CHAPTER VIII.

ECLIPSES AND OCCULTATIONS.

ECLIPSES OF THE MOON.—As the various members of the solar system shine only by virtue of the light which they receive from the sun, they will cease to be visible if by any means they are deprived of the sun’s rays. Each planet or satellite must evidently cast a shadow which is turned directly away from the sun, and any other body passing wholly or partially within such a shadow will be proportionately debarred from receiving the direct light of the sun.

[Illustration:

FIG. 29.—_The Earth’s Shadow._ ]

Were the sun a mere point of light these shadows would be parts of cones, the apex always being at the sun, and they would be prolonged indefinitely into space. As a matter of fact, every individual point upon the sun’s disc is competent to cast a conical shadow, and the net result is that only a relatively small space behind a planet or satellite is really in total darkness. This will be readily understood from Fig. 29, in which S is the sun, and E the earth. The total shadow now becomes a cone, with the apex turned directly away from the sun, but round this there is a region of partial shadow which is only illuminated by portions of the sun. If we imagine a section of the shadow across the line _a b_, we should find a central disc of total darkness called the _umbra_, and surrounding this a ring of half shadow called the _penumbra_.

From the known dimensions of the sun and earth, and the distance between them, it is easy to calculate the size of the earth’s shadow-cone, and its length is found to be greater than the distance of the moon. The axis of this shadow will, of course, always be in the plane of the ecliptic. If, then, at the time of opposition, the moon is sufficiently near the plane of the ecliptic, it will pass through the shadow, and we shall have the phenomena of a _lunar eclipse_. When the moon is wholly immersed in the umbra, the eclipse is total, and if it further passes quite symmetrically through the shadow, the eclipse is said to be central. This would always be the state of affairs if the moon performed its monthly journey in the plane of the ecliptic, and a total eclipse would occur every month. The moon’s orbit, however, is inclined to the ecliptic, so that for a central eclipse, the moon must be simultaneously at opposition and at a node. If the moon be near the node when at opposition, a total eclipse may occur, but it cannot be central, and the duration of the total obscuration will be reduced. Still further from the node, the moon will be above or below the ecliptic, and will be only partially involved in the shadow-cone; such an eclipse is called a partial one. Beyond a certain distance from the node, the inclination of the moon’s orbit will take the moon entirely out of the umbral shadow, and no eclipse will be possible.

The circumstances of an eclipse of the moon thus vary very considerably, and there is still another reason why we may expect them to be different. We have seen that the earth’s distance from the sun changes throughout the year, and, in consequence, its shadow will be of varying length, and the diameter of the shadow at any specified distance will not be constant. The moon, again, is not always at the same distance from the earth, and it will, therefore, pass through varying depths of shadow in different eclipses, and with different velocities.

The breadth of the earth’s umbral shadow at the point where the moon passes through it is, on the average, about three times the moon’s diameter, and the time taken for the moon to traverse this distance is about two hours. The duration of totality in a central eclipse may, therefore, amount to two hours, while an additional two hours may be occupied by the partial phases.

[Illustration:

FIG. 30.—_The Lunar Ecliptic Limit._ ]

THE LUNAR ECLIPTIC LIMIT.—The greatest distance of the moon from a node at which a partial eclipse is possible, is called the _lunar ecliptic limit_, and is very easily calculated. In Fig. 30, let E N represent a part of the ecliptic, N being the node of the moon’s orbit, and E the centre of the earth’s shadow. As the orbit of the moon is inclined about 5° 9′ to the ecliptic, it may be represented by the line N M, inclined at an angle to N E. If E A be the radius of the earth’s shadow, which, on the average, is about three-quarters of a degree, and M A the moon’s apparent semi-diameter (about a quarter a degree), it is clear that the point beyond which no eclipse is possible is that in which the line M E, perpendicular to N M, is equal to the sum of the semi-diameters. All the quantities for solving the triangle N E M are thus known, and it can be readily calculated that N M, the greatest distance of the moon from the node at which an eclipse would be possible, under average conditions is about 11°.

Taking into account the varying distances between the sun, earth, and moon, it is found that an eclipse must always occur if the moon is within 9° of the node, and may occur if it be 12° from the node. These figures refer to the passage of the moon through the umbra, as the effect of its entrance into the penumbra is too slight to be observed.

The entrance of the moon into the earth’s shadow is a definite phenomenon, which is independent of the observer’s position on the earth, and the phases of the eclipse are seen at exactly the same moment from all places where the moon is above the horizon. The computation of the circumstances at a given place is accordingly a simple one.

