Astronomy in a nutshell

1. The Sun. By the term solar system is meant the sun together with the system of bodies (planets, asteroids, comets and meteors) revolving round it. The sun, being a star, every other star, for all that we can tell, may be the ruler of a similar system. In fact, we know that a few stars have huge dark bodies revolving round them, which may be likened to gigantic planets. The reason why the sun is the common centre round which the other members of the solar system move, is because it vastly exceeds all of them put together in mass, or quantity of matter, and the power of any body to set another body in motion by its attractive force depends upon mass. If a great body and a small body attract each other, both will move, but the motion of the small body will be so much more than that of the great one that the latter will seem, relatively, to stand fast while the small one moves. Then, if the small body had originally a motion across the direction in which the great body attracts it, the result of the combination will be to cause the small body to revolve in an orbit (more or less elliptical according to the direction and velocity of its original motion) about the great body. If the difference of mass is very great, the large body will remain virtually immovable. This is the case with the sun and its planets. The sun has 332,000 times as much mass (or, we may say, is 332,000 times as heavy) as the earth. It has a little more than a thousand times as much mass as its largest planet, Jupiter. It has millions of times as much as the greatest comet. The consequence is that all of these bodies revolve around the sun, in orbits of various degrees of eccentricity, while the sun itself remains practically immovable, or just swaying a little this way and that, like a huntsman holding his dogs in leash.

The distance of the sun from the earth—about 93,000,000 miles—has been determined by methods which will be briefly explained in the next section. Knowing its distance, it is easy to calculate its size, since the apparent diameter of all objects varies directly with their distance. The diameter of the sun is thus found to be about 866,400 miles, or nearly 110 times that of the earth. In bulk it exceeds the earth about 1,300,000 times, but its mass, or quantity of matter, is only 332,000 times the earth's, because its average density is but one quarter that of the earth. This arises from the fact that the earth is a solid, compact body, while the sun is a body composed of gases and vapours (though in a very compressed state). It is the high temperature of the sun which maintains it in this state. Its temperature has been calculated at about 16,000° Fahrenheit, but various estimates differ rather widely. At any rate, it is so hot that the most refractory substances known to us would be reduced to the state of vapour, if removed to the sun. The quantity of heat received upon the earth from the sun can only be expressed in terms of the mechanical equivalent of heat. The unit of heat in engineering is the calorie, which means the amount of heat required to raise the temperature of one kilogram of water (2.2 pounds) one degree Centigrade (1°.8 Fahrenheit). Now observation shows that the sun furnishes 30 of these calories per minute upon every square metre (about 1.2 square yard) of the earth's surface. Perhaps there is no better illustration of what this means than Prof. Young's statement, that “the heat annually received on each square foot of the earth's surface, if employed in a perfect heat engine, would be able to hoist about a hundred tons to the height of a mile.” Or take Prof. Todd's illustration of the mechanical power of the sunbeams: “If we measure off a space five feet square, the energy of the sun's rays when falling vertically upon it is equivalent to one horse power.” Astronomers ordinarily reckon the solar constant in “small calories,” which are but the thousandth part of the engineer's calorie, and the latest results of the Smithsonian Institution observations indicate that the solar constant is about 1.95 of these small calories per square centimeter per second. About 30 per cent. must be deducted for atmospheric absorption.

Heat, like gravitation and like light, varies inversely in intensity with the square of the distance; hence, if the earth were twice as near as it is to the sun it would receive four times as much heat and four times as much light, and if it were twice as far away it would receive only one quarter as much. This shows how important it is for a planet not to be too near, or too far from, the sun. The earth would be vapourised if it were carried within a quarter of a million miles of the sun.

The sun rotates on an axis inclined about 7½° from a perpendicular to the plane of the ecliptic. The average period of its rotation is about 25⅓ days—we say “average” because, not being a solid body, different parts of its surface turn at different rates. It rotates faster at the equator than at latitudes north-and-south of the equator, the velocity decreasing toward the poles. The period of rotation at the equator is about 25 days, and at 40° north or south of the equator it is about 27 days. The direction of rotation is the same as that of the earth's.

The surface of the sun, when viewed with a telescope, is often seen more or less spotted. The spots are black, or dusky, and frequently of very irregular shapes, although many of them are nearly circular. Generally they appear in groups drawn out in the direction of the solar rotation. Some of these groups cover areas of many millions of square miles, although the sun is so immense that even then they appear to the naked eye (guarded by a dark glass) only as small dark spots on its surface. The centres of sun-spots, are the darkest parts. Generally around the borders of the spots the surface seems to be more or less heaped up. Often, in large sun-spots, immense promontories, very brilliant, project over the dark interior, and many of these are prolonged into bridges of light, apparently traversing the chasms beneath. Constant changes of shape and arrangement take place, and there are few more astonishing telescopic objects than a great sun-spot.

The spots are not always visible in equal numbers, and in some years but few are seen, and they are small. It has been found that they occur in periods, averaging about eleven years from maximum to minimum, although the length of the period is very irregular. It has also been observed that when the first spots of a new period appear, they are generally seen some 30° from the equator, either toward the north or toward the south, and that as the period progresses the spots increase in size, and seem to draw toward the equator, the last spots of the period being seen quite close to the equator, on one side or the other. The duration of individual spots is variable; some last but a day or two, and others continue for weeks, sometimes being carried out of view by the rotation of the sun and brought into view again from the other side.

