Reliable records of solar and lunar eclipses go back as far as 750 B. C. They bear on such questions as whether the sun is shrinking or the earth is not spinning as fast as it once did

Observers on our planetâastronomers, historians and even poetsâhave been recording eclipses of the sun and the moon for more than 2,500 years. Whatever their motivation, their records, both ancient and more recent, can help to answer questions that challenge investigators today. One such question is: Why is the length of the day (or the earth's rate of rotation) changing? Another is: Is the sun shrinking? On the first question eclipse observations long before the rise of telescopic astronomy have provided information of much value. On the second only the records of total solar eclipses since the 18th century are pertinent.

THREE PARTIAL SOLAR ECLIPSES (in 1530, 1532 and 1534) and three total lunar eclipses are predicted on this page of Calaulariurn Romanum Magnum, published in 1518. The author, Johann Stoffler of Tubingen, was a prominent Renaissance astronomer-mathematician. The handwriting in this copy of Stoffler's work, now in the library of the University of Uppsala, is that of Nicolaus Copernicus.

We owe the term "eclipse" to the ancient Greeks: ekleipsis means "failure," in the sense of something gone wrong. The image is apt, and if the orbits of the earth and the moon were in exactly the same plane, these failures would be far more frequent: two per month. At each conjunction, or new moon, the sun would be eclipsed; at each opposition, or full moon, the moon would be eclipsed. Actually, since the orbital planes are tilted with respect to each other by some five degrees, eclipses can come only when the new or full moon happens to be near one of the two "nodes" of its orbit. These are the points, 180 degrees apart, where the plane of the moon's orbit intersects the plane of the earth's. This limitation means that any one year may have as few as two eclipses (the number in 1984) or as many as seven (the number this year).

Weather permitting, a man in his lifetime might expect to see some 50 lunar eclipses, more than half of them total, and perhaps 30 partial solar eclipses. A total eclipse of the sun, however, is a rare event at any one location. For example, the last total solar eclipse visible in the vicinity of New York City was in 1925 and the next will not be until 2079. What makes the spectacle so rare is that the sizes of the sun and the moon in the sky are almost identical, and as a result the conical shadow cast by the moon barely reaches the surface of the earth. The path of totality may be some 15,000 kilometers long, sweeping across as much as 140 degrees of longitude, but the umbra, or region of dark shadow, is seldom more than 250 kilometers wide.

Whether a given solar eclipse is total or annular (with a bright ring of sun surrounding the disk of the moon) depends on the position of the moon in its elliptical orbit. When the moon is near perigee, its point of closest approach to the earth, it is able to cover the sun completely for as long as 7.5 minutes. When the moon is near apogee, its point of most distant recession, its shadow falls considerably short of the earth and the eclipse is annular. The duration of an annular eclipse can be as long as 12.5 minutes. Astronomers call total, annular and near-total eclipses of the sun large events, as opposed to the smaller events of partial eclipses.

Is the sun really shrinking? Two large bodies of data bearing on the subject are the daily observations, weather permitting, of the transit of the sun (in order to measure its right ascension) at the Royal Observatory in Britain since 1750 and at the U.S. Naval Observatory in Washington since 1846. The observations include the time required for the sun's image to pass a wire fixed in the eyepiece of a telescope; the interval, of course, also measures the size of the image. In 1979, after analyzing substantial amounts of the data from both observatories, John A. Eddy of the High Altitude Observatory of the National Center for Atmospheric Research and Aram A. Boornazian, a mathematician at S. Ross and Company in Boston, announced their conclusion that the sun is indeed shrinking, and at a considerable rate. They estimated the shrinkage of the sun's horizontal diameter to be about two seconds of arc, or about .1 percent, per century.

The sun's disk is brilliant, however, and the transparency of the earth's atmosphere is both imperfect and variable; these factors make accurate determination of the solar diameter by this kind of observation difficult. It is therefore not surprising that individual transit observations are less than precise and are also subject to considerable observer bias. As a result at least part of the trend detected by Eddy and Boornazian could actually be an artifact of observational error. An alternative and independent source of data regarding solar shrinkage is the duration of total solar eclipses. (A second independent check is provided by the time the planet Mercury takes to cross the solar disk.) Such observations allow a monitoring of changes in the sun's diameter at fairly regular intervals back to about the start of the 18th century, or roughly twice the span of time covered by the British and American transit data analyzed by Eddy and Boornazian.

Few total solar eclipses were visible in Europe in the 17th century. I know of only two observations: one made in southern Italy in 1605 and one made in northern Ireland in 1652. Indeed, the first known telescopic observation of a total solar eclipse was made in France in 1706. The first total solar eclipse to be carefully timed by a substantial number of observers in Europe was the eclipse of 1715, which was on May 3 (according to the Gregorian calendar). Most of the credit for this effort goes to Edmund Halley. Well before the event he "caused a small map of England, describing the Track and Bounds [of the eclipse], to be dispersed all over the Kingdom, with a Request to the Curious to observe what they could about it, but more especially to note the time of total Darkness, as requiring no other instrument than a Pendulum Clock with which most Persons are furnish'd, and as being determinable with the utmost Exactness, by reason of the momentaneous [sic] Occultation and Emersion of 'the luminous Edge of the Sun, whose least part makes Day."

