Part 13

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.

Mercury.

216. _The Orbit of Mercury._--The orbit of Mercury is more eccentric than that of any of the larger planets, and it has also a greater inclination to the ecliptic. Its eccentricity (43) is a little over a fifth, and its inclination to the ecliptic somewhat over seven degrees. The mean distance of Mercury from the sun is about thirty-five million miles; but, owing to the great eccentricity of its orbit, its distance from the sun varies from about forty-three million miles at aphelion to about twenty-eight million at perihelion.

217. _Distance of Mercury from the Earth._--It is evident, from Fig. 251, that an inferior planet, like Mercury, is the whole diameter of its orbit nearer the earth at inferior conjunction than at superior conjunction: hence Mercury's distance from the earth varies considerably. Owing to the great eccentricity of its orbit, its distance from the earth at inferior conjunction also varies considerably. Mercury is nearest to the earth when its inferior conjunction occurs at its own aphelion and at the earth's perihelion.

218. _Apparent Size of Mercury._--Since Mercury's distance from the earth is variable, the apparent size of the planet is also variable. Fig. 252 shows its apparent size at its extreme and mean distances from the earth. Its apparent diameter varies from five seconds to twelve seconds.

219. _Volume and Density of Mercury._--The real diameter of Mercury is about three thousand miles. Its size, compared with that of the earth, is shown in Fig. 253. The earth is about sixteen times as large as Mercury; but Mercury is about one-fifth more dense than the earth.

220. _Greatest Elongation of Mercury._--Mercury, being an _inferior_ planet (or one within the orbit of the earth), appears to oscillate to and fro across the sun. Its greatest apparent distance from the sun, or its _greatest elongation_, varies considerably. The farther Mercury is from the sun, and the nearer the earth is to Mercury, the greater is its angular distance from the sun at the time of its greatest elongation. Under the most favorable circumstances, the greatest elongation amounts to about twenty-eight degrees, and under the least favorable to only sixteen or seventeen degrees.

221. _Sidereal and Synodical Periods of Mercury._--Mercury accomplishes a complete revolution around the sun in about eighty-eight days; but it takes it a hundred and sixteen days to pass from its greatest elongation east to the same elongation again. The orbital motion of this planet is at the rate of nearly thirty miles a second.

In Fig. 251, _P'''_ represents elongation east of the sun, and _P'_ elongation west. It will be seen that it is much farther from _P'_ around to _P'''_ than from _P'''_ on to _P'_. Mercury is only about forty-eight days in passing from greatest elongation east to greatest elongation west, while it is about sixty-eight days in passing back again.

222. _Visibility of Mercury._--Mercury is too close to the sun for favorable observation. It is never seen long after sunset, or long before sunrise, and never far from the horizon. When visible at all, it must be sought for low down in the west shortly after sunset, or low in the east shortly before sunrise, according as the planet is at its east or west elongation. It is often visible to the naked eye in our latitude; but the illumination of the twilight sky, and the excess of vapor in our atmosphere near the horizon, combine to make the telescopic study of the planet difficult and unsatisfactory.

223. _The Atmosphere and Surface of Mercury._--Mercury seems to be surrounded by a dense atmosphere. One proof of the existence of such an atmosphere is furnished at the time of the planet's _transit_ across the disk of the sun, which occasionally happens. The planet is then seen surrounded by a border, as shown in Fig. 254. A bright spot has also been observed on the dark disk of the planet during a transit, as shown in Fig. 255. The border around the planet seems to be due to the action of the planet's atmosphere; but it is difficult to account for the bright spot.

Schröter, a celebrated German astronomer, at about the beginning of the present century, thought that he detected spots and shadings on the disk of the planet, which indicated both the presence of an atmosphere and of elevations. The shading along the terminator, which seemed to indicate the presence of a twilight, and therefore of an atmosphere, are shown in Fig. 256. It also shows the blunted aspect of one of the cusps, which Schröter noticed at times, and which he attributed to the shadow of a mountain, estimated to be ten or twelve miles high. Fig. 257 shows this mountain near the upper cusp, as Schröter believed he saw it in the year 1800. By watching certain marks upon the disk of Mercury, Schröter came to the conclusion that the planet rotates on its axis in about twenty-four hours. Modern observers, with more powerful telescopes, have failed to verify Schröter's observations as to the indications of an atmosphere and of elevations. Nothing is known with certainty about the rotation of the planet.

The border around Mercury, and the bright spot on its disk at the time of the transit of the planet across the sun, have been seen since Schröter's time, and the existence of these phenomena is now well established; but astronomers are far from being agreed as to their cause.

224. _Intra-Mercurial Planets._--It has for some time been thought probable that there is a group of small planets between Mercury and the sun; and at various times the discovery of such bodies has been announced. In 1859 a French observer believed that he had detected an intra-Mercurial planet, to which the name of _Vulcan_ was given, and for which careful search has since been made, but without success. During the total eclipse of 1878 Professor Watson observed two objects near the sun, which he thought to be planets; but this is still matter of controversy.

Venus.

225. _The Orbit of Venus._--The orbit of Venus has but slight eccentricity, differing less from a circle than that of any other large planet. It is inclined to the ecliptic somewhat more than three degrees. The mean distance of the planet from the sun is about sixty-seven million miles.

226. _Distance of Venus from the Earth._--The distance of Venus from the earth varies within much wider limits than that of Mercury. When Venus is at inferior conjunction, her distance from the earth is ninety-two million miles _minus_ sixty-seven million miles, or twenty-five million miles; and when at superior conjunction it is ninety-two million miles _plus_ sixty-seven million miles, or a hundred and fifty-nine million miles. Venus is considerably more than _six times_ as far off at superior conjunction as at inferior conjunction.

