CHAPTER II.
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.