Halley's motive in promoting the timing experiment was to improve the accuracy of future eclipse predictions. He harvested nine ostensibly accurate measurements from various parts of Britain. The duration of totality (about 3.3 minutes) was expressed to the nearest second of time; all but one of the nine measurements showed a small scatter, not much greater than the rounding error. Even the one discordant observation deviated by only seven seconds from the 200-second mean of the other eight, hardly a bad result. Converting the average of the eight into a measurement of the sun's diameter as it is now standardized, the sun in 1715 was smaller than it is today by two-tenths of a second of arc (with a probable error of four-tenths of a second).

The next total solar eclipse after the one of 1715 that was carefully timed came more than 125 years later. From 1842 until early in this century, however, most total eclipses were accurately timed, and astronomers often traveled to remote places to observe them. After 1925 the focus of eclipse observation shifted, to the neglect of totality timing, to such topics as the identification of lilies in the solar spectrum and the study of the structure of the solar corona. Only lately has the topic of timing, with the specific objective of measuring the diameter of the sun, regained its place. Much of the credit must go to Eddy and Qoornazian.

When the times of total solar eclipses over the past three centuries or so are analyzed in conjunction with the data on the transits, of Mercury, they suggest a conclusion contrary to the one based on solar right-ascension observations. In brief, the data indicate only a negligible change in the sun's diameter. John H. Parkinson of University College London, Leslie V. Morrison of the Royal Greenwich Observatory and I have calculated that the percentage of decrease is .008 ± .007 per century. Surprisingly, however, the data provide fairly strong evidence that the diameter of the sun oscillates. The period of the oscillation is some 80 years and its amplitude is about .025 percent. After investigating a wide variety of data Ronald L. Gilliland of the High Altitude Observatory supports this interpretation. In any event measurement of the sun's diameter on a regular basis seems worth pursuing in the future.
 
 

TOTAL ECLIPSE OF THE SUN in 1980 was visible on February 16 along a track no more than 150 kilometers wide that ran from west of the prime meridian to western China, a distance of 13,500 kilometers. It was visible mainly at sea and totality lasted for only about four minutes.

INNER PART of the sun's corona, normally invisible, rings the circumference of the moon in this photograph of the eclipse of February 16, 1980. Flecks of color are solar prominences;

TOTAL ECLIPSE OF THE MOON at the end of 1982 will also be visible mainly at sea, but if weather permits, it may be seen from start (black ellipse) to finish (colored ellipse) in Iceland, Greenland, all of Canada except eastern Newfoundland, all 50 states of the U.S., aU of Mexico, all of Japan and Korea, much of the eastern and arctic U.S.S.R., most of the Philippines, parts of Indonesia and Australia and all of New Zealand during the night of December 30-31.

TWO COMPONENTS of the earth's shadow appear in this photograph of the total lunar eclipse of January 9,1982, as totality was advancing. What appears to be a crescent missing from the moon's edge is the unibral sector; the lighter band beyond is the deep penumbra) sector.

When it comes to the variations in the earth's rate of rotation, only eclipse data from ancient and medieval times are of value. From about 1620 onward telescopic observations of the occultation of stars by the moon have replaced observations of solar and lunar eclipses as a source of information on the length of the day. The reason is that the occultation of a star is almost instantaneous. Among eclipses only total solar obscurations can be timed with comparable precision, and they are much rarer than occultations.

The study -of star occultations has revealed irregular fluctuations in day length over periods on the order of a decade, hence the term "decade fluctuations." The fluctuations themselves are quite small, no more than two or three milliseconds above or below the average, but their cumulative effect is fairly large. For example, if the length of the day remained continuously about three milliseconds above the average for a full decade, the accumulated total of what is called clock error (the difference between a clock keeping earth time and an "ideal" clock) would be about 10 seconds. Morrison and I have used the occultation data to map the decade fluctuations in detail from the 17th century to the present.
 

HYPOTHESIS OF A SHRINKING SUN, proposed in 1979 following analysis of thousands of right-ascension measurements, is contradicted by measurements based on the observed duration of 30 transits of Mercury {colored dots) and six total solar eclipses from a.d. 1715 to 1925. The two slopes indicate where past measurements of the sun's diameter should have fallen if indeed it has been shrinking at a rate of one second of arc per century (a) or at half that rate (*). Typically each of the eclipses from 1715 to 1925 has been timed by some 10 to 20 observers and the transits of Mercury often by more than 100 observers. The means of the eclipse measurements are entered for the appropriate year, the error bars represent a 95 percent level of confidence. Analysis of both series of observations supports the conclusion that the sun's apparent diameter is changing at a rate of minus .16 ± .14 second of arc per century, essentially a null result. Substantial variations are evident, however, implying that on a time scale of decades fluctuations in the diameter of the sun do take place.

