Part 27

207. The Lunar Ecliptic Limits.--In Fig. 236 the line AB represents the plane of the ecliptic, and the line CD the moon's orbit. The large black circles on the line AB represent sections of the umbra of the earth's shadow, and the smaller circles on CD represent the moon at full. It will be seen, that, if the moon is full at E, she will just graze the umbra of the earth's shadow. In this case she will suffer no eclipse. Were the moon full at any point nearer her node, as at F, she would pass into the umbra of the earth's shadow, and would be partially eclipsed. Were the moon full at G, she would pass through the centre of the earth's shadow, and be totally eclipsed.

It will be seen from the figure that full moon must occur when the moon is within a certain distance from her node, in order that there may be a lunar eclipse; and this space is called the lunar ecliptic limits.

The farther the earth is from the sun, the less rapidly does its shadow taper, and therefore the greater its diameter at the distance of the moon; and, the nearer the moon to the earth, the greater the diameter of the earth's shadow at the distance of the moon. Of course, the greater the diameter of the earth's shadow, the greater the ecliptic limits: hence the lunar ecliptic limits vary somewhat from time to time, according to the distance from the earth to the sun and from the earth to the moon. The limits within which an eclipse is inevitable under all circumstances are called the minor ecliptic limits; and those within which an eclipse is possible under some circumstances, the major ecliptic limits.

208. Lunar Eclipses.--Fig. 237 shows the path of the moon through the earth's shadow in the case of a partial eclipse. The magnitude of such an eclipse depends upon the nearness of the moon to her nodes. The magnitude of an eclipse is usually denoted in digits, a digit being one-twelfth of the diameter of the moon.

Fig. 238 shows the path of the moon through the earth's shadow in the case of a total eclipse. It will be seen from the figure that it is not necessary for the moon to pass through the centre of the earth's shadow in order to have a total eclipse. When the moon passes through the centre of the earth's shadow, the eclipse is both total and central.

At the time of a total eclipse, the moon is not entirely invisible, but shines with a faint copper-colored light. This light is refracted into the shadow by the earth's atmosphere, and its amount varies with the quantity of clouds and vapor in that portion of the atmosphere which the sunlight must graze in order to reach the moon.

The duration of an eclipse varies between very wide limits, being, of course, greatest when the eclipse is central. A total eclipse of the moon may last nearly two hours, or, including the partial portions of the eclipse, three or four hours.

Every eclipse of the moon, whether total or partial, is visible at the same time to the whole hemisphere of the earth which is turned towards the moon; and the eclipse will have exactly the same magnitude at every point of observation.

209. When there will be an Eclipse of the Sun.--There will be an eclipse of the sun whenever any portion of the moon's shadow is thrown on the earth. It will be seen from Fig. 235 that this can occur only when the moon is in conjunction, or at new. It does not occur every month, because, owing to the inclination of the moon's orbit to the ecliptic, the moon's shadow is usually thrown either above or below the earth at the time of new moon. There can be an eclipse of the sun only when new moon occurs at or near one of the nodes of her orbit.

210. Solar Ecliptic Limits.--The distances from the moon's node within which a new moon would throw some portion of its shadow on the earth so as to produce an eclipse of the sun are called the solar ecliptic limits. As in the case of the moon, there are major and minor ecliptic limits; the former being the limits within which an eclipse of the sun is possible under some circumstances, and the latter those under which an eclipse is inevitable under all circumstances.

The limits within which a solar eclipse may occur are greater than those within which a lunar eclipse may occur. This will be evident from an examination of Fig. 235. Were the moon in that figure just outside of the lines AB and CD, it will be seen that the penumbra of her shadow would just graze the earth: hence the moon must be somewhere within the space bounded by these lines in order to cause an eclipse of the sun. Now, these lines mark the prolongation to the sun of the cone of the umbra of the earth's shadow: hence, in order to produce an eclipse of the sun, new moon must occur somewhere within this prolongation of the umbra of the earth's shadow. Now, it is evident that the diameter of this cone is greater on the side of the earth toward the sun than on the opposite side: hence the solar ecliptic limits are greater than the lunar ecliptic limits.

211. Solar Eclipses.--An observer in the umbra of the moon's shadow would see a total eclipse of the sun, while one in the penumbra would see only a partial eclipse. The magnitude of this partial eclipse would depend upon the distance of the observer from the umbra of the moon's shadow.

