Astronomy in a nutshell

1. Definition of Astronomy. Astronomy has to do with the earth, sun, moon, planets, comets, meteors, stars, and nebulæ; in other words, with the universe, or “the aggregate of existing things.” It is the most ancient of all sciences. The derivation of the name from two Greek words, aster, “star,” and nomos, “law,” indicates its nature. It deals with the law of the stars—the word “star” being understood, in its widest signification, as including every heavenly body of whatever kind. The earth itself is such a body. Since we happen to live on the earth, it becomes our standpoint in space, from which we look out at the others. But, if we lived on some other planet, we would see the earth as a distant body in the sky, just as we now see Jupiter or Mars.

Astronomy teaches us that everything in the universe, from the sun and the moon to the most remote star or the most extraordinary nebula, is related to the earth. All are made of similar elementary substances and all obey similar physical laws. The same substance which is a solid upon the earth may be a gas or a vapour in the sun, but that does not alter its essential nature. Iron appears in the sun in the form of a hot vapour, but fundamentally it is the same substance which exists on the earth as a hard, tough, and heavy metal. Its different states depend upon the temperature to which it is subjected. The earth is a cool body, while the sun is an intensely hot one; consequently iron is solid on the earth and vaporous in the sun, just as in winter water is solid ice on the surface of a pond and steamy vapour over the boiler in the kitchen. Even on the earth we can make iron liquid in a blast furnace, and with the still greater temperatures obtainable in a laboratory we can turn it into vapour, thus reducing it to something like the state in which it regularly exists in the sun.

This fact, that the entire universe is made up of similar substances, differing only in state according to the local circumstances affecting them, is the greatest thing that astronomy has to tell us. It may be regarded as the fundamental law of the stars.

2. The Situation of the Earth in the Heavens. One of the greatest triumphs of human intelligence is the discovery of the real place which the earth occupies in the universe. This discovery has been made in spite of the most deceptive appearances. If we accepted the sole evidence of our eyes, as men once did, we could only conclude that the earth was the centre of the universe. In the daytime we see the sun apparently moving through the sky from east to west, as if it were travelling in a circle round the earth, overhead by day and underfoot at night. In the night-time, we see the stars apparently travelling round the earth in the same way as the sun. The fact is, that all of them are virtually motionless with regard to the earth, and their apparent movements through the sky are produced by the earth's rotation on its axis. The earth turns round on itself once every twenty-four hours, like a spinning ball. Imagine a fly on a rotating school globe; the whole room would appear to the fly to be revolving round it as the heavens appear to revolve round the earth. It would have to be a very intelligent insect to correct the deceptive evidence of its eyes.

The actual facts, revealed by many centuries of observation and reasoning, are that the earth is a rotating globe, turning once on its axis every twenty-four hours and revolving once round the sun every three hundred and sixty-five days. The sun is also a globe, 1,300,000 times larger than the earth, but so hot that it glows with intense brilliance, while the substances of which it consists are kept in a gaseous or vaporous state. Besides the earth there are seven other principal globes, or planets, which revolve round the sun, at various distances and in various periods, and, in addition to these, there are hundreds of smaller bodies, called asteroids or small planets. There are also many singular bodies called comets, and swarms of still smaller ones called meteors, which likewise revolve round the sun.

The earth and the other bodies of which we have just spoken are not only cooler than the sun, but most of them are in a solid state and do not shine with light of their own. The sun furnishes both heat and light to the smaller and cooler bodies revolving round it. In fact, the sun is simply a star, resembling the thousands of other stars which surround us in the sky, and its apparent superiority to them is due only to the fact that it is relatively near-by while they are far away. It is probable that all, or most, of the stars also have planets, comets, and meteors revolving round them, but invisible owing to their immense distance.

The “paths” in which the earth and the other planets and bodies travel in their revolutions round the sun are called their orbits. These orbits are all elliptical in shape, but those of the earth and the other large planets are not very different from circles. Some of the asteroids, and all of the comets, however, travel in elliptical orbits of considerable eccentricity, i. e., which differ markedly from circles. The orbit of the earth differs so slightly from a circle that the eccentricity amounts to only about one-sixtieth. The distance of the earth from the sun being, on the average, 93,000,000 miles, the eccentricity of its orbit causes it to approach to within about 91,500,000 miles in winter (of the northern hemisphere) and to recede to about 94,500,000 miles in summer. The point in its orbit where the earth is nearest the sun is called perihelion, and the point where it is farthest from the sun, aphelion. The earth is at perihelion about Jan. 1, and at aphelion about July 4.