The surface of the sun in the neighbourhood of groups of spots is frequently marked by large areas covered with crinkled bright lines and patches, which are called faculæ. These, which are the brightest parts of the sun, appear to be elevated above the general level.

As to the cause and nature of sun-spots much remains to be learned. In 1908, Prof. George E. Hale, by means of an instrument called the spectro-heliograph, which selects out of the total radiation of the solar disk light peculiar to certain elements, and thus permits the use of that light alone in photographing the sun, demonstrated that sun-spots probably arise from vortices, or whirling storms, and that these vortices produce strong magnetic fields in the sun-spots. The phenomenon may be regarded, says Prof. Hale, as somewhat analogous to a tornado or waterspout on the earth. The whirling trombe becomes wider at the top, carrying the gases from below upward. At the centre of the storm the rapid rotation produces an expansion which cools the gases and causes the appearance of a comparatively dark cloud, which we see as the sun-spot. The vortices whirl in opposite directions on opposite sides of the sun's equator, thus obeying the same law that governs the rotation of cyclones on the earth.

It has long been a question whether the condition of the sun as manifested by the spots upon its surface has an influence upon the meteorology of the earth. It is known that the sun-spot period coincides closely with periodical changes in the earth's magnetism, and great outbursts on the sun have frequently been immediately followed by violent magnetic storms and brilliant displays of the aurora borealis on the earth.

The sun undoubtedly exercises other influences upon the earth than those familiar to us under the names of gravitation, light, and heat; but the nature of these other influences is not yet fully understood.

The brilliant white surface of the sun is called the photosphere. It has been likened to a shell of intensely hot clouds, consisting of substances which are entirely vaporous within the body of the sun. Above the photosphere lies an envelope, estimated to be from 5000 to 10,000 miles thick, known as the chromosphere. It consists mainly of hydrogen and helium, and when seen during a total eclipse, when the globe of the sun is concealed behind the moon, it presents a brilliant scarlet colour. Above this are frequently seen splendid red flame-like objects, named prominences. They are of two varieties—one cloud-like in appearance, and the other resembling spikes, or trees with spreading tops,—but often their forms are infinitely varied. The latter, the so-called eruptive prominences, exhibit rapid motion away from the sun's surface, as if they consisted of matter which has been ejected by explosion. Occasionally these objects have been seen to grow to a height of several hundred thousand miles, with velocities of two or three hundred miles per second.

The sun has still another envelope, of changing form,—the corona. This apparently consists of rare gaseous matter, whose characteristic constituent is an element unknown on the earth, called coronium. The corona appears in the form of a luminous halo, surrounding the hidden sun during a total eclipse, and it often extends outward several million miles. Its shape varies in accordance with the sun-spot period. It has a different appearance and outline at a time of maximum sun-spots from those which it presents at a minimum. There are many things about the corona which suggest the play of electric and magnetic forces. The corona, although evidently always existing, is never seen except during the few minutes of complete obscuration of the sun that occurs in a total eclipse. This is because its light is not sufficiently intense to render it visible, when the atmosphere around the observer is illuminated by the direct rays of sunlight.

2. Parallax. We now return to the question of the sun's distance from the earth, which we treat in a separate section, because thus it is possible to present, at a single view, the entire subject of the measurement of the distances of the heavenly bodies. The common basis of all such measurements is furnished by what is called parallax, which may be defined as the difference of direction of an object when viewed alternately from two separate points. The simplest example of parallax is found in looking at an object first with one eye and then with the other without, in the meantime, altering the position of the head. Suppose you sit in front of a window through which you can see the wall of a house on the opposite side of the street. Choose one of the vertical bars of the window-sash, and, closing the left eye, look at the bar with the right and note where it seems to be projected against the wall. Then close the right eye and open the left, and you will observe that the place of projection of the bar has shifted toward the right. This change of direction is due to parallax and its amount depends both upon the distance between the eyes and upon the distance of the window from the observer. To see how this principle is applied by the astronomer, let us suppose that we wish to ascertain the distance of the moon. The moon is so far away that the distance between the eyes is infinitesimal in comparison, so that no parallactic shift in its direction is apparent on viewing it alternately with the two eyes. But by making the observations from widely separated points on the earth we can produce a parallactic shifting of the moon's position which will be easily measurable.

Let one of the points of observation be in the northern hemisphere and the other in the southern, thousands of miles apart. The two observers might then be compared to the eyes of an enormous head, each of which sees the moon in a measurably different direction. If the northern observer carefully ascertains the angular distance of the moon from his zenith, and the southern observer does the same with regard to his zenith, as indicated in Fig. 12, they can, by a combination of their measurements, construct a quadrilateral A C B M, of which all the angles may be ascertained from the two measurements, while the length of the sides A C and B C is already known, since they are each equal to the radius of the earth. With these data it is easy, by the rules of plane trigonometry, to calculate the length of the other sides, and also the length of the straight line from the centre of the earth to the moon. In all such cases the distance between the points of observation is called the base-line, whose length is known to start with, while the angles formed by the lines of direction at the opposite ends of the base-line are ascertained by measurement.

