ECLIPSES AND OCCULTATIONS.
ECLIPSES OF THE MOON.—As the various members of the solar system shine
only by virtue of the light which they receive from the sun, they will
cease to be visible if by any means they are deprived of the sun’s rays.
Each planet or satellite must evidently cast a shadow which is turned
directly away from the sun, and any other body passing wholly or
partially within such a shadow will be proportionately debarred from
receiving the direct light of the sun.
[Illustration:
FIG. 29.—_The Earth’s Shadow._
]
Were the sun a mere point of light these shadows would be parts of
cones, the apex always being at the sun, and they would be prolonged
indefinitely into space. As a matter of fact, every individual point
upon the sun’s disc is competent to cast a conical shadow, and the net
result is that only a relatively small space behind a planet or
satellite is really in total darkness. This will be readily understood
from Fig. 29, in which S is the sun, and E the earth. The total shadow
now becomes a cone, with the apex turned directly away from the sun, but
round this there is a region of partial shadow which is only illuminated
by portions of the sun. If we imagine a section of the shadow across the
line _a b_, we should find a central disc of total darkness called the
_umbra_, and surrounding this a ring of half shadow called the
_penumbra_.
From the known dimensions of the sun and earth, and the distance between
them, it is easy to calculate the size of the earth’s shadow-cone, and
its length is found to be greater than the distance of the moon. The
axis of this shadow will, of course, always be in the plane of the
ecliptic. If, then, at the time of opposition, the moon is sufficiently
near the plane of the ecliptic, it will pass through the shadow, and we
shall have the phenomena of a _lunar eclipse_. When the moon is wholly
immersed in the umbra, the eclipse is total, and if it further passes
quite symmetrically through the shadow, the eclipse is said to be
central. This would always be the state of affairs if the moon performed
its monthly journey in the plane of the ecliptic, and a total eclipse
would occur every month. The moon’s orbit, however, is inclined to the
ecliptic, so that for a central eclipse, the moon must be simultaneously
at opposition and at a node. If the moon be near the node when at
opposition, a total eclipse may occur, but it cannot be central, and the
duration of the total obscuration will be reduced. Still further from
the node, the moon will be above or below the ecliptic, and will be only
partially involved in the shadow-cone; such an eclipse is called a
partial one. Beyond a certain distance from the node, the inclination of
the moon’s orbit will take the moon entirely out of the umbral shadow,
and no eclipse will be possible.
The circumstances of an eclipse of the moon thus vary very considerably,
and there is still another reason why we may expect them to be
different. We have seen that the earth’s distance from the sun changes
throughout the year, and, in consequence, its shadow will be of varying
length, and the diameter of the shadow at any specified distance will
not be constant. The moon, again, is not always at the same distance
from the earth, and it will, therefore, pass through varying depths of
shadow in different eclipses, and with different velocities.
The breadth of the earth’s umbral shadow at the point where the moon
passes through it is, on the average, about three times the moon’s
diameter, and the time taken for the moon to traverse this distance is
about two hours. The duration of totality in a central eclipse may,
therefore, amount to two hours, while an additional two hours may be
occupied by the partial phases.
[Illustration:
FIG. 30.—_The Lunar Ecliptic Limit._
]
THE LUNAR ECLIPTIC LIMIT.—The greatest distance of the moon from a node
at which a partial eclipse is possible, is called the _lunar ecliptic
limit_, and is very easily calculated. In Fig. 30, let E N represent a
part of the ecliptic, N being the node of the moon’s orbit, and E the
centre of the earth’s shadow. As the orbit of the moon is inclined about
5° 9′ to the ecliptic, it may be represented by the line N M, inclined
at an angle to N E. If E A be the radius of the earth’s shadow, which,
on the average, is about three-quarters of a degree, and M A the moon’s
apparent semi-diameter (about a quarter a degree), it is clear that the
point beyond which no eclipse is possible is that in which the line M E,
perpendicular to N M, is equal to the sum of the semi-diameters. All the
quantities for solving the triangle N E M are thus known, and it can be
readily calculated that N M, the greatest distance of the moon from the
node at which an eclipse would be possible, under average conditions is
about 11°.
Taking into account the varying distances between the sun, earth, and
moon, it is found that an eclipse must always occur if the moon is
within 9° of the node, and may occur if it be 12° from the node. These
figures refer to the passage of the moon through the umbra, as the
effect of its entrance into the penumbra is too slight to be observed.
The entrance of the moon into the earth’s shadow is a definite
phenomenon, which is independent of the observer’s position on the
earth, and the phases of the eclipse are seen at exactly the same moment
from all places where the moon is above the horizon. The computation of
the circumstances at a given place is accordingly a simple one.