When a lunar eclipse is not total at any of its phases, it is usual to specify its _magnitude_ by the ratio of the greatest measurement of the obscured part to the moon’s diameter. Thus the magnitude of the partial eclipse of February 28th, 1896, is given in the “Nautical Almanac” as 0·870, the moon’s diameter being taken as unity.

The conditions of lunar eclipses which have been stated have reference to the moon’s passage through the earth’s geometrical shadow, but the actual conditions are greatly modified by the fact that the earth is surrounded by an atmosphere which refracts the suns light so much that the moon is seldom quite obscured during totality. The commencement of the total phase is also rendered difficult of observation by the somewhat indefinite boundary between the umbra and penumbra.

ECLIPSES OF THE SUN.—If the moon performed its revolution in the plane of the ecliptic, it is evident that it must always come between us and the sun once in each month. This it does not do, but occasionally it happens to be in the ecliptic when in conjunction, and the moon is then seen to be projected upon the sun. In other words, there is an eclipse of the sun. Let us consider the circumstances, in the first instance, to an observer placed at the centre of the earth. If the centres of the moon and sun appear in the same straight line, the eclipse will be _total_ or _annular_, according as the moon or sun has the greater apparent diameter. Both these forms of eclipses are possible, on account of the varying apparent diameters of the sun and moon consequent upon their variable distances from the earth. If the moon appear the larger it will evidently cover up the whole of the sun, but when it is the smaller, a ring of sunlight will be visible round the dark holy of the moon, and the eclipse will be an annular one. These conditions are illustrated in Fig. 31, _a_ and _b_ representing a total and an annular eclipse respectively. If the moon and sun be not quite in the same straight line, the moon may still be seen partially projected on the sun’s disc, in which case there will be a _partial eclipse_ of the sun, as in Fig. 31, _c_.

[Illustration:

FIG. 31.—_Eclipses of the Sun._ (_a_) _Total Eclipse_, (_b_) _Annular Eclipse_, (_c_) _Partial Eclipse._ ]

In a total eclipse there are four so-called _contacts_: the first when the moon is seen to encroach upon the sun’s disc, the second when the advancing edge of the moon reaches the opposite limb, the third when the following edge of the moon first touches the sun’s boundary, and the fourth when the projected moon finally passes off the sun. The interval between the second and third contacts marks the duration of totality. As referred to our supposed observer at the centre of the earth, the duration evidently depends upon the apparent rate of the moon’s eastward movement as compared with that of the sun, as well as upon the differences of the apparent diameters of the two bodies.

The production of eclipses of the sun may also be considered as arising from the immersion of an observer in the shadow of the moon. This shadow has its axis turned from the sun, but is so short that it does not always reach the earth. If an observer comes near the axis of the conical shadow, and within the apex, the eclipse will be total; if he is in the axis, but outside the apex, the eclipse will be annular.

[Illustration:

FIG. 32.—_Duration of a Solar Eclipse._ ]

The whole of the shadow of the moon is so small that only a few places on the earth’s surface can be simultaneously immersed in it, and when we come to discuss the conditions of an eclipse with regard to a particular observer, the problem becomes a complicated one. At some places the eclipse may be total, at others it will be only partial, while at others no eclipse will occur at all. These differences are due to the fact that the sun is scarcely appreciably displaced by the change of locality, while the apparent position of the moon may be affected to the extent of nearly a degree. Again, the observer situated on the earth’s surface has a movement of his own, produced by the earth’s rotation, and his rate of motion depends upon the latitude in which he is situated. The effect of this movement upon the conditions of the eclipse are very pronounced. Suppose for a moment that the sun, moon, and earth, are fixed along the same straight line S M E in Fig. 32, a terrestrial observer at _a_ on the earth’s Equator would see an eclipse at noon; if he were not in rotation, and the three bodies remained at rest, the eclipse would be a perpetual one. He is, however, carried onward by the earth’s rotation, and even if the moon were at rest, it would appear to him to pass over the sun in the reverse direction. This retardation of the moon will be less in amount for observers away from the Equator, and also for observers to whom the sun is not on the meridian when eclipsed. The effect of rotation on an observer at _b_ (Fig. 32), for example, is to move him almost in the direction of the line joining the moon and sun, and the backward tendency of the moon due to rotation is very slight. On account of the earth’s rotation, then, the duration of a solar eclipse is lengthened, the greatest increase occurring at those places where the sun is on the meridian at the time of eclipse.

There is another source of gain of duration of an eclipse to the observer who sees the phenomenon about noon. The moon’s apparent diameter is then augmented by a greater amount than at other places, because the observer is then nearest to the moon; while the sun’s apparent diameter is not appreciably affected. The greater the difference in the apparent diameters of the sun and moon, the longer will totality last.