In the case of the sun the distance concerned is so great (about 400 times that of the moon) that the parallax produced by viewing it from different points on the earth is too small to be certainly measured, and a modification of the method has to be employed. One such modification, which has been much used, depends upon the fact that the planet Venus, being nearer the sun than the earth is, appears, at certain times, passing directly over the face of the sun. This is called a transit of Venus. During a transit, Venus is between three and four times nearer the earth than the sun is, and consequently its parallactic displacement, when viewed from widely separated points on the earth, is much greater than that of the sun. One of the ways in which the astronomer takes advantage of this fact is shown in Fig. 13. Let A and B be two points on opposite sides of the earth, but both somewhere near the equator. As Venus swings along in its orbit to pass between the earth and the sun, it will manifestly be seen just touching the sun's edge sooner from A than from B. The observer at A notes with extreme accuracy the exact moment when he sees Venus apparently touch the sun. Several minutes later, the observer at B will see the same phenomenon, and he also notes accurately the time of the apparent contact. Now, since we know from ordinary observation the time that Venus requires to make one complete circuit of its orbit, we can, by simple proportion, calculate, from the time that it takes to pass from v to v¹, the angular distance between the lines A S and B S, or in other words the size of the angle at S, which is equal to the parallactic displacement of the sun, as seen from opposite ends of the earth's diameter. Knowing, to begin with, the distance between A and B, we have the means of determining the length of all the other lines in the triangle, and hence the distance of the sun. This process is known as Delisle's method. There is another method, called Halley's, but in a brief treatise of this kind we cannot enter into a description of it. It suffices to say that both depend upon the same fundamental principles.

It must be added, however, that other ways of measuring the sun's distance than are afforded by transits of Venus have been developed. One of these depends upon observation of the asteroid Eros, which periodically approaches much nearer to the earth than Venus ever does. By observing the parallax of Eros, when it is nearest the earth, its distance can be ascertained, and that being known the distance of the sun is immediately deducible from it, because, by the third law of Kepler (to be explained later), the relative distances of all the planets from the sun are proportional to their periods of revolution, so that if we know any one of the distances in miles we can calculate all the others. It is important here to state the angular amount of the sun's parallax, since it is a quantity which is continually referred to in books on astronomy. According to the latest determination, based on observations of Eros, the solar parallax is 8″.807, which corresponds, in round numbers, to a distance of 92,800,000 miles. A mean parallax of 8″.796 is given by Mr. C. G. Abbot, based on a combination of results from a number of different methods, and this corresponds to a distance of 92,930,000 miles. To the astronomer, who seeks extreme exactness, the slightest difference is important. It should be noted that the figures 8″.807 or 8″.796 represent the parallactic displacement of the sun, as seen not from the opposite ends of the earth's entire diameter, but from opposite ends of its radius, or semi-diameter. Accordingly it is equal to half of the angle at S in Fig. 13. It is for convenience of calculation that, in such cases, the astronomer employs the semi-diameter, instead of the whole diameter for his base-line.

The case of the stars must next be considered, and now we find that the distances involved are so enormous that the diameter, or semi-diameter, of the earth is altogether too insignificant a quantity to afford an available base-line for the measurement. We should have remained forever ignorant of star distances but for the effects produced by the earth's change of place due to its annual revolution round the sun. The mean diameter of the earth's orbit is about 186,000,000 miles, and we are able to make use of this immense distance as a base-line for ascertaining the parallax of a star. Suppose, for instance, that the direction of a star in the sky is observed on the 1st of January, and again on the 1st of July. In the meantime, the earth will have passed from one end of the base-line just described to the other, and unless the star observed is extremely remote, a careful comparison of the two measurements of direction will reveal a perceptible parallax, from which the actual distance of the star in question can be deduced.

It is to be observed that if all the stars were equally distant this method would fail, because then there would be no “background” against which the shift of place could be observed; all of the stars would shift together. But, in fact, the vast majority of the stars are so remote that even a base-line of 186,000,000 miles is insufficient to produce a measurable shift in their direction. It is only the distances of the nearer stars which we can measure, and for them the multitude of more remote ones serves, like the wall of the house in the experiment with the window-bar, as a background on which the shift of place can be noted. Just as in calculations of the sun's parallax the semi-diameter of the earth is chosen for a base-line, so in the case of the stars the semi-diameter of the earth's orbit, amounting to 93,000,000 miles, forms the basis. Measured in this way the parallaxes of the nearest stars come out in tenths, or hundredths, of a second of arc, or angular measurement. Thus the parallax of Alpha Centauri, the nearest known star, is about 0″.75, corresponding to a distance of about 26,000,000,000,000 miles. Now 0″.75 is a quantity inappreciable to the naked eye, and only to be measured with delicate instruments, and yet this almost invisible shift of direction is all that is produced by viewing the nearest star in the sky from the opposite ends of a base-line 93,000,000 miles long!

