THE MOON
The moon is the most interesting of the heavenly bodies not only from a
romantic viewpoint, but from the astronomical as well. Looking at the
practical side, it is due mostly to the moon’s influence of attraction
on the waters of the earth that we have the highly important phenomena
of the tides. The moon is our nearest neighbor in the heavens; in fact,
she is a satellite, that is, revolves around the earth. This movement
is from west to east at an average rate of 51 minutes each day. The
moon’s orbit is elliptical with the earth lying a little out of center,
not unlike the situation of the sun in the earth’s orbital ellipse but
more pronounced. When the moon is at the nearest point to the earth she
is said to be at “perigee” and the point where she is most remote is
called the “apogee.”
The moon is a non-luminous body and gives off nothing but reflected
sunlight. The lunar hemisphere facing the sun is therefore the only
illuminated portion of the body, and as she turns on her axis precisely
as the earth does, the same side is always towards us. The astronomers
have seen but one side of our satellite. This solar illumination
accounts for the various interesting phases of the moon which we see
each month. When this body in her monthly revolution around the earth
passes between us and the sun, the illuminated side is towards the sun
and the dark side towards us. We see no moon at this time and call it
new moon. Two weeks later, she has completed one-half of her revolution
and is now on the other side of the earth and we are between the moon
and the sun. The illuminated face of the moon is now directly towards
us and we call it full moon. At the time of new moon, the eastward
movement quickly brings her out of range with the sun and in a couple
of days we are able to see a fine crescent in the western sky. This is
the very edge of the illuminated face--we can see around the corner
just that much. Day after day the moon’s lighted surface becomes larger
and larger until in about a week she is near our meridian at sunset and
therefore at, roughly (depending on the time of the year), 90° from
the bearing of the sun. The moon now presents to us a face one-half
dark and one-half light. This is called the quadrature. This term also
applies to the similar condition occurring a week after full moon when
she is again bearing at right angles to the sun. These occasions are
also called the first and last quarter, respectively.
The movements of the moon are very rapid. She makes her revolution
around the earth in 27⅓ days, making a change in right ascension of
360° or 24 hours in this interval, a change of over two minutes each
hour. The declination passes through its whole cycle of change from
north to south and return also in 27⅓ days; the sun requires a year
to pass through its extremes of declination and return. The change of
the moon’s declination averages about 9´ per hour. These facts demand
careful attention when employing the moon in navigation.
It is a very curious and happy circumstance that in the higher
latitudes when the short days of the winter sun occur, the moon at
full rides its highest declinations, and consequently gives extra
long nights of moonlight; and that in the summer, when the sun is in
higher declination and the days are long, the moon at full is in low
declination and there is less moonlight when it is least needed. The
reason of these conditions is that the full moon occurs when on the
opposite side of the earth from the sun and at the winter solstice
when the earth’s north pole is inclined away from the sun she must be
inclined towards the moon passing that body in high declination. The
reverse conditions exist at the summer solstice.
