THE EARTH’S REVOLUTION ROUND THE SUN.
APPARENT MOVEMENTS OF THE SUN.—During any day on which we may observe
the sun, it will be seen to rise at a certain place on the horizon,
gradually ascend into the heavens to a certain point, then as steadily
sink towards the west until it disappears at some point on the western
horizon. If we watch the sun about the 20th of March, we shall find it
to rise due east, and set due west; it will be above the horizon for
exactly twelve hours, and below for the same length of time. When this
happens, we have the _vernal_ or _spring equinox_, as the nights are
then equal in all parts of the world. From this time to the third week
in June, we shall find the sun to rise more and more to the north of
east, and to set gradually further north of west. This is accompanied by
a daily increase in the apparent height of the sun at noon, and by
increasing length of day and reduction of night. For some days before
the 21st of June the change of the sun’s place of rising and setting is
very slow, and after this day the places of rising and setting begin to
recede to the south. We then have the _summer solstice_, so-called
because the sun seems to stand still, in so far as its northward travel
is concerned. The point of rising or setting of the sun goes on moving
nearer to the south point of the horizon, until about September 22, we
again have the sun above the horizon for twelve hours, and below the
horizon for an equal period; this is the _autumnal equinox_. The
southward movement is continued until December 21, after which the
rising begins to take place further towards the north. When furthest
south, we have the _winter solstice_ in the Northern Hemisphere, the sun
being above the horizon for only a short time, and reaching only a small
altitude at noon. From December 21 to March 20, the sun rises further to
the north, at first very gradually, and afterwards more rapidly. These
varying amounts of sunshine correspond to the short days of winter, and
the long days of summer. A diagrammatic representation of the apparent
path of the sun at the solstices and equinoxes for some place, such as
London, is given in Fig. 6.
[Illustration:
FIG. 6.—_Apparent Paths of Sun at Equinoxes and Solstices._
]
It is clear, then, that our relations to the sun are very different from
our relation to the stars, inasmuch as the apparent position of the sun,
as projected upon the sky, is constantly changing, but returns to
similar conditions at the end of a year. If our place of observation is
changed, the apparent diurnal movement of the sun is affected in the
same way as that of the stars.
To explain these annual changes of the sun, with regard to an observer’s
horizon, it is only necessary to suppose that the sun marches northwards
towards the celestial pole from the winter to the summer of the Northern
Hemisphere, and southwards from summer to winter. It is not to be
imagined, however, that this apparent movement towards or from the north
celestial pole is necessarily a real movement of the sun; we shall, in
fact, very shortly see that it is only an apparent movement due to the
changing situation of the earth with respect to the sun.
THE ECLIPTIC.—A very small amount of actual observation, without the aid
of instruments, suffices to show that the changes in the sun’s relation
to any observers horizon at different parts of the year are associated
with a change in its situation among the stars. If we direct our gaze
towards the south at midnight, we are looking towards that part of space
which is directly opposite to the sun, as will be evident from Fig. 4,
and if the sun’s apparent movement were only in a polar direction, we
should always see the same stars in the same part of the sky at the same
hour. Such, however, is not the case. The stars are found more and more
towards the west at the same hour as the year advances. Sirius, for
instance, is due south about midnight on December 31; but at the end of
January it will pass through the south point shortly before ten P.M.
Similar changes are noted in the case of all the stars, and they
indicate either an easterly movement of the sun among the stars, or a
westerly motion of the stars with regard to the sun. If it were possible
to see the stars in the immediate neighbourhood of the sun, this
relative motion could be directly observed; but under the actual
circumstances, the apparent track of the sun amongst the stars must be
determined indirectly. When we make observations at midnight, we know
that the sun is opposite to stars which are due south at that moment;
and the height which it reaches above the horizon at noon indicates its
angular distance from the celestial pole. It is thus possible to trace
the sun’s apparent path on a map of the stars, or upon a celestial
globe; this is called the _ecliptic_, and it is found to be a great
circle of the celestial sphere—that is, it is a circle contained in a
plane which passes through the centre of the sphere.
The observed movement of the sun among the stars might be produced
either by a revolution of the sun round the earth in a year, or by a
revolution of the earth round the sun in the same period, the stars
being supposed at rest at a greater distance than the sun. There are
many phenomena which indicate that it is the earth which moves round the
sun, but the most direct proof is found in what is known to astronomers
as the aberration of light.
ABERRATION AS A PROOF OF THE EARTH’S REVOLUTION.—While engaged on an
observation having for its object the determination of the distance of a
star, Dr. Bradley made a discovery of very great interest and importance
to astronomers. What he found practically amounts to this, that in order
to see a star exactly at the centre of the field of view of a telescope
we must direct the optical axis of the instrument at a small angle to
the line joining the earth and star, irrespective of other deviations,
such as that produced by refraction. The direction of this displacement
is constantly changing throughout the year, but it is common to all the
stars, and the fact that the original apparent position is regained at
the end of a year at once associates aberration with a revolution of the
earth round the sun.