3. Spectroscopic Analysis. We have next to deal with the constitution of the sun, or the nature of the substances of which it consists, and for this purpose we must first understand the operation of the spectroscope, in many respects the most wonderful instrument that man has invented. It has given birth to the “chemistry of the sun” and the “chemistry of the stars,” for by its aid we can be as certain of the nature of many of the substances of which they are made as we could be by actually visiting them.

Fundamentally, spectroscopic analysis depends upon the principle of refraction, of which we have spoken in connection with the atmosphere. Although the most powerful spectroscopes are now made on a different plan, the working of the instrument can best be comprehended by considering it in the form in which it was first invented, and in which it is still most often used. In its simplest form the spectroscope consists of a three-angle prism of glass, through which a ray of light is sent from the sun, star, or other luminous object to be examined. Glass, like air or water, has the property of refracting, or bending, all rays of light that enter it in an inclined direction. In passing through two of the opposite-sloping sides of a prism, the ray is twice bent, once on entering and again on leaving, in accordance with the principle that we have already mentioned (see Part II, Sect. 4). Still, merely bending the ray out of its original course would have no important result but for another associated phenomenon, known as dispersion. To explain dispersion we must recall the familiar fact that white light consists of a number of coloured components which, when united, make white. It is usual to speak of these primary, or prismatic, colours, as seven in number. These are red, orange, yellow, green, blue, indigo, and violet. Physicists now assign a different list of primary colours, but these, being generally familiar, will best serve our purpose. Without going into an explanation of the reasons, it will suffice to say that the waves of light producing these fundamental colours are not all equally affected by refraction. The red is least, and the violet most, bent out of its course in passing through the prism, the other colours being bent more and more in proportion to their distance from the red. It follows that the ray, or beam, of light, which was white when it entered the prism, becomes divided or dispersed during its passage into a brush of seven different hues. Thus the prism may be said to analyse the light into its fundamental colours, making them separately visible. This, as a scientific fact, dates from the time of Newton. But Newton did not dream of the further magic that lay in the prism.

It was noticed as early as 1801 that, when the light of the sun was dispersed in the way we have described, not only did the seven primary colours make their appearance, but across the ribbon-like band, called the spectrum, that was thus formed, ran a number of thin black lines, like narrow gaps in the band. The position of these lines was carefully studied by a German astronomer, Fraunhofer, in 1814, and they still bear the name of Fraunhofer lines. But the full explanation of them did not come until 1858 when, with their aid, Kirschoff laid the foundations of spectrum analysis.

This analysis is based upon the fact that the Fraunhofer lines are visual indications of the existence of certain substances in the sun. To explain this we must know three fundamental facts:

1st: Every incandescent body that is either solid or liquid (or, if it consists of gases, is under high pressure) shines with compound white light, which, when dispersed by prisms, gives a continuous coloured band, or spectrum.

2d: Every elementary substance when in the gaseous state, and under low pressure, if brought to incandescence by heat, shines with light which, when dispersed, gives a discontinuous spectrum, made up of separate bright lines; and each different element possesses its own peculiar spectral lines, never coinciding in position with the lines of any other element.

3d: If the light from a body giving a continuous spectrum is caused to pass through a gas which is at a lower temperature, the gas will absorb precisely those light waves, of which its own spectrum is composed and will leave in the spectrum of the body a series of dark lines, or gaps, whose number and position indicate the nature of the gas whose absorptive action has produced them.

Now, to apply these principles to the sun we have only to remember that it is a globe of gaseous substances, which are under great pressure, owing to the immense force of the sun's gravitation. Consequently it gives a continuous spectrum. But, at the same time, it is surrounded with gaseous envelopes, which are not as much compressed as the internal gases are, and which are at a lower temperature because they come in contact with the cold of surrounding space. The light from the body of the sun must necessarily pass through these envelopes, and each of the gases of which they consist absorbs from the passing sunlight its own peculiar rays, with the result that the spectrum of the sun is seen crossed with a great number of black lines—the Fraunhofer lines.

It will be remarked that the evidence which the Fraunhofer lines afford concerning the composition of the sun applies, strictly, only to the outer portion, or to the envelopes of gaseous matter that surround the interior globe. But since there is every reason to believe that the entire body of the sun is in a gaseous state, notwithstanding the internal pressure, and since we see that there is a continual circulation going on between the inner and outer portions, it is logical to conclude that essentially the same elements exist under varying conditions in all parts of the sun.

In this way, then, we have learned the composition of the sun, and we find that it consists of virtually the same elementary substances found upon the earth, but existing there in a gaseous or vaporous state. Among the elements which have been positively identified in the sun by means of their characteristic spectral lines are iron, calcium, sodium, aluminum, copper, zinc, silver, lead, potassium, nickel, tin, silicon, manganese, magnesium, cobalt, hydrogen, and at least twenty others which are likewise found upon the earth. Some elementary substances known on the earth, such as gold and oxygen, have not yet been certainly found in the sun, but there is every reason to believe that they all exist there, though perhaps under conditions which render their detection difficult or impossible. Helium was recognised as an element in the sun, by giving spectral lines different from any known substance, and it received its name “sun-metal,” long before it was discovered on the earth. We have seen that there is at least one element in the sun, coronium, which, as far as we know, does not exist at all upon the earth, and it is not improbable that there may be others which have no counterparts on the earth.

