CHAPTER VI.

THE MOVEMENTS OF THE MOON.

THE MOON’S REVOLUTION.—Apart from the changes in the appearance of the moon due to the ever-varying phases, the first fact which strikes the attentive observer is that the moon has an eastward movement among the stars, and that this motion is much more rapid than that of the sun. Indeed, the moon gains a whole revolution upon the sun in a period of about 29½ days, this being the interval between two successive new or full moons. As referred to the stars, however, it is found that the moon and any particular star which cross the meridian together at a certain time will again do so after the lapse of only 27⅓ days. Besides this eastward movement among the stars, the moon moves towards and away from the Pole; the full moon, for instance, is sometimes seen high in the heavens at midnight, and at other times very low. Indeed, the moon’s apparent movements resemble in a very general way those of the sun, but they cannot be attributed to a revolution of the earth round the moon, as those of the sun are to a real movement of the earth round the sun. We have seen that there are direct proofs of the earth’s revolution round the sun, and a revolution round the moon, even in a smaller orbit, would not be consistent with the observed movements of the greater luminary. Being convinced of the reality of the moon’s movements around the earth, we can next proceed to investigate the circumstances of its varied motions.

Just as we learn the conditions of the earth’s movements by observations of the sun’s apparent movements which are their natural consequence, we can determine the moon’s motions by studying its varying situations with regard to the much more distant stars. We can measure the moon’s right ascension and declination at different times with the transit instrument, and, if desired, we can mark out the apparent path on our star charts or celestial globes. In this way it is found that the moon moves in a plane which is inclined at 5° 9′ to the plane of the ecliptic. As to the shape of the orbit, we have only to observe the changes in the moon’s apparent size; when it is nearest to us it will appear largest, and when furthest removed its apparent diameter will be least. Actual observations show that, like the orbit of the earth, the moon’s orbit is an ellipse, with the earth in one focus. Owing to various causes, the orbit is somewhat variable in shape, and its eccentricity ranges from 0·07 to 0·045. When the moon is at the point of its orbit nearest to the earth, it is said to be in _perigee_; and when at the most distant part of its orbit, in _apogee_.

The earth’s orbit, as we shall see by and by, is very small as compared with stellar distances, and the moon’s apparent movement, with regard to the stars, is not affected by the revolution of the earth and moon round the sun; consequently the interval between its passing a star and overtaking the same star again is a measure of the time in which the moon’s movement round the earth is performed—this is 27 days, 7 hours, 43 minutes, and is called the moon’s _sidereal period_. The direction of the moon’s motion is opposite to that of the hands of a clock, a movement which is said to be _direct_ (motion in the reverse direction would be _retrograde_).

PHASES.—Two circumstances lead us to suppose that the light of the moon is borrowed from the vast store thrown out into space by the sun. First, the fact that it puts on _phases_, for if it were a body shining by its own light we should always see a full moon. Second, the fact that the phase we see depends absolutely on the moon’s situation with regard to the sun and earth.

There is every reason to suppose that the moon is a dark globular body, so that the sun can only illuminate that hemisphere which is turned towards it. At new moon the illuminated part is turned directly away from us, and we are thus led to infer that when new the moon lies directly between the earth and sun. At full moon, on the contrary, the whole of the illuminated part is presented to us, and we therefore conclude that at this time the earth lies between the sun and moon. On account of the inclination of the moon’s orbit to that of the earth, the sun, earth, and moon do not always come exactly in a straight line at new or full moon; when they do, the interesting phenomena of solar and lunar eclipses occur. (Chapter VIII.)

A diagram will help to elucidate the production of the moon’s intermediate phases. Supposing the sun’s rays to proceed from the left, the earth being at O, the moon will be at A when new. Proceeding towards B, a small portion of the illuminated side will be turned towards us, and the moon will be a crescent. On reaching the point C, exactly half of the sunlit hemisphere will be visible to us, and we have the moon’s _first quarter_. Passing to the point D we see more than half of the bright part of our satellite, and it appears gibbous in form, until it reaches E, where it becomes full. Similar phases occur in inverse order during the movement along the other part of the orbit.

[Illustration:

FIG. 18.—_The Moon’s Phases._ ]

Such would be the conditions as to the phases of the moon, if the earth were at rest.

THE MONTH.—If the earth were fixed in space with regard to the sun, the moon’s phases would be repeated in the time corresponding to its period of revolution round the earth. This is 27 days 7 hours 43 minutes, and measures the length of a sidereal month.