Now, in order to make a general picture in the mind of the earth's situation, let the reader suppose himself to be placed out in space as far from the sun as from the other stars. Then, if he could see it, he would observe the earth as a little speck, shining like a mote in the sunlight, and circling in its orbit close around the sun. The universe would appear to him to be somewhat like an immense spherical room filled with scattered electric-light bulbs, suspended above, below, and all around him, each of these bulbs representing a sun, and if there were minute insects flying around each light, these insects would represent the planets belonging to the various suns. One of the glowing bulbs among the multitude would stand for our sun, and one of the insects circling round it would be the earth.

We have already remarked that the rotation of the earth on its axis causes all the other heavenly bodies to appear to revolve round it once every twenty-four hours, and we must now add that the earth's revolution round the sun causes the same bodies to appear to make another, slower revolution round it once every year. This introduces a complication of apparent motions which it is the business of astronomy to deal with, and which we shall endeavour to explain.

3. The Horizon, the Zenith, and the Meridian. First, let us consider what is the ordinary appearance of the sky. When we go out of doors on a clear night we see the heavens in the shape of a great dome arched above us and filled with stars. What we thus see is one half of the spherical shell of the heavens which surrounds us on all sides, the earth being apparently placed at its centre. The other half is concealed from our sight behind, or below, the earth. This spherical shell, of which only one half is visible to us at a time, is called the celestial sphere. Now, the surface of the earth seems to us (for this is another of the deceptive appearances which astronomy has to correct) to be a vast flat expanse, whose level is broken by hills and mountains, and the visible half of the celestial sphere seems to bend down on all sides and to rest upon the earth in a circle which extends all around us. This circle, where the heavens and the earth appear to meet, is called the horizon. As we ordinarily see it, the horizon appears irregular and broken on account of the unevenness of the earth's surface, but if we are at sea, or in the midst of a great level prairie, the horizon appears as a smooth circle, everywhere equally distant from the eye. This circle is called the sensible horizon. But there is another, ideal, horizon, used in astronomy, which is called the rational horizon. It is of the utmost importance that we should clearly understand what is meant by the rational horizon, and for this purpose we must consider another fact concerning the dome of the sky.

We now turn our attention to the centre of that dome, which, of course, is the point directly overhead. This point, which is of primary importance, is called the zenith. The position of the zenith is indicated by the direction of a plumb-line. If we imagine a plumb-line to be suspended from the centre of the sky overhead, and to pass into the earth at our feet, it would run through the centre of the earth, and, if it were continued onward in the same direction, it would, after emerging from the other side of the earth, reach the centre of the invisible half of the sky-dome at a point diametrically opposite to the zenith. This central point of the invisible half of the celestial sphere, lying under our feet, is called the nadir.

Keeping in mind the definitions of zenith and nadir that have just been given, we are in a position to understand what the rational horizon is. It is a great circle whose plane cuts through the centre of the earth, and which is situated exactly half-way between the zenith and the nadir. This plane is necessarily perpendicular, or at right angles, to the plumb-line joining the zenith and the nadir. In other words, the rational horizon divides the celestial sphere into two precisely equal halves, an upper and a lower half. In a hilly or mountainous country the sensible or visible horizon differs widely from the rational, or true horizon, but at sea the two are nearly identical. This arises from the fact, that the earth is so excessively small in comparison with the distances of most of the heavenly bodies that it may be regarded as a mere point in the midst of the celestial sphere.

Besides the horizon and the zenith there is one other thing of fundamental importance which we must learn about before proceeding further,—the meridian. The meridian is an imaginary line, or semicircle, beginning at the north point on the horizon, running up through the zenith, and then curving down to the south point. It thus divides the visible sky into two exactly equal halves, an eastern and a western half. In the ordinary affairs of life we usually think only of that part of the meridian which extends from the zenith to the south point on the horizon (which is sometimes called the "noon-line” because the sun crosses it at noon), but in astronomy the northern half of the meridian is as important as the southern.

4. Altitude and Azimuth. Now, suppose that we wish to indicate the location of a star, or other object, in the sky. To do so, we must have some fixed basis of reference, and such a basis is furnished by the horizon and the zenith. If we tried to describe the position of a star, the most natural thing would be, first, to estimate, or measure, its height above the horizon, and, second, to indicate the direction in which it was situated with regard to the points of the compass. These two measures, if they were accurately made, would enable another person to find the star in the sky. And this is precisely what is done in astronomy. The height above the horizon is called altitude, and the bearing with reference to the points of the compass is called azimuth. Together these are known as co-ordinates. In order to systematise this method of measuring the location of a star, the astronomer uses imaginary circles drawn on the celestial sphere. The horizon and the meridian are two of these circles. In addition to these, other imaginary circles are drawn parallel to the horizon and becoming smaller and smaller until the uppermost one may run close round the zenith, which is the common centre of the entire set. These are called altitude circles, because each one throughout its whole extent is at an unvarying height, or altitude, above the horizon. Such circles may be drawn anywhere we please, so as to pass through any chosen star or stars. If two stars in different quarters of the sky are found to lie on the same circle, then we know that both have the same altitude.