The same kind of analysis applies to the stars, no matter how far away they may be, so long as they give sufficient light to form a spectrum. And in this way it has been found that the stars differ somewhat from the sun and from one another in their composition, and thus a classification of the stars has been made, and it has been possible to draw conclusions concerning their relative age, which show that some stars are comparatively younger than the sun, others older, and others so far advanced in age, or evolution, that they are drawing near extinction. Many dark bodies also exist among the stars, which appear to be completely extinguished suns. It only remains to add on this subject that, according to prevailing theories, the earth itself was once an incandescent body, shining with its own light, and at that time it, too, would have yielded a spectrum showing of what substances it consisted.

4. The Moon. The earth is a satellite of the sun, and the moon is a satellite of the earth. The mean, or average, distance of the sun from the earth is about 93,000,000 miles; the mean distance of the moon is a little less than 239,000 miles. This distance is variable to the extent of about 31,000 miles, owing to the eccentricity of the moon's orbit about the earth. That is, the moon is sometimes nearly 253,000 miles away, and sometimes only about 221,600. The diameter of the moon is 2163 miles. Its bulk is one-forty-ninth that of the earth, but its mass is only one-eightieth, because its mean density is only about six-tenths as great as the earth's.

The moon appears to travel in an orbit round the earth, but in fact the orbit is always concave toward the sun, and the disturbing attraction of the earth, as the two move together round the sun, causes it to appear now on one side and now on the other. But we may treat the moon's orbit as if the earth were the true centre of force, the attraction of the sun being regarded as the disturbing element.

According to a mathematical theory, which has been largely accepted as probably true, but into which we cannot enter here (see Prof. George Darwin's The Tides, or Prof. R. Ball's Time and Tide), the moon was thrown off from the earth many ages ago, as a consequence of tidal “friction.” As it moves round in its orbit the moon keeps the same face toward the earth. This fact is also ascribed to tidal influence.

Apparently the moon has no atmosphere, or if it has any it is too rare to be certainly detected. On its surface, there is no appearance of water. Consequently we cannot suppose it to be inhabited, at least by any forms of life familiar to us on the earth. But when the moon is viewed with a telescope large relatively flat areas are seen, which some think may have been the beds of seas in ancient times. They are still called maria, or “seas,” and are visible to the naked eye in the form of great irregular dusky regions. Nearly two-thirds of the surface of the moon, as we see it, consists of bright regions, which are very broken and mountainous. Most of the mountains of the moon are roughly circular, surrounding enormous depressions, which look like gigantic pits. For this reason they are called lunar volcanoes, but, to say nothing of their immense size—for many are fifty or sixty miles across—they differ in many ways from the volcanoes of the earth. It suffices to point out that what resemble volcanic craters are not situated, as is the case on the earth, at the summits of mountains, but are vast sink-holes, descending thousands of feet below the general surface of the moon. Their real origin is unknown, but it is possible that volcanic forces may have produced them. (For a description, with photographs, of these gigantic formations in the lunar world, see the present author's The Moon.) In addition to the circular mountains, or craters, there are several long and lofty chains of lunar mountains much resembling terrestrial mountain ranges.

As to the absence of air and water from the moon, some have supposed that they once existed, but, in the course of ages, have disappeared, either by absorption, partly mechanical and partly chemical, into the interior rocks, or by escaping into space on account of the slight force of gravity on the moon, which appears to be insufficient to enable it to retain, permanently, such volatile gases as oxygen, hydrogen, and nitrogen. This leads us to consider the force of the moon's attraction at its surface. We have seen that spherical bodies attract as if their whole mass were collected at their centres. We also know that the force of attraction varies directly as the mass of the attracting body and inversely as the square of the distance from its centre. Now the mass of the moon is one-eightieth that of the earth, so that, upon bodies situated at an equal distance from the centres of both, the moon's attraction would be only one-eightieth of the earth's. But the diameter of the moon is not very much more than one quarter that of the earth, and for the sake of round numbers let us call it one quarter. It follows that an object on the surface of the moon is four times nearer the centre of attraction than is an object on the surface of the earth, and since the force varies inversely as the square of the distance the moon's attraction upon bodies on its surface is relatively sixteen times as great as the earth's. But the total force of the earth's attraction is eighty times greater than the moon's. In order, then, to find the real relative attraction of the moon at its surface we must divide 80 by 16, the quotient, 5, showing the ratio of the earth's force of attraction at its surface to that of the moon at its surface. In other words, this calculation shows that the moon draws bodies on its surface with only one-fifth the force with which the same bodies would be drawn on the earth's surface. The weight of bodies of equal mass would, therefore, be only one-fifth as great on the moon as on the earth.

But the real difference is greater than this, for we have used round numbers, which exaggerated the size of the earth as compared with that of the moon. If we employ the fractional numbers which show the actual ratio of the moon's radius (half-diameter) to that of the earth, we shall find that the weight of the same body would be only about one-sixth as great on the moon as on the earth. It has been thought that this relative lack of weight on the moon may account for the gigantic proportions assumed by its craters, since the same elective force would throw volcanic matter to a much greater height and distance there than on our planet.