The umbra of the moon's shadow is just about long enough to reach the earth. Sometimes the point of this shadow falls short of the earth's surface, as shown in Fig. 239, and sometimes it falls upon the earth, as shown in Fig. 240, according to the varying distance of the sun and moon from the earth. The diameter of the umbra at the surface of the earth is seldom more than a hundred miles: hence the belt of a total eclipse is, on the average, not more than a hundred miles wide; and a total eclipse seldom lasts more than five or six minutes, and sometimes only a few seconds. Owing, however, to the rotation of the earth, the umbra of the moon's shadow may pass over a long reach of the earth's surface. Fig. 241 shows the track of the umbra of the moon's shadow over the earth in the total eclipse of 1860.

Fig. 242 shows the track of the total eclipse of 1871 across India and the adjacent seas.

In a partial eclipse of the sun, more or less of one side of the sun's disk is usually concealed, as shown in Fig. 243. Occasionally, however, the centre of the sun's disk is covered, leaving a bright ring around the margin, as shown in Fig. 244. Such an eclipse is called an annular eclipse. An eclipse can be annular only when the cone of the moon's shadow is too short to reach the earth, and then only to observers who are in the central portion of the penumbra.

212. Comparative Frequency of Solar and Lunar Eclipses.--There are more eclipses of the sun in the year than of the moon; and yet, at any one place, eclipses of the moon are more frequent than those of the sun.

There are more lunar than solar eclipses, because, as we have seen, the limits within which a solar eclipse may occur are greater than those within which a lunar eclipse may occur. There are more eclipses of the moon visible at any one place than of the sun; because, as we have seen, an eclipse of the moon, whenever it does occur, is visible to a whole hemisphere at a time, while an eclipse of the sun is visible to only a portion of a hemisphere, and a total eclipse to only a very small portion of a hemisphere. A total eclipse of the sun is, therefore, a very rare occurrence at any one place.

The greatest number of eclipses that can occur in a year is seven, and the least number, two. In the former case, five may be of the sun and two of the moon, or four of the sun and three of the moon. In the latter case, both must be of the sun.

VI. THE THREE GROUPS OF PLANETS.

I. GENERAL CHARACTERISTICS OF THE GROUPS.

213. The Inner Group.--The inner group of planets is composed of Mercury, Venus, the Earth, and Mars; that is, of all the planets which lie between the asteroids and the sun. The planets of this group are comparatively small and dense. So far as known, they rotate on their axes in about twenty-four hours, and they are either entirely without moons, or are attended by comparatively few.

The comparative sizes and eccentricities of the orbits of this group are shown in Fig. 245. The dots round the orbits show the position of the planets at intervals of ten days.

214. The Outer Group.--The outer group of planets is composed of Jupiter, Saturn, Uranus, and Neptune. These planets are all very large and of slight density. So far as known, they rotate on their axes in about ten hours, and are accompanied with complicated systems of moons. Fig. 246, which represents the comparative sizes of the planets, shows at a glance the immense difference between those of the inner and outer group. Fig. 247 shows the comparative sizes and eccentricities of the orbits of the outer planets. The dots round the orbits show the position of the planets at intervals of a thousand days.

215. The Asteroids.--Between the inner and outer groups of planets there is a great number of very small planets known as the minor planets, or asteroids. Over two hundred planets belonging to this group have already been discovered. Their orbits are shown by the dotted lines in Fig. 247. The sizes of the four largest of these planets, compared with the earth, are shown in Fig. 248.

The asteroids of this group are distinguished from the other planets, not only by their small size, but by the great eccentricities and inclinations of their orbits. If we except Mercury, none of the larger planets has an eccentricity amounting to one-tenth the diameter of its orbit (43), nor is any orbit inclined more than two or three degrees to the ecliptic; but the inclinations of many of the minor planets exceed ten degrees, and the eccentricities frequently amount to an eighth of the orbital diameter. The orbit of Pallas is inclined thirty-four degrees to the ecliptic, while there are some planets of this group whose orbits nearly coincide with the plane of the ecliptic.

Fig. 249 shows one of the most and one of the least eccentric of the orbits of this group as compared with that of the earth.

The intricate complexity of the orbits of the asteroids is shown in Fig. 250.

II. THE INNER GROUP OF PLANETS.