When a lunar eclipse is not total at any of its phases, it is usual to
specify its _magnitude_ by the ratio of the greatest measurement of the
obscured part to the moon’s diameter. Thus the magnitude of the partial
eclipse of February 28th, 1896, is given in the “Nautical Almanac” as
0·870, the moon’s diameter being taken as unity.
The conditions of lunar eclipses which have been stated have reference
to the moon’s passage through the earth’s geometrical shadow, but the
actual conditions are greatly modified by the fact that the earth is
surrounded by an atmosphere which refracts the suns light so much that
the moon is seldom quite obscured during totality. The commencement of
the total phase is also rendered difficult of observation by the
somewhat indefinite boundary between the umbra and penumbra.
ECLIPSES OF THE SUN.—If the moon performed its revolution in the plane
of the ecliptic, it is evident that it must always come between us and
the sun once in each month. This it does not do, but occasionally it
happens to be in the ecliptic when in conjunction, and the moon is then
seen to be projected upon the sun. In other words, there is an eclipse
of the sun. Let us consider the circumstances, in the first instance, to
an observer placed at the centre of the earth. If the centres of the
moon and sun appear in the same straight line, the eclipse will be
_total_ or _annular_, according as the moon or sun has the greater
apparent diameter. Both these forms of eclipses are possible, on account
of the varying apparent diameters of the sun and moon consequent upon
their variable distances from the earth. If the moon appear the larger
it will evidently cover up the whole of the sun, but when it is the
smaller, a ring of sunlight will be visible round the dark holy of the
moon, and the eclipse will be an annular one. These conditions are
illustrated in Fig. 31, _a_ and _b_ representing a total and an annular
eclipse respectively. If the moon and sun be not quite in the same
straight line, the moon may still be seen partially projected on the
sun’s disc, in which case there will be a _partial eclipse_ of the sun,
as in Fig. 31, _c_.
[Illustration:
FIG. 31.—_Eclipses of the Sun._ (_a_) _Total Eclipse_, (_b_) _Annular
Eclipse_, (_c_) _Partial Eclipse._
]
In a total eclipse there are four so-called _contacts_: the first when
the moon is seen to encroach upon the sun’s disc, the second when the
advancing edge of the moon reaches the opposite limb, the third when the
following edge of the moon first touches the sun’s boundary, and the
fourth when the projected moon finally passes off the sun. The interval
between the second and third contacts marks the duration of totality. As
referred to our supposed observer at the centre of the earth, the
duration evidently depends upon the apparent rate of the moon’s eastward
movement as compared with that of the sun, as well as upon the
differences of the apparent diameters of the two bodies.
The production of eclipses of the sun may also be considered as arising
from the immersion of an observer in the shadow of the moon. This shadow
has its axis turned from the sun, but is so short that it does not
always reach the earth. If an observer comes near the axis of the
conical shadow, and within the apex, the eclipse will be total; if he is
in the axis, but outside the apex, the eclipse will be annular.
[Illustration:
FIG. 32.—_Duration of a Solar Eclipse._
]
The whole of the shadow of the moon is so small that only a few places
on the earth’s surface can be simultaneously immersed in it, and when we
come to discuss the conditions of an eclipse with regard to a particular
observer, the problem becomes a complicated one. At some places the
eclipse may be total, at others it will be only partial, while at others
no eclipse will occur at all. These differences are due to the fact that
the sun is scarcely appreciably displaced by the change of locality,
while the apparent position of the moon may be affected to the extent of
nearly a degree. Again, the observer situated on the earth’s surface has
a movement of his own, produced by the earth’s rotation, and his rate of
motion depends upon the latitude in which he is situated. The effect of
this movement upon the conditions of the eclipse are very pronounced.
Suppose for a moment that the sun, moon, and earth, are fixed along the
same straight line S M E in Fig. 32, a terrestrial observer at _a_ on
the earth’s Equator would see an eclipse at noon; if he were not in
rotation, and the three bodies remained at rest, the eclipse would be a
perpetual one. He is, however, carried onward by the earth’s rotation,
and even if the moon were at rest, it would appear to him to pass over
the sun in the reverse direction. This retardation of the moon will be
less in amount for observers away from the Equator, and also for
observers to whom the sun is not on the meridian when eclipsed. The
effect of rotation on an observer at _b_ (Fig. 32), for example, is to
move him almost in the direction of the line joining the moon and sun,
and the backward tendency of the moon due to rotation is very slight. On
account of the earth’s rotation, then, the duration of a solar eclipse
is lengthened, the greatest increase occurring at those places where the
sun is on the meridian at the time of eclipse.
There is another source of gain of duration of an eclipse to the
observer who sees the phenomenon about noon. The moon’s apparent
diameter is then augmented by a greater amount than at other places,
because the observer is then nearest to the moon; while the sun’s
apparent diameter is not appreciably affected. The greater the
difference in the apparent diameters of the sun and moon, the longer
will totality last.