The connection of the slight force of gravity on the moon with its ability to retain an atmosphere is shown by the following considerations. It is possible to calculate for any planet of known mass the velocity with which a particle would have to move in order to escape from the control of that planet. In the case of the earth this critical velocity, as it is called, amounts to about 7 miles per second, and in the case of the moon to only 1½ miles per second. Now the kinetic theory of gases informs us that their molecules are continually flying in all directions with velocities varying with the nature and the temperature of the gas. The maximum velocity of the molecules of oxygen is 1.8 miles per second, of hydrogen 7.4 miles, of nitrogen 2 miles, of water vapour 2.5 miles. It is evident, then, that the force of the earth's attraction is sufficient permanently to retain all these gases except hydrogen, and in fact there is no gaseous hydrogen in the atmosphere, that element being found on the earth only in combination with other substances. But oxygen and nitrogen, which constitute the bulk of the atmosphere, have maximum molecular velocities much less than the critical velocity above described. In the case of the moon, however, the critical velocity is less than those of the molecules of oxygen, nitrogen, and water vapour, to say nothing of hydrogen; therefore the moon cannot permanently retain them. We say “permanently,” because they might be retained for a time for the reason that the molecules of a gas fly in all directions, and continual collisions occur among them in the interior of the gaseous mass, so that it would be only those at the exterior of the atmosphere which would escape; but gradually all that remained free from combination would get away.

As the moon travels round the earth it shows itself in different forms, gradually changing from one into another, which are known as phases. If the moon shone with light of its own its outline would always be circular, like the sun's. The apparent change of form is due, first, to its being an opaque globe, reflecting the sunlight that falls upon it, and necessarily illuminated on only one side at a time; and second, to the fact that as it travels round the earth the half illuminated by the sun is sometimes turned directly toward us, at other times only partly toward us, and at still other times directly away from us. When it is in that part of its orbit which passes between the sun and the earth, the moon, so to speak, has its back turned to us, the illuminated side being, of course, toward the sun. It is then invisible, and this unseen phase is the true “new moon.” It is customary, however, to give the name new moon to the narrow, sickle-shaped figure, which it shows in the west, after sunset, a few days after the date of the real new moon. The sickle gradually enlarges into a half circle as the moon passes away from the sun, and the half circle phase, which occurs when the moon arrives at a position in the sky at right angles to the direction of the sun, is called first quarter. After first quarter the moon begins to move round behind the earth, with respect to the sun, and when it has arrived just behind the earth, its whole illuminated face is turned toward the earth, because the sun, which causes the illumination, is on that same side. This phase is called full moon. Afterward the moon returns round the other part of its orbit toward its original position between the earth and the sun, and as it does so, it again assumes, first, the form of a half circle, which in this case is called third, or last, quarter, then that of a sickle, known as “old moon,” and finally disappears once more to become new moon again.

A perfectly evident explanation of these changes of form, clearer than any description, can be graphically obtained in this way. Take a billiard ball, a croquet ball, or a perfectly round, smooth, and tightly rolled ball of white yarn, and, placing yourself not too near a brightly burning lamp and sitting on a piano stool (in order to turn more easily), hold the ball up in the light, and cause it to revolve round you by turning upon the stool. As it passes from a position between you and the lamp to one on the opposite side from the lamp, and so on round to its original position, you will see its illuminated half go through all the changes of form exhibited by the moon, and you will need no further explanation of the lunar phases.

The Harvest Moon and the Hunter's Moon, which are popularly celebrated not only on account of their romantic associations, but also because in some parts of the world they afford a useful prolongation of light after sunset, occur only near the time of the autumnal equinox, and they are always full moons. The full moon nearest the date of the equinox, September 23d, is the Harvest Moon, and the full moon next following is the Hunter's Moon. Their peculiarity is that they rise, for several successive evenings, almost at the same hour, immediately after sunset. This is due to the fact that at that time of the year the ecliptic, from which the moon's path does not very widely depart, is, in high latitudes, nearly parallel with the horizon.

The full moon in winter runs higher in the sky, and consequently gives a brighter light, than in summer. The reason is because, since the full moon must always be opposite to the sun, and since toe sun in winter runs low, being south of the equator, the full moon rides proportionally high.

5. Eclipses. We have mentioned the connection of the moon with the tides, but there is another phenomenon in which the moon plays the most conspicuous part—that of eclipses. There are two kinds of eclipses—solar and lunar. In the former it is the moon that causes the eclipse, by hiding the sun from view; and in the latter it is the moon that suffers the eclipse, by passing through the shadow which the earth casts into space on the side away from the sun. In both cases, in order that there may be an eclipse it is necessary that the three bodies, the moon, the sun, and the earth, shall be nearly on a straight line, drawn through their centres. Since the moon occupies about a month in going round the earth there would be two eclipses in every such period (one of the sun and the other of the moon), if the moon's orbit lay exactly in the plane of the ecliptic, or of the earth's orbit. But, in fact, the orbit of the moon is inclined to that plane at an angle of something over 5°. Even so, there would be eclipses every month if the two opposite points, called nodes, where the moon crosses the plane of the ecliptic, always lay in a direct line with the earth and the sun; but they do not lie thus. If, then, the moon comes between the earth and the sun when she is in a part of her orbit several degrees above or below the plane of the ecliptic, it is evident that she will pass either above or below the straight line joining the centres of the earth and the sun, and consequently cannot hide the latter. But, since eclipses do occur in some months and do not occur in others, we must conclude that the situation of the nodes changes, and such is the fact. In consequence of the conflicting attractions of the sun and the earth, the orbit of the moon, although, like that of the earth, it always retains nearly the same shape and the same inclination, swings round in space, so that the nodes, or crossing points on the ecliptic, continually change their position, revolving round the earth. This motion may be compared to that of the precession of the equinoxes, but it is much more rapid, a complete revolution occurring in a period of about nineteen years.

