In a lunar eclipse it is the earth that is the intervening body, and its shadow falls upon the moon. A solar eclipse can only occur at the time of new moon, and a lunar eclipse only at the time of full moon. The shadow of the earth is much longer and broader than that of the moon, and it never fails to reach the moon, so that it is not necessary here to consider its varying length. The width, or diameter, of the shadow at the average distance of the moon from the earth is about 5700 miles. The moon may pass through the centre of the shadow, or to one side of the centre, or merely dip into the edge of it. When it goes deep enough into the shadow to be entirely covered, the eclipse is total; otherwise it is partial. Since in a total lunar eclipse the entire moon is covered by the shadow, it is evident that such an eclipse, unlike a solar one, may be visible simultaneously from all parts of the earth which, at the time, lie on the side facing the moon. In other words, the earth's shadow does not make merely a narrow track across the face of the moon, but completely buries it. When the moon passes centrally through the shadow, she may remain totally obscured for about two hours. But the moon does not completely disappear at such times, because the refraction of the earth's atmosphere bends a little sunlight round its edges and casts it into the shadow. If the atmosphere round the edges of the earth happens to be thickly charged with clouds, but little light is thus refracted into the shadow, and the moon appears very faint, or almost entirely disappears. But this is rare, and ordinarily the eclipsed moon shines with a pale copperish light.
The occurrence of a lunar eclipse is governed by similar circumstances to those affecting solar eclipses. The lunar ecliptic limits, or the distance on each side of the node within which an eclipse may occur, vary from 9½° to 12¼° in either direction.
Taking all the various circumstances into account, it is found that there may be, though rarely, seven eclipses in a year, two being of the moon and five of the sun, and that the least possible number of eclipses in a year is two, in which case both will be of the sun. Taking into account also all the various positions which the sun and moon occupy with regard to the earth, it is found that there exists a period of 18 years, 11 days, 8 hours, at the return of which eclipses of both kinds begin to recur again in the same order that they occur in the next preceding period. This is called the saros, and it was known to the Chaldeans 2600 years ago.
6. The Planets. We have several times mentioned the fact that, beside the earth, there are seven other principal planets revolving round the sun, in the same direction as the earth, but at various distances. We shall consider each of these in the order of its distance from the sun.
But first it is desirable to explain briefly certain so-called “laws” which govern the motions of all the planets. These are known as Kepler's laws of planetary motion, and are three in number. The demonstration of their truth would carry us beyond the scope of this book, and consequently we shall merely state them as they are recognised by astronomers.
1st Law: The orbit of every planet is an ellipse, having the sun situated in one of the foci.
2d Law: The radius vector of a planet describes equal areas in equal times. By the radius vector is meant the straight line joining the planet to the sun, and the law declares that as the planet moves round the sun, the area of space swept over by this line in any given time, say one day, is equal to the area which it will sweep over in any other equal length of time. If the orbit were a circle it is evident at a glance that the law must be true, because then the sun would be situated in the centre of the circle, the length of the radius vector, no matter where the planet might be in the orbit, would never vary, and the area swept over by it in one day would be equal to the area swept over in any other day, because all these areas would be precisely similar and equal triangles. But Kepler discovered that the same thing is true when the orbit is an ellipse, and when, in consequence of the eccentricity of the orbit, the planet is sometimes farther from the sun than at other times. As the triangular area swept over in a given time increases in length with the planet's recession from the sun, it diminishes in breadth just enough to make up the difference which would otherwise exist between the different areas. This law grows out of the fact that the force of gravitation varies inversely with the square of the distance.
3d Law: The squares of the periods (i. e. times of revolution in their orbits) of the different planets are proportional to the cubes of their mean (average) distances from the sun. The meaning of this will be best explained by an example. Suppose one planet, whose distance we know, has a period only one-eighth as long as that of another planet, whose distance we do not know. Then Kepler's third law enables us to calculate the distance of the second planet. Call the period of the first planet 1, and that of the second 8, and also call the distance of the first 1, since all we really need to know is the relative distance of the second, from which its distance in miles is readily deduced by comparison with the distance of the first. Then, by the law, 12 : 82 : 13 : x3 (“x” representing the unknown quantity). Now, this is simply a problem in proportion where the product of the means is equal to the product of the extremes. But 12 = 1, and also 13= 1; therefore x3 = 82, and x = ∛(82) (the cube root of the square of 8), which is 4. Thus we see that the distance of the second planet must be four times that of the first.
This third law of Kepler is applied to ascertain the distances of newly discovered planets, whose periods are easily ascertained by simple observation. If we know the distance of any one planet by measurement, we can calculate the distances of all the others after observing their periods. The law also works conversely, i. e. from the distances the periods can be calculated.