How can these fluctuations be explained? One hypothesis suggests that fluid motions in the core of the earth, which are responsible for the earth's magnetic field, are coupled, electromagnetically or possibly topographically, with the surrounding mantle and disturb the rotation of the mantle. Such disturbances would then be communicated to the earth's surface. Another hypothesis points out that small changes in the global sea level, produced by the melting or freezing of polar ice, would alter the planet's moment of inertia and so affect its rate of rotation.

For all their relative imprecision ancient and medieval eclipse data are nonetheless valuable for a second kind of study: the long-term changes in the earth's rate of rotation. These changes are masked in recent centuries by the short-term changes described above. For example, it has long been realized that the tides of the earth's oceans, the product of lunar (and to a lesser extent solar) gravitational influences, have a braking effect that is responsible for a gradual increase in the length of the day. The moon's tidal influences can be readily estimated today because of modern studies of the moon's motions, such as lunar laser ranging. These studies show that the orbit of the moon is slowly getting larger, so that our satellite is receding from its planet at a rate of about four centimeters per year.

The two phenomena are interrelated. As the earth's rotation slows, the planet loses angular momentum. The angular momentum of the earth-moon system, however, is conserved, and so what the earth loses the moon gains. An orbiting satellite that gains angular momentum actually loses speed and so recedes from its planet; this is what the moon is doing. Calculations indicate that the tidal gain in the moon's angular momentum adds about .04 second to the length of the month each century.

Like the decade fluctuation, such a small change seems a trifling matter. Its long-term effects are nonetheless important. For example, let it be assumed that tidal friction has been the same for many millions of years. Then 100 million years ago, in mid-Cretaceous times, the mean distance between the earth and the moon would have been 4,000 kilometers less than it is at present, and each month would have been shorter by somewhat more than 11 hours.

How can the record of ancient and medieval eclipses yield useful data on a gradual slowing of the earth? Consider clock error. Over a span of 100 years, the clock keeping earth time would lose some 45 seconds compared with the ideal clock, because of the effect of tides on the earth's rotation. What is more, over still longer periods the clock error increases as the square of the elapsed time. For example, 1,000 years ago the expected accumulated clock error due to tides would have been an hour and a quarter, and 2,000 years ago it would have been five hours. Since at least some eclipse records are well over 2,000 years old, if certain facts about the observation can be established, the record can provide significant information on trends in the earth's of rotation.

TWENTY-EIGHT SOLAR ECLIPSES, either total or annular, are noted in records from eighth century B.C. through the 15th century A.D. All but one of the 10 most ancient eclipses listed in this table were observed by Chinese astronomers. The later predominance of Euro eclipse observers is due to the rise of monastic communities. Multiple sightings are numbered.
 

Before presenting the conclusions that can be drawn from such records it will be helpful to indicate what criteria the early observations must satisfy and to give an abbreviated account of the observations area by area. For early observation to be of value it must fall into one of three categories. The first category consists of the most valuable observations: timed solar and lunar eclipses. The second consists of solar and lunar eclipses that are untimed but are reported as having come near sunrise or sunset. The third consists of solar eclipses that are untimed but are reported as large events: near-total or total.

As for the areas in which the observations were made, they begin with Babylonia. At least as early as 750 b.c. Babylonian astronomers began to take an active interest in the accurate observation of many celestial phenomena, including solar and lunar eclipses. We cannot say how much earlier observations may have been made in Babylonia or anywhere else simply because there is little by way of historical records from more ancient times. Systematic Babylonian observations continued from about 750 b.c. to at least 50 b.c. and possibly well into the first century a.d. This large corpus of astronomical data was well known to the ancient Greeks. The Greek astronomer Ptolemy of Alexandria, writing early in the second century a.d., claimed access to Babylonian eclipse observations going back to 747 b.c. It is a cause for regret that Ptolemy, in his Mathematike Syntaxis (better known today by its Arabic name, Almagest), gives only brief extracts from the Babylonian record.

After about 300 b.c. Babylonia gradually decayed, and by a.d. 100 the city of Babylon was deserted. More than 1,700 years were to pass before the Babylonian astronomical tablets again came to light, accidentally unearthed by scavengers digging up the ancient baked clay bricks of the city to use in new construction. Most of the surviving astronomical tablets, many in fragmentary condition, are now in the British Museum. What was salvaged represents only some 5 percent of the original archive, and much of it is undatable. Only future excavation will determine whether more of the tablets remain to be found.

The traditional Babylon