From this it follows that sometimes the moon in passing its nodes will be in a line with the sun, and sometimes will not. But, owing to the fact that the sun and moon are not mere points, but on the contrary present to our view circular disks, each about half a degree in diameter, an eclipse may occur even if the moon is not in an exact line with the centres of the sun and the earth. The edge of the moon will overlap the sun, and there will be a partial eclipse, if the centres of the two bodies are within one degree apart. Now, the inclination of the moon's orbit to the ecliptic being only a little over 5°, it is apparent that in approaching one of its nodes, along so gentle a slope, it will come within less than a degree of the ecliptic while still quite far from the node. Thus, eclipses occur for a considerable time before and after the moon passes a node. The distances on each side of the node, within which an eclipse of the sun may occur, are called the solar ecliptic limits, and they amount to 18° in either direction, or 36° in sum. Within these limits the sun may be wholly or partially eclipsed according as the moon is nearer to, or farther from, the node. If she is exactly at, or very close to, the node the eclipse will be total.

Solar eclipses vary in another way. What would be a total eclipse, under other circumstances, may be only an annular eclipse if the moon happens to be near her greatest distance from the earth. We have described the variations in her distance due to the eccentricity of her orbit, and we have said that the orbit itself swings round the earth in such a way as to cause the nodes continually to change their places on the ecliptic. The motion of the orbit also causes the lunar apsides, or the points where she is at her greatest and least distances from the earth, to change their places, but their revolution is opposite in direction to that of the nodes, as the revolution of the apsides of the earth's orbit is opposite to that of the equinoxes. The moon's apsides sometimes move eastward and sometimes westward, but upon the whole the eastward motion prevails and the apsides complete one revolution in that direction once in about nine and one-half years. In consequence of the combined effects of the revolution of the nodes and that of the apsides, the moon is sometimes at her greatest distance from the earth at the moment when she passes centrally over the sun, and sometimes at her least distance, or she may be at any intervening distance. If she is in the nearer part of her orbit, her disk just covers that of the sun, and the eclipse is total; if she is in the farther part (since the apparent size of bodies diminishes with increase of distance), her disk does not entirely cover the sun, and a rim of the latter is visible all around the moon. This is called an annular eclipse, because of the ring shape of the part of the sun remaining visible.

The length of the shadow which the moon casts toward the earth during a solar eclipse also plays an important part in these phenomena. This length varies with the distance from the sun. Since the moon accompanies the earth, it follows that when the latter is in aphelion, or at its greatest distance from the sun, the moon is also at its greatest mean distance from the sun, and the length of the lunar shadow may, in such circumstances, be as much as 236,000 miles. When the earth, attended by the moon, is in perihelion, the length of the moon's shadow may be only about 228,000 miles. The average length of the shadow is about 232,000 miles. This is nearly 7000 miles less than the average distance of the moon from the earth, so it is evident that generally the shadow is too short to reach the earth, and it would never reach it, and there would never be a total eclipse of the sun, but for the varying distance of the moon from the earth. When the moon is nearest the earth, or in perigee, its distance may be as small as 221,600 miles, and in all cases when near perigee it is near enough for the shadow to reach the earth.

Inasmuch, as the moon's shadow, even under the most favourable circumstances, is diminished almost to a point before touching the earth, it hardly need be said that it can cover but a very small area on the earth's surface. Its greatest possible diameter cannot exceed about 167 miles, but ordinarily it is much smaller. If both the earth and the moon were motionless, this shadow would be a round or oblong dot on the earth, its shape varying according as it fell square or sloping to the surface; but since the moon is continually advancing in its orbit, and the earth is continually rotating on its axis, the shadow moves across the earth, in a general west to east direction. But the precise direction varies with circumstances, as does also the speed. The latter can never be less than about a thousand miles per hour, and that, only in the neighbourhood of the equator. The moon advances eastward about 2100 miles per hour, and the earth's surface turns in the same direction with a velocity diminishing from about a thousand miles an hour at the equator to 0 at the poles. It is the difference between the velocity of the earth's rotation and that of the moon's orbital revolution which determines the speed of the shadow. The greatest time, which the shadow can occupy in passing a particular point on the earth is only eight minutes, but ordinarily this is reduced to one, two, or three minutes. The true shadow only lasts during the time that the moon covers the whole face of the sun, but before and after this total obscuration of the solar disk the sun is seen partially covered by the moon, and these partial phases of the eclipse may be seen from places far aside from the track which the central shadow pursues. It is only during a total eclipse, and only from points situated within the shadow track, that the solar corona is visible.