Then another set of circles is drawn perpendicular to the horizon, and all intersecting at the zenith and the nadir. These are called vertical circles, from the fact that they are upright to the horizon. That one of the vertical circles which cuts the horizon at the north-and-south points coincides with the meridian, which we have already described. The vertical circle at right angles to the meridian is called the prime vertical. It cuts the horizon at the east and west points, dividing the visible sky into a northern and a southern half. Like the altitude circles, vertical circles may be drawn anywhere we please so as to pass through a star in any quarter of the sky—but the meridian and the prime vertical are fixed.

With the two sets of circles that have just been described, it is possible to indicate accurately the location of any heavenly body, at any particular moment. Its altitude is ascertained by measuring, along the vertical circle passing through it, its distance from the horizon. (Sometimes it is convenient to measure, instead of the altitude of a star, its zenith distance, which is also reckoned on the vertical circle.)

To ascertain the azimuth, we must first choose a point of beginning on the horizon. Any of the cardinal points, i.e., east, west, north, or south, may be employed for this purpose, but in astronomy it is customary to use only the south point, and to carry the measure westward all round the circle of the horizon, and so back to the point of beginning in the south. This involves circular, or degree, measure, to which a few words must now be devoted.

Every circle, no matter how large or how small, is divided into 360 equal parts, called degrees, usually indicated by the sign (°); each degree is subdivided into 60 equal parts called minutes, indicated by the sign (′); and each minute is subdivided into 60 equal parts called seconds, indicated by the sign (″). Thus there are 360°, or 21,600′, or 1,296,000″ in every complete circle. The actual length of a degree in inches, yards, or miles, depends upon the size of the circle, but no circle ever has more than 360°, and a degree of any particular circle is precisely equal to any other degree of that same circle. Thus, if a circle is 360 miles in circumference, every one of its degrees will be one mile long. In mathematics, a degree usually means not a distance measured along the circumference of a circle, but an angle formed at the centre of the circle between two lines called radii (radius in the singular), which lines, where they intersect the circumference, are separated by a distance equal to one 360th of the entire circle. But, for ordinary purposes, it is simpler to think of a degree as an arc equal in length to one 360th of the circle. Now, since the horizon, and the other imaginary lines drawn in the sky, are all circles, it is evident that the principle of circular measure may be applied to them, and indeed must be so applied in order that they shall be of use to us in indicating the position of a star.

To return, then, to the measurement of the azimuth of a star. Since the south point is the place of beginning, we mark it 0°, and we divide the circle of the horizon into 360°, counting round westward. Suppose we see a star somewhere in the south-western quarter of the sky; then the point where the vertical circle passing through that star intersects the horizon will indicate its azimuth. Suppose that this point is found to be 25° west of south; then 25° will be the star's azimuth. Suppose it is 90°; then the azimuth is 90°, and the star must be on the prime vertical in the west, because west, being one quarter of the way round the horizon from south, is 90° in angular distance from the south point. Suppose the azimuth is 180°; then the star must be on the meridian north of the zenith, because north is exactly half-way, or 180° round the horizon from the south point. Suppose the azimuth is 270°; then the star must be on the prime vertical in the east, because east is 270°, or three quarters of the way round from the south point. If the star is on the meridian in the south its azimuth may be called either 0° or 360°, because on any graduated circle the mark indicating 360° coincides in position with 0°, that being at the same time the point of beginning and the point of ending.

The same system of angular measure is applied in ascertaining a star's altitude. Since the horizon is half-way between the zenith and the nadir it must be just 90° from either. If a star is in the zenith, then its altitude is 90°, and if it is below the zenith its altitude lies somewhere between 0° and 90°. In any case it cannot be less than 0° nor more than 90°. Having measured the altitude and the azimuth we have the two co-ordinates which are needed to indicate accurately the place of a star in the sky. But, as we shall see in a moment, other co-ordinates beside altitude and azimuth are needed for a complete description of the places of the stars on the celestial sphere. Owing to the apparent revolution of the heavens round the earth, the altitudes and azimuths of the celestial bodies are continually changing. We shall now study the causes of these changes.