These and other circumstances have all to be taken into account in computing the conditions under which an eclipse will be seen at any given place.

According to an eminent authority, Professor Young, the greatest possible diameter of the moon’s shadow, where it strikes the earth, is 167 miles. It may, however, cover a larger space on the earth’s surface, because the latter does not pass perpendicularly through the shadow. To all persons within the shadow, the eclipse will be total, but to those on its outer boundary the duration of totality will be for an instant only. The penumbral shadow has a cross section about 4,500 miles in diameter, covering sometimes a space on the earth’s surface 6,000 miles across. To all persons within this area, but not in the central shadow, the eclipse will be partial. The shadow spot travels over the earth’s surface, because of the moon’s movement, but its track and speed are greatly modified by the earth’s rotation. The movement of the shadow, as affected by the earth’s rotation, would be along a parallel of latitude; but its ultimate direction of movement, though trending eastwards, depends upon this, combined with the direction of the moon’s movement at the time of the eclipse. Thus, a portion of the track of the total eclipse of April 16, 1893, is as that shown in Fig. 33.

[Illustration:

FIG. 33.—_Track of Eclipse of April 16, 1893._ ]

These considerations will suffice to explain the necessity for very precise calculations as to the position of the central line of an eclipse, when observers are sent out for the purpose of recording the phenomena.

Under the most favourable combination of conditions, that is, when the eclipse occurs at noon at a place on the Equator, an eclipse cannot be total for more than 7 minutes 58 seconds, nor be annular for a longer time than 12 minutes 24 seconds. From first to last contact may occupy as much as 2 hours, when all the circumstances are similarly favourable. (Loomis.)

THE SOLAR ECLIPTIC LIMIT.—In order that an eclipse of the sun may occur, the moon must be so near the ecliptic that it can be seen projected on the sun, either wholly or partially, from some point on the earth. It must therefore not be very far from the node, and the distance it may be from the node, while still being seen upon the sun, is called the _solar ecliptic limit_. As in the case of lunar eclipses, this distance is determined by the inclination of the moon’s orbit, and the distances of the moon and sun from the earth. The latter being variable quantities, the limit is not always the same. It is calculated without much difficulty that an eclipse _must_ occur if the new moon happens when it is within 15° 21′ of the node, and may occur within 18° 31′. These are called the minor and major ecliptic limits respectively. For total or annular eclipses, the limits are respectively 9° 55′ and 11° 50′.

NUMBER OF ECLIPSES IN A YEAR.—If the moon’s nodes were fixed, the sun would pass through the line of nodes twice a year. At such times an eclipse of the sun must necessarily occur if the moon were within 15° 21′ of the node on either side. The sun requires more than a month to traverse this space of 30° 42′, and the moon must therefore pass through each node at least once while the sun is traversing these limits. It follows, then, that there must be at least two eclipses of the sun in a year. Since the line of nodes of the moon’s orbit revolves backwards in a period of about nineteen years, the sun returns to the same node after an interval of 346·6 days, and there must accordingly be two solar eclipses in this interval. If, then, there be an eclipse early in January, there will be another about the middle of the year, and another at the end of the year, so that on this ground alone there is a possibility of three solar eclipses in a year.

Again, while the sun is passing through the ecliptic limits, it may happen that an eclipse occurs on its entrance, and then another will occur before it gets beyond on the other side of the line of nodes. In this way two eclipses may occur in the region of each node passage, and if the first of the series occurs early in January, five eclipses of the sun may occur in a single year.

The sun, however, is not a month in traversing the lunar ecliptic limit. Consequently, a whole year may elapse without the moon being sufficiently near the node to pass within the earth’s shadow, and in many years there are accordingly no eclipses of the moon. Only one full moon can occur within the lunar ecliptic limits when the sun passes the node, but if there be an eclipse at one node, there may also be one six months later at the other node. As in the case of the solar eclipses, the “eclipse year” is one of 346·6 days, so that if there be an eclipse of the moon early in January, there may possibly be three altogether in the course of the year, but there could not be three lunar eclipses if the extra solar eclipse were possible. Altogether, then, there may be seven eclipses in the course of a year—five of the sun and two of the moon. Usually there are four or five, some particulars of which are furnished by all respectable almanacs. It will be observed that the number of solar eclipses is much larger than that of lunar ones, but as the latter are visible at all places having the moon above the horizon, while the former are restricted to small parts of the earth’s surface, more lunar than solar eclipses are visible at any specified place.

