A Text-Book of Astronomy

by George C. Comstock

Is it true that if at any time the axis of the shadow cone comes within 2,100 miles of the earth's surface a partial eclipse will be visible in those parts of the earth nearest the axis of the shadow?

65. Different characteristics of lunar and solar eclipses.—One marked difference between lunar and solar eclipses which has been already suggested, may be learned from [Fig. 33]. The full moon, M', will be seen eclipsed from every part of the earth where it is visible at all at the time of the eclipse—that is, from the whole night side of the earth; while the eclipsed sun will be seen eclipsed only from those parts of the day side of the earth upon which the moon's shadow or penumbra falls. Since the point of the shadow at best but little more than reaches to the earth, the amount of space upon the earth which it can cover at any one moment is very small, seldom more than 100 to 200 miles in length, and it is only within the space thus actually covered by the shadow that the sun is at any given moment totally eclipsed, but within this region the sun disappears, absolutely, behind the solid body of the moon, leaving to view only such outlying parts and appendages as are too large for the moon to cover. At a lunar eclipse, on the other hand, the earth coming between sun and moon cuts off the light from the latter, but, curiously enough, does not cut it off so completely that the moon disappears altogether from sight even in mid-eclipse. The explanation of this continued visibility is furnished by the broken lines extending, in [Fig. 33], from the earth through the moon. These represent sunlight, which, entering the earth's atmosphere near the edge of the earth (edge as seen from sun and moon), passes through it and emerges in a changed direction, refracted, into the shadow cone and feebly illumines the moon's surface with a ruddy light like that often shown in our red sunsets. Eclipse and sunset alike show that when the sun's light shines through dense layers of air it is the red rays which come through most freely, and the attentive observer may often see at a clear sunset something which corresponds exactly to the bending of the sunlight into the shadow cone; just before the sun reaches the horizon its disk is distorted from a circle into an oval whose horizontal diameter is longer than the vertical one (see [§ 50]).

Query.—At a total lunar eclipse what would be the effect upon the appearance of the moon if the atmosphere around the edge of the earth were heavily laden with clouds?

66. The track of the shadow.—We may regard the moon's shadow cone as a huge pencil attached to the moon, moving with it along its orbit in the direction of the arrowhead ([Fig. 34]), and as it moves drawing a black line across the face of the earth at the time of total eclipse. This black line is the path of the shadow and marks out those regions within which the eclipse will be total at some stage of its progress. If the point of the shadow just reaches the earth its trace will have no sensible width, while, if the moon is nearer, the point of the cone will be broken off, and, like a blunt pencil, it will draw a broad streak across the earth, and this under the most favorable circumstances may have a breadth of a little more than 160 miles and a length of 10,000 or 12,000 miles. The student should be able to show from the known distance of the moon (240,000 miles) and the known interval between consecutive new moons (29.5 days) that on the average the moon's shadow sweeps past the earth at the rate of 2,100 miles per hour, and that in a general way this motion is from west to east, since that is the direction of the moon's motion in its orbit. The actual velocity with which the moon's shadow moves past a given station may, however, be considerably greater or less than this, since on the one hand when the shadow falls very obliquely, as when the eclipse occurs near sunrise or sunset, the shifting of the shadow will be very much greater than the actual motion of the moon which produces it, and on the other hand the earth in revolving upon its axis carries the spectator and the ground upon which he stands along the same direction in which the shadow is moving. At the equator, with the sun and moon overhead, this motion of the earth subtracts about 1,000 miles per hour from the velocity with which the shadow passes by. It is chiefly on this account, the diminished velocity with which the shadow passes by, that total solar eclipses last longer in the tropics than in higher latitudes, but even under the most favorable circumstances the duration of totality does not reach eight minutes at any one place, although it may take the shadow several hours to sweep the entire length of its path across the earth.

According to Whitmell the greatest possible duration of a total solar eclipse is 7m. 40s., and it can attain this limit only when the eclipse occurs near the beginning of July and is visible at a place 5° north of the equator.

The duration of a lunar eclipse depends mainly upon the position of the moon with respect to the earth's shadow. If it strikes the shadow centrally, as at M', [Fig. 33], a total eclipse may last for about two hours, with an additional hour at the beginning and end, during which the moon is entering and leaving the earth's shadow. If the moon meets the shadow at one side of the axis, as at P, the total phase of the eclipse may fail altogether, and between these extremes the duration of totality may be anything from two hours downward.

Fig. 34.—Relation of the lunar nodes to eclipses.

67. Relation of the lunar nodes to eclipses.—To show why the moon sometimes encounters the earth's shadow centrally and more frequently at full moon passes by without touching it at all, we resort to [Fig. 34], which represents a part of the orbit of the earth about the sun, with dates showing the time in each year at which the earth passes the part of its orbit thus marked. The orbit of the moon about the earth, M M', is also shown, with the new moon, M, casting its shadow toward the earth and the full moon, M', apparently immersed in the earth's shadow. But here appearances are deceptive, and the student who has made the observations set forth in [Chapter III] has learned for himself a fact of which careful account must now be taken. The apparent paths of the moon and sun among the stars are great circles which lie near each other, but are not exactly the same; and since these great circles are only the intersections of the sky with the planes of the earth's orbit and the moon's orbit, we see that these planes are slightly inclined to each other and must therefore intersect along some line passing through the center of the earth. This line, N' N'', is shown in the figure, and if we suppose the surface of the paper to represent the plane of the earth's orbit, we shall have to suppose the moon's orbit to be tipped around this line, so that the left side of the orbit lies above and the right side below the surface of the paper. But since the earth's shadow lies in the plane of its orbit—i. e., in the surface of the paper—the full moon of March, M', must have passed below the shadow, and the new moon, M, must have cast its shadow above the earth, so that neither a lunar nor a solar eclipse could occur in that month. But toward the end of May the earth and moon have reached a position where the line N' N'' points almost directly toward the sun, in line with the shadow cones which hide it. Note that the line N' N'' remains very nearly parallel to its original position, while the earth is moving along its orbit. The full moon will now be very near this line and therefore very close to the plane of the earth's orbit, if not actually in it, and must pass through the shadow of the earth and be eclipsed. So also the new moon will cast its shadow in the plane of the ecliptic, and this shadow, falling upon the earth, produced the total solar eclipse of May 28, 1900.