Eclipses

astronomical phenomena during which the sun, the moon, a planet, a planetary satellite, or a star ceases to be visible, either completely or partially, to an observer on the earth. Eclipses occur either because one celestial body covers another or because the shadow of a body that is not self-luminous falls across another such body. Thus, solar eclipses are observed when the moon blocks the sun out, lunar eclipses when the earth’s shadow falls across the moon, eclipses of planetary satellites when they pass into the shadow of the planet, and eclipses of binary systems when one star covers the other. Also related to eclipses are the transits of a satellite’s shadow across a planet’s disk, occultations of stars and planets by the moon, the transits of the inner planets—Mercury and Venus—across the solar disk, and transits of satellites across a planet’s disk. With the advent of manned space flights, the possibility of observing eclipses of the sun by the earth from spacecraft has emerged. Of great interest are solar and lunar eclipses, which are linked to the motion of the moon around the earth.

Solar eclipses. The moon’s shadow cone, formed by the external tangents to the sun and moon, extends out into space. The vertex of the cone is located at a distance ranging from 368,000 to 380,000 km from the center of the moon. This cone is long enough to reach the earth, which is located at a distance of from 363,000 to 406,000 km from the moon (see Figure 1). The diameter of the moon’s shadow that sweeps across the earth does not exceed 270 km—this is the maximum size of the region where a total solar eclipse can occur at a given moment. In this region the moon completely covers the sun. Beyond the vertex, the cone broadens, forming the region of annular (ring-shaped) eclipse. In observations from this region, the angular diameter of the moon is less than the diameter of the sun, and the moon covers only the central part of the sun’s disk, leaving the rim of the sun visible in the form of a narrow bright ring. This is the annular solar eclipse. Because of the motion of the moon along its orbit and the rotation of the earth around its axis, the moon’s shadow sweeps across the earth’s surface from west to east with a velocity on the order of 1 km/sec, tracing out a narrow (the width depends on the distances from the earth to the moon and sun, which vary somewhat owing to the ellipticity of the earth and lunar orbits) but long (up to 15,000 km) band in which a total eclipse is successively observed. The internal tangents to the sun and moon limit the partial shadow (penumbra) to a radius of about 3,500 km, from where the partial solar eclipse is visible; the smaller the phase, the further from the center of the umbra (total shadow) and the nearer to the edge of the penumbra is the point of observation (the phase of an eclipse is designated as that fraction of the solar diameter covered by the moon). During a partial solar eclipse the sun’s disk is not completely covered. The duration of a partial solar eclipse of large phase reaches two hours; in the middle of this time interval, if the point of observation is located in the path of the moon’s shadow, a total (or annular) eclipse occurs, with a duration not exceeding TVi minutes (for an annular eclipse—not exceeding 12 minutes). The successive positions of the moon’s penumbra and the bands of total or annular eclipse are depicted on a geographical map that graphically shows the course of the eclipse for the earth as a whole. For any one point on the earth, a more detailed calculation is usually performed on the basis of the theory developed by the German astronomer F. Bessel.

Figure 1. Diagram of the moon’s umbra and penumbra: S₁, S₂, and S₃ are the regions of total, annular, and partial eclipse

At the onset of a partial eclipse, a barely perceptible indentation appears at the right-hand western rim of the solar disk; this is actually the moon’s disk beginning to cover the sun. As the moon advances the still uncovered part of the sun takes on the appearance of a crescent of gradually diminishing width. If the given point on the earth lies in the band of total eclipse, then before its onset the bright silver of the sun’s rim breaks up into a row of glittering circular points, the so-called Baily’s beads, caused by the last solar rays shining through the depressions between the mountains on the edge of the moon. This phenomenon lasts only several seconds, after which total eclipse begins. During this time the silvery solar corona glows around the dark lunar disk, around the rim of which the red fringe of the solar chromosphere is still visible and individual prominences stand out. For several seconds the spectra of flares—bright emission lines of the chromosphere—are visible in a spectroscope. Stars and planets appear in the darkened sky. The landscape becomes darkened as in twilight, and a glowing ring spreads along the horizon—the earth’s atmosphere illuminated by the sun beyond the limits of the moon’s shadow. At the completion of the total phase of the eclipse the phenomena occur in reverse order: the first rays of the sun emerge, the corona and prominences disappear, and daylight returns; the narrow crescent of the sun widens and in approximately one hour the indentation at the rim of the solar disk disappears—the partial eclipse ends. The observation of total solar eclipses is of great scientific interest, since during this time the moon not only covers the bright sun but also darkens part of the earth’s atmosphere and thereby removes the hindrances to the visibility of the regions closest to the sun, including the corona and the chromosphere. Stars that are visible around the darkened sun allow one to observe the so-called Einstein effect—one of the astronomical consequences of the theory of relativity (this effect consists of the displacement of stars located on the celestial sphere near the sun as a result of the bending of the light rays of these stars under the influence of the sun’s gravitational field). All this has prompted the outfitting of special expeditions to places where total eclipses can be observed.