RECURRENCE OF ECLIPSES.—We have seen that the sun requires only 346·6 days to travel from one of the moon’s nodes back to the same node again, in consequence of the regression of the nodes, while the moon requires 27·2 days. Suppose, then, that the moon and sun are at a node, and there is an eclipse at new moon; after 346·6 days the sun will return to the same node, but the moon will not be at the node, nor will it be exactly new. It will not be until the sun has returned nineteen times to the node that the moon is also very nearly new at the same node again. Nineteen returns of the sun to the moon’s nodes occupy a period of 6,585·78 days; 223 intervals between successive new moons (synodic months) cover 6,585·32 days, while 242 node passages of the moon require 6,585·357 days. In this period of 18 years 11⅓ days (or 10⅓ days if there are five, and 12⅓ if there are three leap years in the interval), the sun and moon thus return to nearly the same conditions as affecting the possibility of eclipses. This period was called the _Saros_ by the Chaldeans, by whom it was employed in the prediction of eclipses. The adjustment of periods, however, is not quite precise, so that predictions based upon the Saros are only approximations, which serve as a guide for more accurate computations.

This eclipse period is still more remarkable from the fact that it almost exactly represents 239 passages of the moon through perigee, so that after the lapse of 18 years 11⅓ days the moon is almost at the same distance from the earth, as well as nearly at the same phase and the same distance from a node.

As the Saros includes a fraction of a day, an eclipse is not necessarily repeated at the same place after the lapse of 18 years 11⅓ days, for the reason that the eclipse will not occur at the same time of day, and the sun may be below the horizon. After three Saroses, however, the eclipse will be repeated nearly at the same hour, but even then it will not be seen under the same conditions, because the track of the shadow will be in different latitudes, for the reason that the moon does not return _exactly_ to the node in the interval between 223 new or full moons, and eclipses can only occur when the moon is new or full.

Beginning as a partial eclipse, an eclipse of the moon will gradually become of greater magnitude at successive intervals of 18 years 11 days, until it becomes a total eclipse, and will again gradually become of smaller magnitude, until it ceases to be reproduced at all. Altogether, it would be repeated once in every 223 months for 865 years.

Since the solar ecliptic limit is greater than the lunar, a solar eclipse is repeated at similar intervals of 18 years for about 1200 years. Most of these eclipses would be partial, 27 would be annular, and 18 total. During this period, the track of the central eclipse would shift northwards if the moon were at a descending node, and southwards if at an ascending node, until finally it passed altogether clear of the earth.

It must be remarked, however, that, in the period corresponding to a single Saros, about 28 eclipses of the moon, and 43 of the sun, usually appear, so that altogether about 71 series of eclipses are in progress. Of the solar eclipses which occur during a period of 18 years, about 12 are total at some places upon the earth.

OCCULTATIONS OF STARS AND PLANETS BY THE MOON.—In its monthly round, the moon is constantly passing in front of some of the stars which lie in its apparent path, and these luminaries will, therefore, at times, be hidden temporarily by the moons disc. Occasionally a planet may appear in the same line of vision as the moon, and that also will pass from view until subsequent motion again removes the intercepting body. These disappearances are closely allied to the phenomena of eclipses, and receive the name of _occultations_. On account of the moon’s eastward movement, it is evident that the disappearance of stars or planets when occulted will take place on the eastern edge of the moon; but since the moon trends north or south in some parts of its orbit, the disappearance near the northern and southern edges may occur slightly on the western side of the north or south point of the moons limb. Similarly, the reappearance generally occurs on the western side of the moon, but occasionally may occur on the eastern side—that is, when the northern or southern edge of the moon does not much more than appear to graze the stars.

The calculation of the circumstances of an occultation is very similar to that involved in the computation of eclipses. (A simple graphical method for working out the conditions of an occultation is described by Major Grant, R.E., in the _Geographical Journal_ for June, 1896.)

ECLIPSES AND OCCULTATIONS OF SATELLITES BY PLANETS.—Just as we find the moon eclipsed by passing through the earth’s shadow, we find the satellites of other planets to be at times invisible for a similar reason. We thus observe _eclipses_ of the satellites. The satellites may also be invisible to us for the reason that they are behind the planet, and they are then said to be _occulted_. These satellite phenomena are especially remarked in the case of Jupiter, and their observation is one of great interest. When a satellite passes between the sun and the planet it throws a shadow on the surface of the planet similar to that of the moon upon the earth. This is visible to us as a dark spot, and from the centre of that dusky patch an inhabitant of Jupiter would undoubtedly see a total eclipse of the sun. To us on the earth the passage of such a shadow across the planet’s disc is but a “transit of the shadow” with its “ingress” and “egress.”

The times of all these appearances are computed from a knowledge of the movements of the satellites.