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CHAP. VI.

ON THE MOON.

213

CHAP. VI.

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OF THE MOON. ITS SIDEREAL PERIOD. ITS APPARENT DIA-
METER. — ITS PARALLAX, DISTANCE, AND REAL DIAMETER.
FIRST APPROXIMATION TO ITS ORBIT. AN ELLIPSE ABOUT
THE EARTH IN THE FOCUS. -ITS ECCENTRICITY AND IN-
CLINATION.MOTION OF THE NODES OF ITS ORBIT. OC-
CULTATIONS. SOLAR ECLIPSES. PHASES OF THE MOON.
ITS SYNODICAL PERIOD. LUNAR ECLIPSES. MOTION OF
THE APSIDES OF ITS ORBIT. PHYSICAL CONSTITUTION OF THE
MOON. ITS MOUNTAINS. ATMOSPHERE. ROTATION ON

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AXIS. -LIBRATION. APPEARANCE OF THE EARTH FROM IT.

(338.) THE moon, like the sun, appears to advance among the stars with a movement contrary to the general diurnal motion of the heavens, but much more rapid, so as to be very readily perceived (as we have before observed) by a few hours' cursory attention on any moonlight night. By this continual advance, which, though sometimes quicker, sometimes slower, is never intermitted or reversed, it makes the tour of the heavens in a mean or average period of 27d 7h 43m 11s.5, returning, in that time, to a position among the stars nearly coincident with that it had before, and which would be exactly so, but for causes presently to be stated.

(339.) The moon, then, like the sun, apparently describes an orbit round the earth, and this orbit cannot be very different from a circle, because the apparent angular diameter of the full moon is not liable to any great extent of variation.

(340.) The distance of the moon from the earth is concluded from its horizontal parallax, which may be found either directly, by observations at remote geographical stations, exactly similar to those described in art. 302., in the case of the sun, or by means of the phenomena called occultations (art. 346.), from which also its apparent diameter is most readily and correctly found.

From such observations it results that the mean or average distance of the center of the moon from that of the earth is 59.9643 of the earth's equatorial radii, or about 237000 miles. This distance, great as it is, is little more than one fourth of the diameter of the sun's body, so that the globe of the sun would nearly twice include the whole orbit of the moon; a consideration wonderfully calculated to raise our ideas of that stupendous luminary!

(341.) The distance of the moon's center from an observer at any station on the earth's surface, compared with its apparent angular diameter as measured from that station, will give its real or linear diameter. Now, the former distance is easily calculated when the distance from the earth's center is known, and the apparent zenith distance of the moon also determined by observation; for if we turn to the figure of art. 298., and suppose S the moon, A the station, and C the earth's center, the distance S C, and the earth's radius C A, two sides of the triangle A C S are given, and the angle CA S, which is the supplement of Z A S, the observed zenith distance, whence it is easy to find A S, the moon's distance from A. From such observations and calculations it results, that the real diameter of the moon is 2160 miles, or about 0.2729 of that of the earth, whence it follows that, the bulk of the latter being considered as 1, that of the former will be 0.0204, or about

(342.) By a series of observations, such as described in art. 340., if continued during one or more revolutions of the moon, its real distance may be ascertained at every point of its orbit; and if at the same time its apparent places in the heavens be observed, and reduced by means of its parallax to the earth's center, their angular intervals will become known, so that the path of the moon may then be laid down on a chart supposed to represent the plane in which its orbit lies, just as was explained in the case of the solar ellipse (art. 292.). Now, when this is done, it is found that, neglecting certain small (though very perceptible) deviations (of which a satisfac

CHAP. VI. REVOLUTION OF THE MOON'S NODES.

215

tory account will hereafter be rendered), the form of the apparent orbit, like that of the sun, is elliptic, but considerably more eccentric, the eccentricity amounting to 0.05484 of the mean distance, or the major semi-axis of the ellipse, and the earth's center being situated in its focus.

(343.) The plane in which this orbit lies is not the ecliptic, however, but is inclined to it at an angle of 5° 8′ 48′′, which is called the inclination of the lunar orbit, and intersects it in two opposite points, which are called its nodes—the ascending node being that in which the moon passes from the southern side of the ecliptic to the northern, and the descending the reverse. points of the orbit at which the moon is uearest to, and farthest from, the earth, are called respectively its perigee and apogee, and the line joining them and the earth the line of apsides.