[Illustration:
FIG. 7.—_Aberrational Orbit of a Star._
]
In Fig. 7 we have a perspective view of the earth’s orbit with the sun
at S. A star _s_ would appear in the direction A _s_ when seen from the
earth, supposed at rest at the point A; actually it is seen at _a_,
ahead of its place, and in the course of a year it describes the
_aberrational orbit_, _a b c d_, these points corresponding to positions
A B C D of the earth in its annual path.
As a result of aberration, then, each star appears to revolve once a
year in a small elliptic path about its average position. The breadths
of these ellipses vary according to their angular distances from the
ecliptic, but all have precisely the same length of about 41″. Half the
length of the ellipses, which amounts to 20″.5, is accordingly called
the _constant_ of _aberration_.
The fact that the earth’s velocity in its orbit forms a sensible
fraction of the velocity of light is the cause of aberration. If we let
an object fall down the middle of a tube which is at rest, it will fall
to the bottom without touching the side if the tube be held vertically.
When the tube has a forward movement, however, it must be inclined at an
angle in order that the falling body may pass clear to the bottom, and
the greater the speed of the tube the more it must be inclined. So it is
with light which comes from a star and traverses the tube of a telescope
situated on a moving earth; the tube must be inclined to the actual path
of the light rays.
Other proofs that it is the earth which moves round the sun are
furnished by the parallaxes of the stars, and by spectroscopic measures
of the earth’s velocity.
APPROXIMATE SCALE OF EARTH’S ORBIT.—A very beautiful application of the
constant of aberration is in the measurement of the distance of the
earth from the sun. We have only to bear in mind that the apparent size
of the sun does not change very much, in order to realise that the path
of the earth must be very nearly a circle; if the distance changed very
much there would be a correspondingly great change in the sun’s apparent
diameter. Now the constant of aberration is a measure of the relative
velocity of the earth in its orbit and the velocity of light. There are
several ways of determining the velocity of light, and it is known to be
very nearly 186,300 miles per second. In a right-angled triangle having
one angle equal to the constant of aberration, the side opposite to this
angle would represent the velocity of the earth, if the longer side
represented that of light. In such a triangle the proportion between
these sides would be nearly as 1 to 10,000. That is, the velocity of
light is about 10,000 times that of the earth in its orbit. The earth’s
velocity is thus found to be about 18½ miles per second, so that the
distance which it traverses in a year is found by a simple
multiplication. In this way the circumference of the earth’s orbit is
obtained, and it is easily deduced that the radius of the orbit, which
is nothing more than the sun’s distance, is not far from 93,000,000
miles.
THE ZODIAC.—The space about 8° above and below the ecliptic constitutes
what is called the _zodiac_. The zodiac is of very great antiquity, and
marks out the region traversed by the sun and all the planets known to
the ancients. It is divided into twelve parts of 30° each, called signs
of the zodiac, from the supposed outlines of animals, etc., marked out
by the stars. The names of these signs are probably familiar to everyone
from the well-known rhyme:
“_The Ram, the Bull, the Heavenly Twins,
And next the Crab the Lion shines,
The Virgin, and the Scales,
The Scorpion, Archer, and the Goat,
The man that bears the Watering-Pot,
And Fish with glittering tails._”
The astronomical names and symbols corresponding to these are as
follows:—
♈︎ Aries, The Ram.
♉︎ Taurus, The Bull.
♊︎ Gemini, The Twins.
♋︎ Cancer, The Crab.
♌︎ Leo, The Lion.
♍︎ Virgo, The Virgin.
♎︎ Libra, The Balance.
♏︎ Scorpio, The Scorpion.
♐︎ Sagittarius, The Archer.
♑︎ Capricornus, The Goat.
♒︎ Aquarius, The Water-Bearer.
♓︎ Pisces, The Fishes.
The sun enters the sign Aries at the vernal equinox in March, and the
others in successive months. On account of the precession of the
equinoxes (see p. 69), however, the sun no longer enters the
_constellation_ Aries at the vernal equinox, but it is still said to
enter the _sign_ Aries.