5. The Apparent Motion of the Heavens. We have likened the earth to a rotating school globe. As such a globe turns, any particular spot on it is presented in succession toward the various sides of the room. In precisely the same way any spot on the earth is turned by its rotation successively toward various parts of the surrounding sky. To understand the effect of this, a little patient watching of the actual heavens will be required, but this has the charm of all out-of-doors observation of nature, and it will be found of fascinating interest as the facts begin to unfold themselves.

It is best to begin by finding the North Star, or pole star. If you are living not far from latitude 40° north, which is the median latitude of the United States, you must, after determining as closely as you can the situation of the north point, look upward along the meridian in the north until your eyes are directed to a point about 40° above the horizon. Forty degrees is somewhat less than half-way from the horizon to the zenith, which, as we have seen, are separated by an arc of 90°. At that point you will notice a lone star of what astronomers call the second magnitude. This is the celebrated North Star. It is the most useful to man of all the stars, except the sun, and it differs from all the others in a way presently to be explained. But first it is essential that you should make no mistake in identifying it. There are certain landmarks in the sky which make such identification certain. In the first place, it is always so close to the meridian in the north, that by naked-eye observation you would probably never suspect that it was not exactly on the meridian. Then, its altitude is always equal, or very nearly equal, to the latitude of the place where you happen to be on the earth, so that if you know your latitude you know how high to carry your eye above the northern horizon. If you are in latitude 50°, the star will be at 50° altitude, and if your latitude is 30°, the altitude of the star will be 30°. Next you will notice that the North Star is situated at the end of the handle of a kind of dipper-shaped figure formed by stars, the handle being bent the wrong way. All of the stars forming this “dipper” are faint, except the two which are farthest from the North Star, in the outer edge of the bowl, one of which is about as bright as the North Star itself. Again, if you carry your eye along the handle to the bowl, and then continue onward about as much farther, you will be led to another, larger, more conspicuous, and more perfect, dipper-shaped figure, which is in the famous constellation of Ursa Major, or the Great Bear. This striking figure is called the Great Dipper (known in England as The Wain). It contains seven conspicuous stars, all of which, with one exception, are equal in brightness to the North Star. Now, look particularly at the two stars which indicate the outer side of the bowl of this dipper, and you will find that if you draw an imaginary line through them toward the meridian in the north, it will lead your eye directly back to the North Star. These two significant stars are often called The Pointers. With their aid you can make sure that you have really found the North Star.

Having found it, begin by noting the various groups of stars, or constellations, in the northern part of the sky, and, as the night wears on, observe whether any change takes place in their position. To make our description more definite, we will suppose that the observations begin at nine o'clock P.M. about the 1st of July. At that hour and date, and from the middle latitudes of the United States, the Great Dipper is seen in a south-westerly direction from the North Star, with its handle pointing overhead. At the same time, on the opposite side of the North Star, and low in the north-east, appears the remarkable constellation of Cassiopeia, easily recognisable by a zigzag figure, roughly resembling the letter W, formed by its five principal stars. Fix the relative positions of these constellations in the memory, and an hour later, at 10 P.M., look at them again. You will find that they have moved, the Great Dipper sinking, while Cassiopeia rises. Make a third observation at 11 P.M., and you will perceive that the motion has continued, The Pointers having descended in the north-west, until they are on a level with the North Star, while Cassiopeia has risen to nearly the same level in the north-east. In the meantime, the North Star has remained apparently motionless in its original position. If you repeat the observation at midnight, you will find that the Great Dipper has descended so far that its centre is on a level with the North Star, and that Cassiopeia has proportionally risen in the north-east. It is just as if the two constellations were attached to the ends of a rod pivoted at the centre upon the North Star and twirling about it.

In the meantime you will have noticed that the figure of the “Little Dipper,” attached to the North Star, which had its bowl toward the zenith at 9 P.M., has swung round so that at midnight it is extended toward the south-west. Thus, you will perceive that the North Star is like a hub round which the heavens appear to turn, carrying the other stars with them.