These and other circumstances have all to be taken into account in
computing the conditions under which an eclipse will be seen at any
given place.
According to an eminent authority, Professor Young, the greatest
possible diameter of the moon’s shadow, where it strikes the earth, is
167 miles. It may, however, cover a larger space on the earth’s surface,
because the latter does not pass perpendicularly through the shadow. To
all persons within the shadow, the eclipse will be total, but to those
on its outer boundary the duration of totality will be for an instant
only. The penumbral shadow has a cross section about 4,500 miles in
diameter, covering sometimes a space on the earth’s surface 6,000 miles
across. To all persons within this area, but not in the central shadow,
the eclipse will be partial. The shadow spot travels over the earth’s
surface, because of the moon’s movement, but its track and speed are
greatly modified by the earth’s rotation. The movement of the shadow, as
affected by the earth’s rotation, would be along a parallel of latitude;
but its ultimate direction of movement, though trending eastwards,
depends upon this, combined with the direction of the moon’s movement at
the time of the eclipse. Thus, a portion of the track of the total
eclipse of April 16, 1893, is as that shown in Fig. 33.
[Illustration:
FIG. 33.—_Track of Eclipse of April 16, 1893._
]
These considerations will suffice to explain the necessity for very
precise calculations as to the position of the central line of an
eclipse, when observers are sent out for the purpose of recording the
phenomena.
Under the most favourable combination of conditions, that is, when the
eclipse occurs at noon at a place on the Equator, an eclipse cannot be
total for more than 7 minutes 58 seconds, nor be annular for a longer
time than 12 minutes 24 seconds. From first to last contact may occupy
as much as 2 hours, when all the circumstances are similarly favourable.
(Loomis.)
THE SOLAR ECLIPTIC LIMIT.—In order that an eclipse of the sun may occur,
the moon must be so near the ecliptic that it can be seen projected on
the sun, either wholly or partially, from some point on the earth. It
must therefore not be very far from the node, and the distance it may be
from the node, while still being seen upon the sun, is called the _solar
ecliptic limit_. As in the case of lunar eclipses, this distance is
determined by the inclination of the moon’s orbit, and the distances of
the moon and sun from the earth. The latter being variable quantities,
the limit is not always the same. It is calculated without much
difficulty that an eclipse _must_ occur if the new moon happens when it
is within 15° 21′ of the node, and may occur within 18° 31′. These are
called the minor and major ecliptic limits respectively. For total or
annular eclipses, the limits are respectively 9° 55′ and 11° 50′.
NUMBER OF ECLIPSES IN A YEAR.—If the moon’s nodes were fixed, the sun
would pass through the line of nodes twice a year. At such times an
eclipse of the sun must necessarily occur if the moon were within 15°
21′ of the node on either side. The sun requires more than a month to
traverse this space of 30° 42′, and the moon must therefore pass through
each node at least once while the sun is traversing these limits. It
follows, then, that there must be at least two eclipses of the sun in a
year. Since the line of nodes of the moon’s orbit revolves backwards in
a period of about nineteen years, the sun returns to the same node after
an interval of 346·6 days, and there must accordingly be two solar
eclipses in this interval. If, then, there be an eclipse early in
January, there will be another about the middle of the year, and another
at the end of the year, so that on this ground alone there is a
possibility of three solar eclipses in a year.
Again, while the sun is passing through the ecliptic limits, it may
happen that an eclipse occurs on its entrance, and then another will
occur before it gets beyond on the other side of the line of nodes. In
this way two eclipses may occur in the region of each node passage, and
if the first of the series occurs early in January, five eclipses of the
sun may occur in a single year.
The sun, however, is not a month in traversing the lunar ecliptic limit.
Consequently, a whole year may elapse without the moon being
sufficiently near the node to pass within the earth’s shadow, and in
many years there are accordingly no eclipses of the moon. Only one full
moon can occur within the lunar ecliptic limits when the sun passes the
node, but if there be an eclipse at one node, there may also be one six
months later at the other node. As in the case of the solar eclipses,
the “eclipse year” is one of 346·6 days, so that if there be an eclipse
of the moon early in January, there may possibly be three altogether in
the course of the year, but there could not be three lunar eclipses if
the extra solar eclipse were possible. Altogether, then, there may be
seven eclipses in the course of a year—five of the sun and two of the
moon. Usually there are four or five, some particulars of which are
furnished by all respectable almanacs. It will be observed that the
number of solar eclipses is much larger than that of lunar ones, but as
the latter are visible at all places having the moon above the horizon,
while the former are restricted to small parts of the earth’s surface,
more lunar than solar eclipses are visible at any specified place.