The

(344.) There are, however, several remarkable circumstances which interrupt the closeness of the analogy, which cannot fail to strike the reader, between the motion of the moon around the earth, and of the earth round the sun. In the latter case, the ellipse described remains, during a great many revolutions, unaltered in its position and dimensions; or, at least, the changes which it undergoes are not perceptible but in a course of very nice observations, which have disclosed, it is true, the existence of "perturbations," but of so minute an order, that, in ordinary parlance, and for common purposes, we may leave them unconsidered. But this cannot be done in the case of the moon. Even in a single revolution, its deviation from a perfect ellipse is very sensible. It does not return to the same exact position among the stars from which it set out, thereby indicating a continual change in the plane of its orbit. And, in effect, if we trace by observation, from month to month, the point where it traverses the ecliptic, we shall find that the nodes of its orbit are in a continual state of retreat upon the ecliptic. Suppose O to be the earth, and Abad that portion of the plane of the ecliptic

which is intersected by the moon, in its alternate passages through it, from south to north, and vice versâ; and let A B C D E F be a portion of the moon's orbit, embracing a complete sidereal revolution. Sup

B

D

pose it to set out from the ascending node, A; then, if the orbit lay all in one plane, passing through O, it would have a, the opposite point in the ecliptic, for its descending node; after passing which, it would again ascend at A. But, in fact, its real path carries it not to a, but along a certain curve, A B C, to C, a point in the ecliptic less than 180° distant from A; so that the angle A O C, or the arc of longitude described between the ascending and the descending node, is somewhat less than 180°. It then pursues its course below the ecliptic, along the curve C D E, and rises again above it, not at the point c, diametrically opposite to C, but at a point E, less advanced in longitude. On the whole, then, the arc described in longitude between two consecutive passages from south to north, through the plane of the ecliptic, falls short of 360° by the angle A O E; or, in other words, the ascending node appears to have retreated in one lunation, on the plane of the ecliptic by that amount. To complete a sidereal revolution, then, it must still go on to describe an arc, A F, on its orbit, which will no longer, however, bring it exactly back to A, but to a point somewhat above it, or having north latitude.

(345.) The actual amount of this retreat of the moon's node is about 3' 10"-64 per diem, on an average, and in a period of 6793.39 mean solar days, or about 18.6 years, the ascending node is carried round in a direction

CHAP. VI.

ECLIPSES AND OCCULTATIONS.

217

contrary to the moon's motion in its orbit (or from east to west) over a whole circumference of the ecliptic. Of course, in the middle of this period the position of the orbit must have been precisely reversed from what it was at the beginning. Its apparent path, then, will lie among totally different stars and constellations at different parts of this period; and, this kind of spiral revolution being continually kept up, it will, at one time or other, cover with its disc every point of the heavens within that limit of latitude or distance from the ecliptic which its inclination permits; that is to say, a belt or zone of the heavens, of 10° 18' in breadth, having the ecliptic for its middle line. Nevertheless, it still remains true that the actual place of the moon, in consequence of this motion, deviates in a single revolution very little from what it would be were the nodes at rest. Supposing the moon to set out from its node A, its latitude, when it comes to F, having completed a revolution in longitude, will not exceed 8'; and it must be borne in mind that it is to account for, and represent geometrically, a deviation of this small order, that the motion of the nodes is devised.

(346.) Now, as the moon is at a very moderate distance from us (astronomically speaking), and is in fact our nearest neighbour, while the sun and stars are in comparison immensely beyond it, it must of necessity happen, that at one time or other it must pass over and occult or eclipse every star and planet within the zone above described (and, as seen from the surface of earth, even somewhat beyond it, by reason of parallax, which may throw it apparently nearly a degree either way from its place as seen from the center, according to the observer's station). Nor is the sun itself exempt from being thus hidden, whenever any part of the moon's disc, in this her tortuous course, comes to overlap any part of the space occupied in the heavens by that luminary. On these occasions is exhibited the most striking and impressive of all the occasional phenomena of astronomy, an eclipse of the sun, in which a greater or less

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