227. _Apparent Size of Venus._--Owing to the great variation in the distance of Venus from the earth, her apparent diameter varies from about ten seconds to about sixty-six seconds. Fig. 258 shows the apparent size of Venus at her extreme and mean distances from the earth.

228. _Volume and Density of Venus._--The real size of Venus is about the same as that of the earth, her diameter being only about three hundred miles less. The comparative sizes of the two planets are shown in Fig. 259. The density of Venus is a little less than that of the earth.

229. _The Greatest Elongation of Venus._--Venus, like Mercury, appears to oscillate to and fro across the sun. The angular value of the greatest elongation of Venus varies but slightly, its greatest value being about forty-seven degrees.

230. _Sidereal and Synodical Periods of Venus._--The _sidereal_ period of Venus, or that of a complete revolution around the sun, is about two hundred and twenty-five days; her orbital motion being at the rate of nearly twenty-two miles a second. Her _synodical_ period, or the time it takes her to pass around from her greatest eastern elongation to the same elongation again, is about five hundred and eighty-four days, or eighteen months. Venus is a hundred and forty-six days, or nearly five months, in passing from her greatest elongation east through inferior conjunction to her greatest elongation west.

231. _Venus as a Morning and an Evening Star._--For a period of about nine months, while Venus is passing from superior conjunction to her greatest eastern elongation, she will be east of the sun, and will therefore set after the sun. During this period she is the _evening star_, the _Hesperus_ of the ancients. While passing from inferior conjunction to superior conjunction, Venus is west of the sun, and therefore rises before the sun. During this period of nine months she is the _morning star_, the _Phosphorus_, or _Lucifer_, of the ancients.

232. _Brilliancy of Venus._--Next to the sun and moon, Venus is at times the most brilliant object in the heavens, being bright enough to be seen in daylight, and to cast a distinct shadow at night. Her brightness, however, varies considerably, owing to her phases and to her varying distance from the earth. She does not appear brightest when at full, for she is then farthest from the earth, at superior conjunction; nor does she appear brightest when nearest the earth, at inferior conjunction, for her phase is then a thin crescent (see Fig. 258). She is most conspicuous while passing from her greatest eastern elongation to her greatest western elongation. After she has passed her eastern elongation, she becomes brighter and brighter till she is within about forty degrees of the sun. Her phase at this point in her orbit is shown in Fig. 260. Her brilliancy then begins to wane, until she comes too near the sun to be visible. When she re-appears on the west of the sun, she again becomes more brilliant; and her brilliancy increases till she is about forty degrees from the sun, when she is again at her brightest. Venus passes from her greatest brilliancy as an evening star to her greatest brilliancy as a morning star in about seventy-three days. She has the same phase, and is at the same distance from the earth, in both cases of maximum brilliancy. Of course, the brilliancy of Venus when at the maximum varies somewhat from time to time, owing to the eccentricities of the orbits of the earth and of Venus, which cause her distance from the earth, at her phase of greatest brilliancy, to vary. She is most brilliant when the phase of her greatest brilliancy occurs when she is at her aphelion and the earth at its perihelion.

233. _The Atmosphere and Surface of Venus._--Schröter believed that he saw shadings and markings on Venus similar to those on Mercury, indicating the presence of an atmosphere and of elevations on the surface of the planet. Fig. 261 represents the surface of Venus as it appeared to this astronomer. By watching certain markings on the disk of Venus, Schröter came to the conclusion that Venus rotates on her axis in about twenty-four hours.

It is now generally conceded that Venus has a dense atmosphere; but Schröter's observations of the spots on her disk have not been verified by modern astronomers, and we really know nothing certainly of her rotation.

234. _Transits of Venus._--When Venus happens to be near one of the nodes of her orbit when she is in inferior conjunction, she makes a transit across the sun's disk. These transits occur in pairs, separated by an interval of over a hundred years. The two transits of each pair are separated by an interval of eight years, the dates of the most recent being 1874 and 1882. Venus, like Mercury, appears surrounded with a border on passing across the sun's disk, as shown in Fig. 262.

Mars.

235. _The Orbit of Mars._--The orbit of Mars is more eccentric than that of any of the larger planets, except Mercury; its eccentricity being about one-eleventh. The inclination of the orbit to the ecliptic is somewhat under two degrees. The mean distance of Mars from the sun is about a hundred and forty million miles; but, owing to the eccentricity of his orbit, the distance varies from a hundred and fifty-three million miles to a hundred and twenty-seven million miles.

236. _Distance of Mars from the Earth._--It will be seen, from Fig. 263, that a _superior_ planet (or one outside the orbit of the earth), like Mars, is nearer the earth, by the whole diameter of the earth's orbit, when in opposition than when in conjunction. The mean distance of Mars from the earth, at the time of opposition, is a hundred and forty million miles _minus_ ninety-two million miles, or forty-eight million miles. Owing to the eccentricity of the orbit of the earth and of Mars, the distance of this planet when in opposition varies considerably. When the earth is in aphelion, and Mars in perihelion, at the time of opposition, the distance of the planet from the earth is only about thirty-three million miles. On the other hand, when the earth is in perihelion, and Mars in aphelion, at the time of opposition, the distance of the planet is over sixty-two million miles.

The mean distance of Mars from the earth when in conjunction is a hundred and forty million miles _plus_ ninety-two million miles, or two hundred and thirty-two million miles. It will therefore be seen that Mars is nearly five times as far off at conjunction as at opposition.

237. _The Apparent Size of Mars._--Owing to the varying distance of Mars from the earth, the apparent size of the planet varies almost as much as that of Venus. Fig. 264 shows the apparent size of Mars at its extreme and mean distances from the earth. The apparent diameter varies from about four seconds to about thirty seconds.