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.