It is much more useful, however, to refer the month to the phases actually observed. If in Fig. 19 we have the sun, earth, and moon represented at a full moon by S, E, and M respectively, the next full moon will not occur until the three bodies occupy the positions S, E′, and M′, the earth having travelled about 30° along its orbit. Between two full moons, then, the moon must make a complete revolution round the earth, and through an additional angle, A E′ M′, which will be equal to the earth’s angular motion in the interval. This movement of the moon occupies 29 days 12 hours 44 minutes, and is the duration of a _lunar month_. It also determines the _synodic period_ of our satellite, a term which, taken generally, signifies the period in which a planet or satellite recovers the same position with respect to the sun when observed from the earth.

[Illustration:

FIG. 19.—_The Lunar Month._ ]

A calendar month, of which there are twelve in a year, must of necessity consist of a whole number of days, and the average duration of such a month is longer than that of a lunar month.

A remarkable relation exists between the synodic month and the length of the year. In 19 Julian years of 365¼ days there are almost exactly 235 synodic months, so that after the completion of this period full moons again occur on the same days of the month. The discovery of this cycle is usually ascribed to Meton, a Greek astronomer, 433 B.C. It is accordingly known as the _Metonic Cycle_, and is still used in the calculation of the moveable festival of Easter.[1]

ROTATION AND LIBRATIONS.—Even observations made without instrumental assistance show that the surface of our satellite always presents the same face to us, and without further inquiry one might suppose that it had no axial movement corresponding to that of its primary. If there were no rotation, however, we should in turn see all parts of the moon, and the observed circumstances indicate that it must rotate on an axis, in the same direction as that of its orbital movement, and in the same time. In Fig. 20 let E represent the earth, and _a b c_ the part of the moon which is turned towards us when it is at M. When the moon arrives at M′, observations show us that the same part is presented to our view, so that the part corresponding to that we saw in position M is represented by _a′ b′ c′_. Now, if the moon had not rotated in the interval, the line joining _a_ and _c_ would have retained the same direction, and would have been in the position _d e_; the part _c′ e_ would thus have been carried out of sight, while another part which was not seen when the moon was at M would have come into view. In order that we may see the same part of the moon in two different positions, M and M′, the dividing-line _a c_ between the visible and invisible portions must turn through an angle equal to that between the lines _d e_ and _a′ c′_; and since this angle is equal to that described by the moon in the same time, the period of the moon’s rotation on its axis must be equal to that of its revolution round the earth.

On account of the elliptical form of its orbit, the angular movement of the moon is not quite uniform; like the earth, it is subject to the law of areas. Hence, as the rotation is equable, the foregoing explanation does not strictly hold. In fact, this varying velocity results in a _libration in longitude_, which means that we sometimes see a little more of the western edge and sometimes of the eastern edge. There is also a _libration in latitude_ on account of the fact that the moon’s axis is inclined to the plane of its orbit, so that at different times we see more of the North or South Pole, as the case may be; in this respect the moon behaves to the earth somewhat as the earth does to the sun in regard to the seasons, but the inclination is not so great.

[Illustration:

FIG. 20.—_The Moon’s Rotation._ ]

The moon is so near to us that the portion of it which we see depends to a slight extent upon our terrestrial location. When the moon is rising we see a little more of its western edge than will be seen by an observer to the east of us, where the moon is in the south, and more than we ourselves shall see when it has come to our own meridian. Just before the time of setting we get to see a little beyond the eastern edge. This is called the _diurnal libration_, and never amounts to more than a degree.

Thanks to these librations, we are enabled to make telescopic observations of 9 per cent. of the moon’s surface which would not otherwise be open to our investigations.

CHANGES OF THE MOON’S ORBIT.—The moon’s orbit is by no means to be regarded as a hard and fast geometrical figure. Indeed, it is subject to such great distortions in consequence of “perturbations” that the computation of the moon’s position at any future time is one of great complexity. One of the most easily recognised changes in the orbit is the revolution of its _nodes_, that is, of the points where it crosses the plane of the ecliptic.