INCLINATION OF THE EARTH’S AXIS.—The revolution of the earth round the
sun provides us with a very satisfactory explanation of the apparent
easterly movement of the sun among the stars. There is, however, another
very important point. We have seen that during a year the sun has a
movement towards and from the Pole, as well as an easterly movement. The
plane of the earth’s orbit, therefore, cannot be coincident with the
plane of the Equator; if it were, the sun would have the same apparent
movement every day—it would always rise due east, and set due west, in
all parts of the earth. The ecliptic, moreover, would be coincident with
the celestial equator. When the ecliptic is determined by observations
in the way already explained (p. 57), it is found to intersect the
celestial equator in two points, and the plane containing it is inclined
at an angle of very nearly 23½° to the equatorial plane. This
inclination of the Equator to the ecliptic, or “obliquity of the
ecliptic,” indicates that the earth’s axis of rotation is inclined to
the plane in which the revolution round the sun is performed, the actual
inclination being about r66½°.
Further, the axis of rotation must remain parallel to itself during the
revolution of the earth. Otherwise, the situation of the celestial pole
would be seen to change, and the Pole Star would no longer serve to show
us which way lies north.
It is precisely this inclination of the earth’s axis which brings about
the varying lengths of days and nights which we associate with different
seasons.
THE SEASONS.—Let us in the first place contrast the conditions in summer
with those which obtain in winter. Imagine that we can view the sun and
earth from a very distant point lying in the plane of the ecliptic, and
situated so that a line joining it with the sun is perpendicular to the
line joining the sun and earth in summer or winter.
[Illustration:
FIG. 8.—_The Sun’s Altitude in Summer and Winter._
]
The sun will thus appear in some position represented by O in Fig. 8; in
the summer of the Northern Hemisphere the earth will be in the position
S, and in winter in the position W, since it travels half way round its
orbit in six months’ time. An observer situated at London will be 38½°
from the North Pole, and he is represented by the point A in our
diagram. The horizon at noon of such an observer is represented by the
line H R, tangential to the surface of the sphere at the point A. At
noon, then, the altitude of the sun is equal to the angle O A H. When it
is winter in the Northern Hemisphere, the earth’s axis is inclined away
from the sun, and our observer at London is so situated that at noon his
horizon is the line H′ R′, while the sun’s altitude is the angle O A′
R′, which is no less than 47° smaller than in summer. People who dwell
in the Southern Hemisphere enjoy the long days of summer at the time
when our own days are shortest, and _vice versâ_, and the reason for
this is clearly that when the position of the earth’s axis presents the
greatest part of the Northern Hemisphere towards the sun, the greater
part of the southern half of our globe is turned away from the sun.
At the equinoxes, which occur very nearly midway between the solstices,
the earth’s axis is directed neither towards nor away from the great
source of light and heat, so that both hemispheres are presented to the
sun under exactly the same conditions. This state of affairs is shown
diagrammatically in Fig. 9. The sun’s altitude at noon at the
commencement of spring is equal to that at the beginning of autumn, and
depends only upon the observer’s latitude. The half of our globe which
is then flooded with the sun’s rays comprises both the North and South
Poles, and it is evident that as the earth turns round, every place upon
it, whether in Arctic or equatorial regions, receives the benefit of
twelve hours sunshine, and at the same time has a night of twelve hours
duration.
[Illustration:
FIG. 9.—_The Sun’s Altitude at the Equinoxes._
]
THE MIDNIGHT SUN.—The facilities which are now offered for foreign
travel have induced many people to pay a visit to the north of Norway,
one of the objects in view frequently being to witness the so-called
“midnight sun.” It seems somewhat paradoxical to speak of night when the
sun is above the horizon, but it simply means that in high latitudes the
sun may be seen over the northern horizon when it is midnight at places
further south which have the same longitude. We have seen that in our
own country there are certain stars which never set, and when we get to
the Pole itself, all the stars which are there visible will present this
peculiarity.
In order to see the sun at midnight, then, what we have to do is to
travel towards the Pole until we reach a latitude where the sun itself
becomes circumpolar. At the Pole this would be the state of things
during the whole of the northern summer, when the sun is north of the
Equator, and since the sun never travels northward more than 23½°, it
can only be circumpolar at places within that angular distance from the
Pole, that is, within the Arctic Circle.
[Illustration:
FIG. 10.—_The Midnight Sun._
]
Let A in Fig. 10 be such a place, the sun being to the left. At noon the
horizon of A is represented by H R, and the sun will appear in the south
at a certain altitude, S A H. At midnight the earth’s rotation will
change the observers position to A′ and his horizon to H′ R′, but it
will not have taken him out of sunshine. The sun will then appear due
north, but, except at the Pole, its altitude, S A′ H′, will be lower
than at noon. At a place situated on the Arctic circle, latitude 66½°,
the midnight sun would only be visible for one night at the summer
solstice, were it not that refraction causes it to appear above the
horizon when it is geometrically more than its own apparent diameter
below.
At Tromsö the midnight sun is visible from May 19 to July 22, and at the
North Cape from May 12 to July 29.
Nature, however, exacts compensation for this lavish share of summer
sunshine in high latitudes, and there is a correspondingly number of
dreary days in winter when the sun does not rise at all.