A Text-Book of Astronomy

by George C. Comstock

ECLIPSES

63. The nature of eclipses.—Every planet has a shadow which travels with the planet along its orbit, always pointing directly away from the sun, and cutting off from a certain region of space the sunlight which otherwise would fill it. For the most part these shadows are invisible, but occasionally one of them falls upon a planet or some other body which shines by reflected sunlight, and, cutting off its supply of light, produces the striking phenomenon which we call an eclipse. The satellites of Jupiter, Saturn, and Mars are eclipsed whenever they plunge into the shadows cast by their respective planets, and Jupiter himself is partially eclipsed when one of his own satellites passes between him and the sun, and casts upon his broad surface a shadow too small to cover more than a fraction of it.

But the eclipses of most interest to us are those of the sun and moon, called respectively solar and lunar eclipses. In [Fig. 33] the full moon, M', is shown immersed in the shadow cast by the earth, and therefore eclipsed, and in the same figure the new moon, M, is shown as casting its shadow upon the earth and producing an eclipse of the sun. From a mere inspection of the figure we may learn that an eclipse of the sun can occur only at new moon—i. e., when the moon is on line between the earth and sun—and an eclipse of the moon can occur only at full moon. Why? Also, the eclipsed moon, M', will present substantially the same appearance from every part of the earth where it is at all visible—the same from North America as from South America—but the eclipsed sun will present very different aspects from different parts of the earth. Thus, at L, within the moon's shadow, the sunlight will be entirely cut off, producing what is called a total eclipse. At points of the earth's surface near J and K there will be no interference whatever with the sunlight, and no eclipse, since the moon is quite off the line joining these regions to any part of the sun. At places between J and L or K and L the moon will cut off a part of the sun's light, but not all of it, and will produce what is called a partial eclipse, which, as seen from the northern parts of the earth, will be an eclipse of the lower (southern) part of the sun, and as seen from the southern hemisphere will be an eclipse of the northern part of the sun.

Fig. 33.—Different kinds of eclipse.

The moon revolves around the earth in a plane, which, in the figure, we suppose to be perpendicular to the surface of the paper, and to pass through the sun along the line M' M produced. But it frequently happens that this plane is turned to one side of the sun, along some such line as P Q, and in this case the full moon would cut through the edge of the earth's shadow without being at any time wholly immersed in it, giving a partial eclipse of the moon, as is shown in the figure.

In what parts of the earth would this eclipse be visible? What kinds of solar eclipse would be produced by the new moon at Q? In what parts of the earth would they be visible?

64. The shadow cone.—The shape and position of the earth's shadow are indicated in [Fig. 33] by the lines drawn tangent to the circles which represent the sun and earth, since it is only between these lines that the earth interferes with the free radiation of sunlight, and since both sun and earth are spheres, and the earth is much the smaller of the two, it is evident that the earth's shadow must be, in geometrical language, a cone whose base is at the earth, and whose vertex lies far to the right of the figure—in other words, the earth's shadow, although very long, tapers off finally to a point and ends. So, too, the shadow of the moon is a cone, having its base at the moon and its vertex turned away from the sun, and, as shown in the figure, just about long enough to reach the earth.

It is easily shown, by the theorem of similar triangles in connection with the known size of the earth and sun, that the distance from the center of the earth to the vertex of its shadow is always equal to the distance of the earth from the sun divided by 108, and, similarly, that the length of the moon's shadow is equal to the distance of the moon from the sun divided by 400, the moon's shadow being the smaller and shorter of the two, because the moon is smaller than the earth. The radius of the moon's orbit is just about 1/400th part of the radius of the earth's orbit—i. e., the distance of the moon from the earth is 1/400th part of the distance of the earth from the sun, and it is this "chance" agreement between the length of the moon's shadow and the distance of the moon from the earth which makes the tip of the moon's shadow fall very near the earth at the time of solar eclipses. Indeed, the elliptical shape of the moon's orbit produces considerable variations in the distance of the moon from the earth, and in consequence of these variations the vertex of the shadow sometimes falls short of reaching the earth, and sometimes even projects considerably beyond its farther side. When the moon's distance is too great for the shadow to bridge the space between earth and moon there can be no total eclipse of the sun, for there is no shadow which can fall upon the earth, even though the moon does come directly between earth and sun. But there is then produced a peculiar kind of partial eclipse called annular, or ring-shaped, because the moon, although eclipsing the central parts of the sun, is not large enough to cover the whole of it, but leaves the sun's edge visible as a ring of light, which completely surrounds the moon. Although, strictly speaking, this is only a partial eclipse, it is customary to put total and annular eclipses together in one class, which is called central eclipses, since in these eclipses the line of centers of sun and moon strikes the earth, while in ordinary partial eclipses it passes to one side of the earth without striking it. In this latter case we have to consider another cone called the penumbra—i. e., partial shadow—which is shown in [Fig. 33] by the broken lines tangent to the sun and moon, and crossing at the point V, which is the vertex of this cone. This penumbral cone includes within its surface all that region of space within which the moon cuts off any of the sunlight, and of course it includes the shadow cone which produces total eclipses. Wherever the penumbra falls there will be a solar eclipse of some kind, and the nearer the place is to the axis of the penumbra, the more nearly total will be the eclipse. Since the moon stands about midway between the earth and the vertex of the penumbra, the diameter of the penumbra where it strikes the earth will be about twice as great as the diameter of the moon, and the student should be able to show from this that the region of the earth's surface within which a partial solar eclipse is visible extends in a straight line about 2,100 miles on either side of the region where the eclipse is total. Measured along the curved surface of the earth, this distance is frequently much greater.