To convince yourself that this motion is common to the stars in all parts of the sky, you should also watch the conduct of those which pass overhead, and those which are in the southern quarter of the heavens. For instance, at 9 P.M. (same date), you will see near the zenith a beautiful coronet which makes a striking appearance although all but one of its stars are relatively faint. This is the constellation Corona Borealis, or the Northern Crown. As the hours pass you will see the Crown swing slowly westward, descending gradually toward the horizon, and if you persevere in your observations until about 5 A.M., you will see it set in the north-west. The curve that it describes is concentric with those followed by the Great Dipper and Cassiopeia, but, being farther from the North Star than they are, and at a distance greater than the altitude of the North Star, it sinks below the horizon before it can arrive at a point directly underneath that star. Then take a star far in the south. At 9 o'clock, you will perceive the bright reddish star Antares, in the constellation Scorpio, rather low in the south and considerably east of the meridian. Hour after hour it will move westward, in a curve larger than that of the Northern Crown, but still concentric with it. A little before 10 P.M., it will cross the meridian, and between 1 and 2 A.M., it will sink beneath the horizon at a point south of west.

So, no matter in what part of the heavens you watch the stars, you will see not only that they move from east to west, but that this motion is performed in curves concentric round the North Star, which alone appears to maintain its place unchanged. Along the eastern horizon you will perceive stars continually rising; in the middle of the sky you will see others continually crossing the meridian—a majestic march of constellations,—and along the western horizon you will find still others continually setting. If you could watch the stars uninterruptedly throughout the twenty-four hours (if daylight did not hide them from sight during half that period), you would perceive that they go entirely round the celestial sphere, or rather that it goes round with them, and that at the end of twenty-four hours they return to their original positions. But you can do this just as well by looking at them on two successive nights, when you will find that at the same hour on the second night they are back again, practically in the places where you saw them on the first night.

Of course, what happens on a July night happens on any other night of the year. We have taken a particular date merely in order to make the description clearer. It is only necessary to find the North Star, the Great Dipper, and Cassiopeia, and you can observe the apparent revolution of the heavens at any time of the year. These constellations, being so near the North Star that they never go entirely below the horizon in middle northern latitudes, are always visible on one side or another of the North Star.

Now, call upon your imagination to deal with what you have been observing, and you will have no difficulty in explaining what all this apparent motion of the stars means. You already know that the heavens form a sphere surrounding the earth. You have simply to suppose the North Star to be situated at, or close to, the north end, or north pole, of an imaginary axle, or axis, round which the celestial sphere seems to turn, and instantly the whole series of phenomena will fall into order, and the explanation will stare you in the face. That explanation is that the motion of all the stars in concentric circles round the North Star is due to an apparent revolution of the whole celestial sphere, like a huge hollow ball, about an axis, the position of one of whose poles is graphically indicated in the sky by the North Star. The circles in which the stars seem to move are perpendicular to this axis, and inclined to the horizon at an angle depending upon the altitude of the North Star at the place on the earth where the observations are made.

Another important fact demands our attention, although the thoughtful reader will already have guessed it—the north pole of the celestial sphere, whose position in the sky is closely indicated by the North Star, is situated directly over the north pole of the earth. This follows from the fact that the apparent revolution of the celestial sphere is due to the real rotation of the earth. You can see that the two poles, that of the earth and that of the heavens, must necessarily coincide, by taking a school globe and imagining that you are an intelligent little being dwelling on its surface. As the globe turned on its axis you would see the walls of the room revolving round you, and the poles of the apparent axis round which the room turned, would, evidently, be directly over the corresponding poles of the globe itself. Another thing which you could make clear by this experiment is that, as the poles of the celestial sphere are over the earth's poles, so the celestial equator, or equator of the heavens, must be directly over the equator of the earth.

We can determine the location of the poles of the heavens by watching the revolution of the stars around them, and we can fix the position of the circle of the equator of the heavens, by drawing an imaginary line round the celestial sphere, half-way between the two poles. We have spoken specifically only of the north pole, but, of course, there is a corresponding south pole situated over the south pole of the earth, but whose position is invisible from the northern hemisphere. It happens that the place of the south celestial pole is not indicated to the eye, like that of the northern, by a conspicuous star.

6. Locating the Stars on the Celestial Sphere. Having found the poles and the equator of the celestial sphere, we begin to see how it is possible to make a map, or globe, of the heavens just as we do of the earth, on which the objects that they contain may be represented in their proper positions. When we wish to describe the location of an object on the earth, a city for instance, we have to refer to a system of imaginary circles, drawn round the earth and based upon the equator and the poles. These circles enable us to fix the place of any point on the earth with accuracy. One set of circles called parallels of latitude are drawn east and west round the globe parallel to the equator, and becoming smaller and smaller until the smallest runs close round their common central point, which is one of the poles. Each pole of the earth is the centre of such a set of circles all parallel to the equator. Since each circle is unvarying in its distance from the equator, all places which are situated anywhere on that circle have the same latitude, or distance from the equator, either north or south.