Another fortunate provision for lovers of moonlight nights is the
fact that the plane of the moon’s orbit is not in the same plane as
that of the earth’s orbit, for if such were the case each time the
three bodies, the earth, sun and moon, came in range there would be an
eclipse. The new moon coming in between the earth and the sun would
cause an eclipse of the sun, and at full moon when the earth is between
the sun and moon, there would be an eclipse of the moon. Therefore,
there would be an eclipse twice a month. This fortunately is avoided by
the angle of 5° that the plane of the moon’s orbit takes with that of
the earth. As a result they only come in exact range occasionally when
the moon at new and full happens to be on the ecliptic--the earth’s
orbit. If, to repeat, this occurs at full there is an eclipse of the
moon, if it occurs at new, there is an eclipse of the sun. the moon
moves eastward through the heavens on her monthly course of revolution;
it then becomes apparent that she must return to the meridian later and
later each day the amount of “retardation,” as it is called. This
retardation is a variable quantity dependent upon the moon’s irregular
change in right ascension. It is caused by the moon’s motion in her
elliptical orbit and at the inclination which her orbit takes with the
celestial equator. These causes are precisely the same in character as
those producing the equation of time in the conditions relative to the
sun and the earth’s orbit, but those of the moon are much greater. The
errors causing a variation in the right ascension of the sun requiring
a year where the similar conditions in the moon are brought about in a
month, which accounts for the marked changes in the moon’s rate of
eastward motion. The _average_ daily retardation, or average later
time in arriving at the meridian, is very close to 51 minutes. Yet the
extremes of retardation range from 38 to 66 minutes. The average of 51
minutes daily retardation is also noticed in the later rising and
setting of the moon. The extreme times between successive risings or
settings during the year, while they average 51 minutes like the
crossing of the meridian, they do not maintain the same extremes,
changing on account of the latitude of the observer as well as upon
her own motions. At 41° north the retardation on successive risings
and settings ranges between 23 minutes and 1 hour and 17 minutes. As
the vessel proceeds farther north the range is greater until near 66°
north when the moon is in her average greatest declination north she
does not set at all becoming circumpolar for a certain time each
month. In the duration of a month the moon changes her right ascension
24 hours, where the sun takes a year to accomplish this amount as it
(apparently for navigational purposes) moves eastward around the
earth. This shows the much more rapidly increasing change in right
ascension in the case of our satellite. Thus again the moon’s rapid
motions are accounted for.
The moon’s orbit around the earth is not coincident--does not lie
in the same plane as the earth’s orbit (the ecliptic) but takes an
angle of about 5° 8´ with it. The point of intersection between the
moon’s orbit and the ecliptic are called nodes (corresponding with the
equinoxes). The point crossed by the moon as it passes from southern
to the northern side of the ecliptic is called the ascending and the
other the descending node. The moon’s axis is very slowly describing a
circle in the heavens similar to that of the earth; and in consequence
the nodes are slowly moving westward along the ecliptic year by year.
Just as is the equinox by the movement of precession, but at a much
greater rate (see remarks on precession elsewhere). The moon’s axis
completes its revolution in about 19 years, while the earth requires
26,000 years. This is called the lunar cycle. At the time in the lunar
cycle when the ascending node of the moon’s orbit is in range with the
vernal equinox the moon has her greatest range of declination--about
57° from extreme north to extreme south. She is then 23° north, the
amount that the ecliptic is from the equator and 5° more, the amount
that the moon’s orbit is above the ecliptic. About 9½ years later when
the moon’s axis has listed in the opposite direction and the descending
node coincides with the vernal equinox, the moon’s maximum declination
equals 23° minus 5° or 18° north or south, a range of only about 26°.
[Illustration: This figure is viewed from the sun looking towards the
earth on march 21st--the vernal equinox.
FIG. 12.]
In the autumn, there occurs an interesting phenomenon regarding the
moon called the Harvest Moon. This is the time of unusually fine
moonlight nights in which the moon rises for three or four evenings at
about the same time instead of the usual rapid retardation. The time
the sun or moon is above our horizon depends upon its declination and
our latitude. As the sun moves northward in declination from March to
June, our days lengthen by the sun rising earlier and farther in the
northeast, and setting later and farther to the northwest. Similarly
the moon in September is moving northward in declination very rapidly
and would be rising earlier each evening were it not for its own
eastward movement of revolution which causes her to slip eastward an
average of 51 minutes daily and causes her later rising at night. The
result is that these two influences at work almost counteract each
other and cause the moon to rise at about the same time for several
days giving us three or four glorious moonlight nights called the
Harvest Moon.
It will be seen by the foregoing that great care must be exercised in
having the time of observation accurately determined owing to those
rapid movements of the moon. It is also a matter of great difficulty
to correct the observed altitude of this body on account of numerous
errors that become considerable in amounts due to her proximity to the
earth. And for these reasons this body is not popular for observations
with the general run of navigators. In the case of the semi-diameter,
considerable error is apparent and is fully described, with parallax,
which is excessive, under “Corrections for Observed Altitudes.”