (with 126 film) to take a few photographs of the sun projected onto the screen. I’ve included here one of those long-ago photos. The April 8, 2024, eclipse is three saros cycles later, so the upcoming eclipse is a bit special to me. I hope that it is not cloudy that day like it was the night of the lunar eclipse I missed last year. Fairborn is in the path of totality this time. We moved away from that house 50 years ago. I had given thought to contacting the people in that house for permission to restage my first solar eclipse experience in the exact same spot with the exact same equipment (plus additional equipment), but they might think that strange. Plus, that location is well off the centerline of the eclipse, so I would sacrifice more than two minutes of totality to do that.

Saros Families and Series

In the 1950s, the Dutch amateur astronomer George van den Bergh studied the periodicities of eclipses (there are a few other cycles than the saros cycle). He organized eclipses into saros families, or series, that he numbered, a convention that is still followed. Successive members of a saros family of eclipses are separated by a little more than 18 years, but there are multiple saros families of eclipses going on at the same time. The eclipses from one eclipse season to the next are members of different families of eclipses. For instance, the total solar eclipse this April is number 30 of 71 solar eclipses in series number 139. The eclipse of this series I saw in 1970 is number 27 in the series 139. There are 180 numbered saros series. There are as few as 69 eclipses in a series, and as many as 87 eclipses in a series. Consequently, the duration of a series may be between 1,226 years and 1,550 years.

It is interesting to watch the development of the members of a saros series over time. For instance, this website lists information of all eclipses in series number 139. The first eclipse in series 139 was a barely partial eclipse seen only in the Arctic on May 17, 1501. It was barely a partial eclipse because the moon’s umbra passed high above the earth’s location. But with each successive eclipse in the series, the moon’s umbra passed closer and closer to the earth with each partial eclipse lasting longer and being visible farther south. After seven partial eclipses, a hybrid eclipse (annular on either end and total near the middle) happened on August 11, 1627, but the annular and total eclipses were seen only in the Arctic. With each eclipse, the path of totality continued to move southward. As the members of eclipse series approach the equator, the duration of maximum totality increases until the tropics are reached. The maximum totality of saros series 139 will be on July 16, 2187. Afterward, the members of series 139 will continue to move southward, with the last total eclipse being on March 26, 2601, visible only in the Antarctic. The final partial eclipse of series 139 will be on July 3, 2763, which again will be visible only in the Antarctic. That is the nature of saros series: they begin as partial eclipses visible either in the Arctic or Antarctic, develop into total or annular eclipses at lower latitudes, and then depart the earth at the opposite polar regions. Half the members of the series progress southward, and the other half progress northward. An example of a northward moving saros series is number 134, of which the October 14, 2023, annular eclipse is a member. Series 134 began as a partial eclipse in the Antarctic in 1248, and it will end as a partial eclipse seen in the Arctic in 2510.

The Babylonians appear to be the earliest civilizations to have discovered the saros cycle, probably about 2,500 years ago.

Early Discoveries

The Babylonians appear to be the earliest civilizations to have discovered the saros cycle, probably about 2,500 years ago. That information likely was transmitted to the Greeks because Hipparchus in the second century BC knew about it, as did Pliny the elder in the first century AD and Ptolemy in the second century. Civilizations in the Far East later independently discovered the saros cycle. How accurately can the saros cycle predict eclipses? The saros cycle can give an idea of roughly when an eclipse will occur, typically within a few hours. This can be useful in anticipating roughly when, within a few hours, and where a lunar eclipse will be visible. But the saros cycle is of no help in predicting where a total solar eclipse will be seen. The path of totality is narrow, less than 200 miles, and the earth rotates 15 degrees per hour. The uncertainty in times of eclipses using the saros cycle is a few hours, so there is no way that one can use the saros cycle to predict the path of totality with any accuracy.

Herodotus reported that Thales predicted a total solar eclipse, most likely the one of May 28, 585 BC. Herodotus wrote his Histories about a century and a half later, so he was not a primary source for this claim. Herodotus’ Histories is a blend of true history and legends. For events that occurred before his lifetime, Herodotus relied upon the words of others, whether written or oral traditions. Thales probably did not know about the saros cycle, and he certainly did not have access to later, better methods of eclipse predictions. Therefore, modern historians of science dismiss this account of Thales’ eclipse prediction as legend.