But to know the latitude of any place on the earth is not sufficient; we must also know what is called its longitude, or its angular distance east or west of some chosen point on the equator. This knowledge is obtained with the aid of another set of circles drawn north-and-south round the earth, and all meeting and crossing at the poles. These are called meridians of longitude. In order to make use of them we must, as already intimated, select some particular meridian whose crossing point on the equator will serve as a place of beginning. By common consent of the civilised world, the meridian which passes through the observatory at Greenwich, near London, has been chosen for this purpose. It is, like all the meridians, perpendicular to the equator, and it is called the prime meridian of the earth.

In locating any place on the earth, then, we ascertain by means of the parallel of latitude passing through it how far in degrees, it is north or south of the equator, and by means of its meridian of longitude how far it is east or west of the prime meridian, or meridian of Greenwich. These two things being known, we have the exact location of the place on the earth. Let us now see how a similar system is applied to ascertain the location of a heavenly body on the celestial sphere.

We have observed that the poles of the heavens correspond in position, or direction, with those of the earth, and that the equator of the heavens runs round the sky directly over the earth's equator. It follows that we can divide the celestial sphere just as we do the surface of the earth by means of parallels and meridians, corresponding to the similar circles of the earth. On the earth, distance from the equator is called latitude, and distance from the prime meridian, longitude. In the heavens, distance from the equator is called declination, and distance from the prime meridian, right ascension; but they are essentially the same things as latitude and longitude, and are measured virtually in the same way. In place of parallels of latitude, we have on the celestial sphere circles drawn parallel to the equator and centring about the celestial poles, which are called parallels of declination, and in place of meridians of longitude, we have circles perpendicular to the equator, and drawn through the celestial poles, which are called hour circles. The origin of this name will be explained in a moment. For the present it is only necessary to fix firmly in the mind the fact that these two systems of circles, one on the earth and the other in the heavens, are fundamentally identical.

Just as on the earth geographers have chosen a particular place, viz. Greenwich, to fix the location of the terrestrial prime meridian, so astronomers have agreed upon a particular point in the heavens which serves to determine the location of the celestial prime meridian. This point, which lies on the celestial equator, is known as the vernal equinox. We shall explain its origin after having indicated its use. The hour circle which passes through the vernal equinox is the prime meridian of the heavens, and the vernal equinox itself is sometimes called the “Greenwich of the Sky.”

If, now, we wish to ascertain the exact location of a star on the celestial sphere, as we would that of New York, London, or Paris, on the earth, we measure along the hour circle running through it, its declination, or distance from the celestial equator, and then, along its parallel of declination, we measure its right ascension, or distance from the vernal equinox. Having these two co-ordinates, we possess all that is necessary to enable us to describe the position of the star, so that someone else looking for it, may find it in the sky, as a navigator finds some lone island in the sea by knowing its latitude and longitude.

Declination, as we have seen, is simply another name for latitude, but right ascension, which corresponds to longitude, needs a little additional explanation. It differs from longitude, first, in that, instead of being reckoned both east and west from the prime meridian, it is reckoned only toward the east, the reckoning being continued uninterruptedly entirely round the circle of the equator; and, second, in that it is usually counted not in degrees, minutes, and seconds of arc, but in hours, minutes, and seconds of time. The reason for this is that, since the celestial sphere makes one complete revolution in twenty-four hours, it is convenient to divide the circuit into twenty-four equal parts, each corresponding to the distance through which the heavens appear to turn in one hour. This explains the origin of the term hour circles applied to the celestial meridians, which, by intersecting the equator, divide it into twenty-four equal parts, each part corresponding to an hour of time. In expressing right ascension in time, the Roman numerals—I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII, XIII, XIV, XV, XVI, XVII, XVIII, XIX, XX, XXI, XXII, XXIII, XXIV—are employed for the hours, and the letters m and s respectively for the minutes and seconds. Since there are 360° in every circle, it is plain that one hour of right ascension corresponds to 15°. So, too, one minute of right ascension corresponds to 15′, and one second to 15″. It will be found useful to memorise these relations.

7. Effects Produced by Changing the Observer's Place on the Earth. The reader will recall that in Sect. 4 we described another system of circles for determining the places of stars, a system based on the horizon and the zenith. This horizon-zenith system takes no account of the changes produced by the apparent motion of the heavens, and consequently it is not applicable to determining the absolute positions of the stars on the celestial sphere. It simply shows their positions in the visible half of the sky, as seen at some particular time from some definite point on the earth. In order to show the changing relations of this system to that which we have just been describing, let us consider the effects produced by shifting our place of observation on the earth. Since the zenith is the point overhead and the nadir the point underfoot, and the horizon is a great circle drawn exactly half-way between the zenith and the nadir, it is evident, upon a moment's consideration, that every place on the earth has its own zenith and its own horizon. It is also clear that every place must have its own meridian, because the meridian is a north-and-south line running directly over the observer's head. You can see how this is, if you reflect that for an observer situated on the other side of the earth what is overhead for you will be underfoot for him, and vice versa. Thus the direction of our zenith is the direction of the nadir for our antipodes, and the direction of their zenith is the direction of our nadir. They see the half of the sky which is invisible to us, and we the half which is invisible to them.