Lunar eclipses. The darkening of the moon during its pas-sage through the penumbra of the earth’s shadow (see Figure 2) is so insignificant and occurs so slowly that it is almost imperceptible to the naked eye. A partial lunar eclipse begins when the moon enters the umbra of the earth’s shadow. Partial eclipses can last up to 3¾ hours; within this interval of time there can be a total lunar eclipse of up to 1¾ hours duration. During a total eclipse the moon takes on a dull reddish brown tinge, because some of the sun’s rays, having been refracted in the earth’s atmosphere, fall on it. Depending on the presence of clouds in the peripheral regions of the atmosphere the intensity and color of such rays varies, so that the degree of darkening of the moon is also nonuniform; in rare instances the moon becomes totally invisible.

Figure 2. Diagram of the earth’s umbra and penumbra: S is the region of lunar eclipses

Periodicity of eclipses. Solar eclipses occur only at new moons and lunar eclipses only at full moons, and not every time but only when the sun and moon are sufficiently close to the nodes of the lunar orbit, at which the apparent paths of the sun and moon intersect on the celestial sphere. A solar eclipse occurs if at new moon the angular separation of the moon from the nearest node does not exceed 17.9°; a lunar eclipse occurs if at full moon this separation does not exceed 12.0°. At other positions of the moon and sun, owing to the fact that the plane of the lunar orbit is inclined at an angle of about 5° to the ecliptic, the moon at full moon and new moon is too far from the line joining the earth to the sun, and eclipses do not occur. The nearer the moon and sun are located to the nodes at this time, the greater the duration and phase of the eclipse.

The nodes of the lunar orbit slowly move along the ecliptic toward the sun, such that the sun passes through the same node approximately every 346.6 days (the draconic year); the moon returns to the same node on the average every 27.21 days (the draconic month). Thus there occur in a calendar year two periods, separated by an interval equal to one half an eclipse year, in which eclipses can occur. In years when the first such period occurs at the beginning of January, there is also a third period favorable for eclipses in December of the same year. At each period one or two (but small-phase) solar eclipses occur. Inasmuch as the period favorable for lunar eclipses is less, the moon can pass through it having been eclipsed only once or not at all. Thus every year there are from two to five solar eclipses and not more than three lunar eclipses. For the earth as a whole solar eclipses occur more frequently than lunar eclipses, but the latter are visible from an entire terrestrial hemisphere, which at this time is facing the moon, whereas solar eclipses are visible in a much smaller region, where the moon’s penumbra or small umbra fall. Total solar eclipses at any one place on the earth happen on the average once in 300-400 years.

In the alternation of eclipses there exists a periodicity, caused by the fact that 242 nodical months, determining the return of the moon to the nodes of its orbit, are almost exactly equal to 223 synodic months, with which the phases of the moon are linked. Therefore, at the expiration of such a term, equal to 6,5851/3 days, or 18 years and 111/3 days (or l01/3 days if in this interval of time there were not four but rive leap years), all solar and lunar eclipses repeat in the same sequence. This period was already well-known in the sixth century B.C. and was called the saros. In the course of one saros 43 solar eclipses can occur (15 partial, 14 annular, two total annular, and 12 total) and 28 lunar eclipses, of which about half are total. These numbers change somewhat in the course of time because of the imperfect accuracy of the aforementioned equality and because of centuries-old changes in the motion of the moon. The saros allows one to predict the day of a future eclipse; additional calculations are necessary to determine the place, exact time, and phase of visibility. For this purpose the passage of the moon’s umbra and penumbra across the earth during a solar eclipse or the passage of the moon in the earth’s shadow is computed step by step. The accuracy of such computations is very high: the error in the time of a contemporary eclipse does not exceed 2-3 seconds, and the position of the band of total eclipse on the earth’s surface is computed with an accuracy up to 1 km.

Lunar and particularly solar eclipses have always produced a strong impression on people, and many records of them have been preserved in the chronicles of various peoples. This has helped to establish the dates of certain important historical events and to clarify the correspondence between various systems of calendar chronology. In addition, these records have made it possible to more accurately determine the motion of the sun and moon over several thousands of years. In connection with the great significance of eclipses for history, chronology, and theoretical astronomy, T. von Oppolzer (Austria) in the 1880’s computed the moments of 8,000 solar and 5,200 lunar eclipses between 1207 B.C. and A.D. 2163 and published his results in the monumental work Canon der Finsternisse. M. A. Vil’ev in 1915 compiled data for eclipses from 1060 to 1715 which were visible on the territory of European Russia, and in 1966, J. Meeus, C. Grosjean, and W. Vanderleen compiled the most precise and comprehensive tabulations of all solar eclipses between 1898 and 2510.

Eclipses of planetary satellites. The four bright (so-called Galilean) satellites of Jupiter are eclipsed frequently; of them, the three nearest to the planet are eclipsed on every revolution, and only the fourth can bypass Jupiter’s shadow. Observing these eclipses, the Danish astronomer O. Roemer in 1675 first determined the velocity of light. Before Jupiter’s opposition, it is possible to observe only the beginning of an eclipse, that is, the start of the satellite’s passage through the shadow and after opposition, only its emergence from the shadow. At opposition eclipses are not visible, since the satellites are occulted behind the planet’s disk. Near Jupiter’s quadrature it is possible to observe both the beginning and the end of an eclipse. Passing in front of Jupiter’s disk (transit), the satellites throw their shadow back on it, producing an eclipse of the sun on its surface. The eclipses of Saturn’s satellites occur both in the planet’s shadow and in the shadow of the ring, which complicates the theory of these phenomena. Eclipses of the satellites of Mars, Uranus, and Neptune are almost impossible to observe due to their extreme faintness.