RECURRENCE OF ECLIPSES.—We have seen that the sun requires only 346·6
days to travel from one of the moon’s nodes back to the same node again,
in consequence of the regression of the nodes, while the moon requires
27·2 days. Suppose, then, that the moon and sun are at a node, and there
is an eclipse at new moon; after 346·6 days the sun will return to the
same node, but the moon will not be at the node, nor will it be exactly
new. It will not be until the sun has returned nineteen times to the
node that the moon is also very nearly new at the same node again.
Nineteen returns of the sun to the moon’s nodes occupy a period of
6,585·78 days; 223 intervals between successive new moons (synodic
months) cover 6,585·32 days, while 242 node passages of the moon require
6,585·357 days. In this period of 18 years 11⅓ days (or 10⅓ days if
there are five, and 12⅓ if there are three leap years in the interval),
the sun and moon thus return to nearly the same conditions as affecting
the possibility of eclipses. This period was called the _Saros_ by the
Chaldeans, by whom it was employed in the prediction of eclipses. The
adjustment of periods, however, is not quite precise, so that
predictions based upon the Saros are only approximations, which serve as
a guide for more accurate computations.
This eclipse period is still more remarkable from the fact that it
almost exactly represents 239 passages of the moon through perigee, so
that after the lapse of 18 years 11⅓ days the moon is almost at the same
distance from the earth, as well as nearly at the same phase and the
same distance from a node.
As the Saros includes a fraction of a day, an eclipse is not necessarily
repeated at the same place after the lapse of 18 years 11⅓ days, for the
reason that the eclipse will not occur at the same time of day, and the
sun may be below the horizon. After three Saroses, however, the eclipse
will be repeated nearly at the same hour, but even then it will not be
seen under the same conditions, because the track of the shadow will be
in different latitudes, for the reason that the moon does not return
_exactly_ to the node in the interval between 223 new or full moons, and
eclipses can only occur when the moon is new or full.
Beginning as a partial eclipse, an eclipse of the moon will gradually
become of greater magnitude at successive intervals of 18 years 11 days,
until it becomes a total eclipse, and will again gradually become of
smaller magnitude, until it ceases to be reproduced at all. Altogether,
it would be repeated once in every 223 months for 865 years.
Since the solar ecliptic limit is greater than the lunar, a solar
eclipse is repeated at similar intervals of 18 years for about 1200
years. Most of these eclipses would be partial, 27 would be annular, and
18 total. During this period, the track of the central eclipse would
shift northwards if the moon were at a descending node, and southwards
if at an ascending node, until finally it passed altogether clear of the
earth.
It must be remarked, however, that, in the period corresponding to a
single Saros, about 28 eclipses of the moon, and 43 of the sun, usually
appear, so that altogether about 71 series of eclipses are in progress.
Of the solar eclipses which occur during a period of 18 years, about 12
are total at some places upon the earth.
OCCULTATIONS OF STARS AND PLANETS BY THE MOON.—In its monthly round, the
moon is constantly passing in front of some of the stars which lie in
its apparent path, and these luminaries will, therefore, at times, be
hidden temporarily by the moons disc. Occasionally a planet may appear
in the same line of vision as the moon, and that also will pass from
view until subsequent motion again removes the intercepting body. These
disappearances are closely allied to the phenomena of eclipses, and
receive the name of _occultations_. On account of the moon’s eastward
movement, it is evident that the disappearance of stars or planets when
occulted will take place on the eastern edge of the moon; but since the
moon trends north or south in some parts of its orbit, the disappearance
near the northern and southern edges may occur slightly on the western
side of the north or south point of the moons limb. Similarly, the
reappearance generally occurs on the western side of the moon, but
occasionally may occur on the eastern side—that is, when the northern or
southern edge of the moon does not much more than appear to graze the
stars.
The calculation of the circumstances of an occultation is very similar
to that involved in the computation of eclipses. (A simple graphical
method for working out the conditions of an occultation is described by
Major Grant, R.E., in the _Geographical Journal_ for June, 1896.)
ECLIPSES AND OCCULTATIONS OF SATELLITES BY PLANETS.—Just as we find the
moon eclipsed by passing through the earth’s shadow, we find the
satellites of other planets to be at times invisible for a similar
reason. We thus observe _eclipses_ of the satellites. The satellites may
also be invisible to us for the reason that they are behind the planet,
and they are then said to be _occulted_. These satellite phenomena are
especially remarked in the case of Jupiter, and their observation is one
of great interest. When a satellite passes between the sun and the
planet it throws a shadow on the surface of the planet similar to that
of the moon upon the earth. This is visible to us as a dark spot, and
from the centre of that dusky patch an inhabitant of Jupiter would
undoubtedly see a total eclipse of the sun. To us on the earth the
passage of such a shadow across the planet’s disc is but a “transit of
the shadow” with its “ingress” and “egress.”
The times of all these appearances are computed from a knowledge of the
movements of the satellites.