Now, suppose that we should go to the north pole. The celestial north pole would then be in our zenith, and the equator would correspond with the horizon. Thus, for an observer at the north pole the two systems of circles that we have described would fall into coincidence. The zenith would correspond with the pole of the heavens; the horizon would correspond with the celestial equator; the vertical circles would correspond with the hour circles; and the altitude circles would correspond with the circles of declination. The North Star, being close to the pole of the heavens, would appear directly overhead. Being at the zenith, its altitude would be 90° (see Sect. 4). Peary, if he had visited the pole during the polar night, would have seen the North Star overhead, and it would have enabled him with relatively little trouble to determine his exact place on the earth, or, in other words, the exact location of the north terrestrial pole. With the pole star in the zenith, it is evident that the other stars would be seen revolving round it in circles parallel to the horizon. All the stars situated north of the celestial equator would be simultaneously and continuously visible. None of them would either rise or set, but all, in the course of twenty-four hours, would appear to make a complete circuit horizontally round the sky. This polar presentation of the celestial sphere is called the parallel sphere, because the stars appear to move parallel to the horizon. No man has yet beheld the nocturnal phenomena of the parallel sphere, but if in the future some explorer should visit one of the earth's poles during the polar night, he would behold the spectacle in all its strange splendour.

Next, suppose that you are somewhere on the earth's equator. Since the equator is everywhere 90°, or one quarter of a circle, from each pole, it is evident that looking at the sky from the equator you would see the two poles (if there was anything to mark their places) lying on the horizon one exactly in the north and the other exactly in the south. The celestial equator would correspond with the prime vertical, passing east and west directly over your head, and all the stars would rise and set perpendicularly to the horizon, each describing a semicircle in the sky in the course of twelve hours. During the other twelve hours, the same stars would be below the horizon. Stars situated near either of the poles would describe little semi-circles near the north or the south point; those farther away would describe larger semi-circles; those close to the celestial equator would describe semi-circles passing overhead. But all, no matter where situated, would describe their visible courses in the same period of time. This equatorial presentation of the celestial sphere is called the right sphere, because the stars rise and set at a right angle to the plane of the horizon. Comparing it with the system of circles on which right ascension and declination are based, we see that, as the prime vertical corresponds with the celestial equator, so the horizon must represent an hour circle. The meridian also represents an hour circle. It may require a little thought to make this clear, but it will be a good exercise.

Finally, if you are somewhere between the equator and one of the poles, which is the actual situation of the vast majority of mankind, you see either the north or the south pole of the heavens elevated to an altitude corresponding with your latitude, and the stars apparently revolving round it in circles inclined to the horizon at an angle depending upon the latitude. The nearer you are to the equator, the steeper this angle will be. This ordinary presentation of the celestial sphere is called the oblique sphere. Its horizon does not correspond with either the equator or the prime vertical, and its zenith and nadir lie at points situated between the celestial poles and the celestial equator.

8. The Astronomical Clock and the Ecliptic. It will be remembered that the meridian of any place on the earth is a straight north and south line running through the zenith and perpendicular to the horizon. More strictly speaking, the meridian is a circle passing from north to south directly overhead and corresponding exactly with the meridian of longitude of the place of observation. Now, let us consider the hour circles on the celestial sphere. They are drawn in the same way as the meridians on the earth. But the celestial sphere appears to revolve round the earth, and as it does so it must carry the hour circles with it, since they are fixed in position upon its surface. Fix your attention upon the first of these hour circles, i. e., the one which runs through the vernal equinox. Its right ascension is called 0 hours, because it is the starting point. Suppose that at some time we find the vernal equinox exactly in the south; then the 0 hour circle, or the prime meridian of the heavens, will, at that instant, coincide with the meridian of the place of observation. But one hour later, in consequence of the motion of the heavens, the vernal equinox, together with the circle of 0 hours, will be 15°, or one hour of right ascension, west of the meridian, and the hour circle marked I will have come up to, and for an instant will be blended with, the meridian. An hour later still, the circle of II hours right ascension will have taken its place on the meridian, while the vernal equinox and the circle of 0 hours will be II hours, or 30°, west of the meridian. And so on, throughout the entire circuit of the sky.