Beyond the Saros Cycle

Ptolemy improved upon the crude saros cycle for predicting eclipses. Ptolemy knew the distance to the moon in terms of the earth’s radius, and he also knew the angular diameters of the sun and moon. The saros cycle does not take these things into account, though they are important in honing eclipse predictions. Ptolemy’s eclipse model was similar to his epicyclic model for planetary motion and the motion of the sun and moon. Rather than using the periodicity of the saros cycle, Ptolemy’s method of eclipse prediction relied upon starting positions and the periods of motion of the sun and moon. As with the planets, one merely stepped the motions forward in time from their starting positions and looked for times when the moon was within the eclipse limits for an eclipse to happen. Ptolemy’s method was a slight improvement for solar eclipses but was much better at predicting lunar eclipses than relying on the saros cycle. His method could be used to foretell more accurately the time of a lunar eclipse, but it also was better at predicting whether a lunar eclipse would be total or partial, and in the case of partial eclipses, predict how much of the moon was obscured at maximum eclipse. Ptolemy’s method remained the standard method of predicting eclipses for more than 1,500 years.

The situation changed dramatically when, shortly before the May 3, 1715, total solar eclipse over the United Kingdom, Edmund Halley published his prediction for the eclipse. The time of Halley’s prediction was off by four minutes, and his path of totality was off by about 20 miles. While that is not so impressive by modern standards, it was revolutionary in that no one before had been able to predict a solar eclipse with such precision. Why was Halley’s prediction off? The most important factor in predicting eclipses is to have an accurate lunar ephemeris, an algorithm for calculating the moon’s position. Modern lunar ephemerides are much more accurate than the one available in Halley’s time. A century later, Friedrich Wilhelm Bessel improved upon Halley’s method of computing eclipses, with later refinements by William Chauvenet. This method pioneered by Halley remains the technique used today to predict eclipses.

For solar eclipses, the method begins by defining the fundamental plane, the plane passing through the earth perpendicular to the line between the earth’s center and the sun. Knowing the distance of the sun and the distance of the moon, one can compute the circular intersection of the conical shapes of the moon’s umbra and penumbra with the fundamental plane. Since the moon moves through the course of the eclipse, these circles move through the fundamental plane and hence must be computed as a function of time. Once this function is established, one computes the intersection of the moon’s umbra and penumbra with the earth’s surface. To facilitate the work, Bessel defined eight Besselian elements, which are computed at time intervals throughout the eclipse. For instance, the Besselian elements for the April 8, 2023, eclipse are found here. The approach to lunar eclipses is similar to that of solar eclipses. The fundamental plane is defined for the moon, with the plane passing through the moon’s center and perpendicular to the sun-earth line, and the earth’s umbra and penumbra are computed in the fundamental plane. The circumstances of a lunar eclipse are calculated by treating the moon as a circle moving through the shadows in the fundamental plane.

Theodor von Oppolzer oversaw the calculation of a vast number of eclipses using the modern method. In 1887, the Imperial Academy of Sciences of Vienna published Canon der Finsternisse (Canon of Eclipses), Oppolzer’s computations for all solar eclipses and umbral lunar eclipses between 1207 BC and AD 2161 (more than 13,000 eclipses!). This was the standard reference for eclipses for a century, though eventually more detailed calculations were done for eclipses of interest. NASA eventually began to provide bulletins for eclipse predictions, using computers programmed with the best algorithms available. Fred Espenak, an employee at NASA’s Goddard Space Flight Center, took over this task in 1978. He eventually published canons of eclipses, culminating in his Five Millennium Catalog of Solar Eclipses, and a Five Millennium Catalog of Lunar Eclipses. The predictions of these catalogs are extremely accurate, and they are the basis of modern eclipse predictions.

God has given us a wonderful gift in that solar eclipses are awe-inspiring but also quite rare.

Conclusion

Total solar eclipses are the most incredible phenomena in the world. God has given us a wonderful gift in that solar eclipses are awe-inspiring but also quite rare. God has also endowed man with the capability to understand how eclipses happen and how to predict when and where eclipses can be seen. But this can exist only in a world that operates by mechanisms that can be understood and are consistent. Earlier methods of eclipse prediction, such as the saros cycle, can be used to only crudely estimate when an eclipse might happen. Improvements in technology have enabled man to learn more about the intricacies of the creation and to predict eclipses with unprecedented accuracy. This is less a testimony of man’s ingenuity (which comes from God) as it is a testimony of how God operates the world in a consistent manner moment by moment (Colossians 1:16–17; Hebrews 1:3), thus revealing a little bit about the character of God. By all means, enjoy the eclipse on April 8, but keep in mind Who is behind the splendor of a total solar eclipse, realizing that the glory of totality can’t compare with God’s glory.