[Illustration:

FIG. 21.—_The Moon’s Nodes._ ]

The latter being a plane of indefinite extent, to which the moon’s orbit is inclined at 5° 9′, the moon will be alternately above and below the ecliptic for about half its period of revolution. The point where it passes from south to north of the ecliptic, A in Fig. 21, is the _ascending node_, and the corresponding point on its southward path is the _descending node_ of the orbit. Connecting these two points is the line of nodes (A B), and by observations of the points where the moon’s path intersects the ecliptic at different times it is found that the line of nodes _regredes_ or moves backwards. The rate of this revolution of the moon’s nodes is very irregular, but a whole revolution is made in 18·6 years.

This retrogression of the moon’s nodes may be well illustrated by the following heliocentric longitudes of the ascending node as given in recent “Nautical Almanacs”:

1892 January 1 53° 51′·56. 1893 „ 34° 28′·69. 1894 „ 15° 19′·00. 1895 „ 355° 49′·31. 1896 „ 336° 29′·61.

The line of apsides of the moon’s orbit joins the perigee and apogee; the direction of this line in space changes in a very variable manner, but in the long run it makes a complete revolution in 8·9 years.

When the sun is passing through the moon’s line of apsides it temporarily increases the eccentricity of the orbit; when at right angles to this line, the orbit becomes more nearly circular. This disturbance of the moon has accordingly a period equal to that required for two successive passages of the sun over the apse line of the moon’s orbit.

Such are a few of the movements which come within the province of the _lunar theory_, a fuller treatment of which is beyond our scope.

THE HARVEST MOON.—The full moon which occurs nearest to the autumnal equinox is called the _harvest moon_, for the reason that it rises very nearly at the same hour for several nights together, and so gives us a greater share of moonlight, by which harvest operations may be extended. At that time the sun will be at the autumnal equinoctial point, and when it is setting in the west, the vernal equinoctial point, and the moon with it, must be rising due east. The part of the ecliptic then above the horizon will extend from the east to the west point, but will lie wholly below the celestial equator (Fig. 22). As the moon’s path is very slightly inclined to the ecliptic, its movement will thus make only a small angle with the horizon, and for several nights together it will rise at nearly the same time.

In March, when the sun is near the vernal equinox, the full moon will be near the autumnal equinoctial point; when the sun is setting, the moon will be rising as before, but in this case the part of the ecliptic which is above the horizon lies wholly above the celestial equator. The ecliptic is thus inclined at an angle to the horizon greater by 47° than when the vernal equinox is rising in autumn; the moons path being near the ecliptic, its movement during a day will at this time carry it a long way below the Equator, and it will rise much later the following day.

[Illustration:

FIG. 22.—_Position of Ecliptic at Sunset at Vernal Equinox_ (E A W) _and Autumnal Equinox_ (E B W). ]

In the Southern Hemisphere, the conditions are reversed, the harvest moon occurring at our vernal equinox, which, however, is the commencement of the southern autumn quarter.

The phenomena of the harvest moon recur, but are not so marked, in the month of October, and it is then called the hunter’s moon.

It is important to bear in mind that this rising of the moon at nearly the same hour for several days occurs every month, but as the risings then occur either in daylight or after midnight, and the moon is not full, no special attention is drawn to them.

Again, since the phenomenon of the harvest moon depends upon the small inclination of the path of the full moon to the horizon when it is at the equinoctial point, the circumstances will be modified by the latitude of the place of observation. At the Equator, for example, there will be no harvest moon, as there the ecliptic is always greatly inclined to the horizon; in fact, it will be inclined at the same angle in spring as in autumn.

The moon’s path being inclined to the ecliptic, the conditions as to the harvest moon will depend to a small extent upon the position of the moon’s nodes, which, as we have seen, revolve in a period of a little less than 19 years. At times, then, the moon’s path will be inclined 5° more, and 9 years afterwards 5° less, than is the plane of ecliptic, and under the latter conditions the harvest moon will be most pronounced.

HIGH AND LOW MOONS.—At the time of full moon, the moon is in the opposite part of the heavens to that occupied by the sun, sometimes being 5° above and other times 5° below. Manifestly, then, if the sun be high in the heavens at mid-day, it will be only a little below the northern horizon at midnight, and the moon, consequently, will be only a small distance above the southern horizon. In summer, then, quite apart from the fact that the nights are shorter, there is less moonlight. In winter, on the other hand, the sun descends far below the northern horizon at midnight, and the full moon has a high elevation in the southern part of the sky. By this happy arrangement, the full moon is longest above the horizon when its light is of greatest benefit to mankind.