What has just been said makes it evident that the apparent motion of the heavens resembles the movement of a clock, the vernal equinox, or the circle of 0 hours, serving as a hand, or pointer, on the dial. Astronomers use it in exactly that way, for astronomical clocks are made with dials divided into twenty-four hour spaces, and the time reckoning runs continuously from 0 hours to XXIV hours. The “astronomical day” begins when the vernal equinox is on the meridian. At that instant the hands of the astronomical clock mark 0 hours, 0 minutes, 0 seconds. Thus the clock follows the motion of the heavens, and the astronomer can tell by simply glancing at the dial, and without looking at the sky, where the vernal equinox is, and what is the right ascension of any body which may at that moment be on the meridian.

We must now explain a little more fully what the vernal equinox is, and why it has been chosen as the “Greenwich of the Sky.” Its position is not marked by any star, but is determined by means of the intersecting circles that we have described. There is one other such circle, that we have not yet mentioned, which bears a peculiar relation to the vernal equinox. This is the ecliptic. Just as the daily, or diurnal, rotation of the earth on its axis causes the whole celestial sphere to appear to make one revolution every day, so the yearly or annual revolution of the earth in its orbit about the sun causes the sun to appear to make one revolution through the sky every year. As the earth moves onward in its orbit, the sun seems to move in the opposite direction. Inasmuch as there are 360° in a complete circle and 365 days in a year, the apparent motion of the sun amounts to nearly 1° per day, or 30° per month. In twelve months, then, the sun comes back again to the place in the sky which it occupied at the beginning of the year. Since the motion of the earth in its orbit is from west to east (the same as that of its rotation on its axis), it follows that the direction of the sun's apparent annual motion in the sky is from east to west (like its daily motion). Thus, while in fact the earth pursues a path, or orbit, round the sun, the sun seems to pursue a path round the earth. This apparent path of the sun, projected against the background of the sky, is called the ecliptic. The name arises from the fact that eclipses only occur when the moon is in or near the plane of the sun's apparent path.

As the apparent motion of the sun round the ecliptic is caused by the real motion of the earth round the sun, we may regard the ecliptic as a circle marking the intersection of the plane of the earth's orbit with the celestial sphere. In other words, if we were situated on the sun instead of on the earth, we would see the earth travelling round the sky in the circle of the ecliptic. We must keep this fact, that the ecliptic indicates the plane of the earth's orbit, firmly in mind, in order to understand what follows.

The ecliptic is not coincident with the celestial equator, for the following reason: The axis of the earth's daily rotation is not parallel to, or does not point in the same direction as, the axis of its yearly revolution round the sun. As the axis of rotation is perpendicular to the equator, so the axis of the yearly revolution is perpendicular to the ecliptic, and since these two axes are inclined to one another, it results that the equator and the ecliptic must lie in different planes. The inclination of the plane of the ecliptic to that of the equator amounts to about 23½°.

As it is very important to have a clear conception of this subject, we may illustrate it in this way: Take a ball to represent the earth, and around it draw a circle to represent the equator. Then, through the centre of the ball, and at right angles to its equator, put a long pin to represent the axis. Set it afloat in a tub of water, weighting it so that it will be half submerged, and placing it in such a position that the pin will be not upright but inclined at a considerable angle from the vertical. Now, imagine that the sun is situated in the centre of the tub, and cause the ball to circle slowly round it, while maintaining the pin always in the same position. Then the surface of the water will represent the plane of the ecliptic, or plane of the earth's orbit, and you will see that, in consequence of the inclination of the pin, the plane of the equator does not coincide with that of the ecliptic (or the surface of the water), but is tipped with regard to it in such a manner that one half of the equator is below and the other half above it. Instead of actually trying this experiment, it will be a useful exercise of the imagination to represent it to the mind's eye just as if it were tried.

We have said that the inclination of the equator to the ecliptic amounts to 23½°, and this angle should be memorised. Now, since both the ecliptic and the equator are great circles of the celestial sphere, i. e., circles whose planes cut through the centre of the sphere, they must intersect one another at two opposite points. In the experiment just described, these two points lie on opposite sides of the ball, where the equator cuts the level of the water. These points of intersection of the equator and the ecliptic on the celestial sphere are called the equinoxes, or equinoctial points, because when the sun appears at either of those points it is perpendicular over the equator, and when it is in that position day and night are of equal length all over the earth. (Equinox is from two Latin words meaning “equal night.”)