In a lunar eclipse it is the earth that is the intervening body, and its shadow falls upon the moon. A solar eclipse can only occur at the time of new moon, and a lunar eclipse only at the time of full moon. The shadow of the earth is much longer and broader than that of the moon, and it never fails to reach the moon, so that it is not necessary here to consider its varying length. The width, or diameter, of the shadow at the average distance of the moon from the earth is about 5700 miles. The moon may pass through the centre of the shadow, or to one side of the centre, or merely dip into the edge of it. When it goes deep enough into the shadow to be entirely covered, the eclipse is total; otherwise it is partial. Since in a total lunar eclipse the entire moon is covered by the shadow, it is evident that such an eclipse, unlike a solar one, may be visible simultaneously from all parts of the earth which, at the time, lie on the side facing the moon. In other words, the earth's shadow does not make merely a narrow track across the face of the moon, but completely buries it. When the moon passes centrally through the shadow, she may remain totally obscured for about two hours. But the moon does not completely disappear at such times, because the refraction of the earth's atmosphere bends a little sunlight round its edges and casts it into the shadow. If the atmosphere round the edges of the earth happens to be thickly charged with clouds, but little light is thus refracted into the shadow, and the moon appears very faint, or almost entirely disappears. But this is rare, and ordinarily the eclipsed moon shines with a pale copperish light.

The occurrence of a lunar eclipse is governed by similar circumstances to those affecting solar eclipses. The lunar ecliptic limits, or the distance on each side of the node within which an eclipse may occur, vary from 9½° to 12¼° in either direction.

Taking all the various circumstances into account, it is found that there may be, though rarely, seven eclipses in a year, two being of the moon and five of the sun, and that the least possible number of eclipses in a year is two, in which case both will be of the sun. Taking into account also all the various positions which the sun and moon occupy with regard to the earth, it is found that there exists a period of 18 years, 11 days, 8 hours, at the return of which eclipses of both kinds begin to recur again in the same order that they occur in the next preceding period. This is called the saros, and it was known to the Chaldeans 2600 years ago.

6. The Planets. We have several times mentioned the fact that, beside the earth, there are seven other principal planets revolving round the sun, in the same direction as the earth, but at various distances. We shall consider each of these in the order of its distance from the sun.

But first it is desirable to explain briefly certain so-called “laws” which govern the motions of all the planets. These are known as Kepler's laws of planetary motion, and are three in number. The demonstration of their truth would carry us beyond the scope of this book, and consequently we shall merely state them as they are recognised by astronomers.

1st Law: The orbit of every planet is an ellipse, having the sun situated in one of the foci.

2d Law: The radius vector of a planet describes equal areas in equal times. By the radius vector is meant the straight line joining the planet to the sun, and the law declares that as the planet moves round the sun, the area of space swept over by this line in any given time, say one day, is equal to the area which it will sweep over in any other equal length of time. If the orbit were a circle it is evident at a glance that the law must be true, because then the sun would be situated in the centre of the circle, the length of the radius vector, no matter where the planet might be in the orbit, would never vary, and the area swept over by it in one day would be equal to the area swept over in any other day, because all these areas would be precisely similar and equal triangles. But Kepler discovered that the same thing is true when the orbit is an ellipse, and when, in consequence of the eccentricity of the orbit, the planet is sometimes farther from the sun than at other times. As the triangular area swept over in a given time increases in length with the planet's recession from the sun, it diminishes in breadth just enough to make up the difference which would otherwise exist between the different areas. This law grows out of the fact that the force of gravitation varies inversely with the square of the distance.

3d Law: The squares of the periods (i. e. times of revolution in their orbits) of the different planets are proportional to the cubes of their mean (average) distances from the sun. The meaning of this will be best explained by an example. Suppose one planet, whose distance we know, has a period only one-eighth as long as that of another planet, whose distance we do not know. Then Kepler's third law enables us to calculate the distance of the second planet. Call the period of the first planet 1, and that of the second 8, and also call the distance of the first 1, since all we really need to know is the relative distance of the second, from which its distance in miles is readily deduced by comparison with the distance of the first. Then, by the law, 1² : 8² : 1³ : x³ (“x” representing the unknown quantity). Now, this is simply a problem in proportion where the product of the means is equal to the product of the extremes. But 1² = 1, and also 1³= 1; therefore x³ = 8², and x = ∛(8²) (the cube root of the square of 8), which is 4. Thus we see that the distance of the second planet must be four times that of the first.

This third law of Kepler is applied to ascertain the distances of newly discovered planets, whose periods are easily ascertained by simple observation. If we know the distance of any one planet by measurement, we can calculate the distances of all the others after observing their periods. The law also works conversely, i. e. from the distances the periods can be calculated.

We now take up the various planets singly. The nearest to the sun, as far as known, is Mercury, its average distance being only 36,000,000 miles. But its orbit is so eccentric that the distance varies from 28,500,000 miles at perihelion to 43,500,000 at aphelion. In consequence its speed in its orbit is very variable, and likewise the amount of heat and light received by it from the sun. On the average it gets more than 6½ times as much solar light and heat as the earth gets. But at perihelion it gets 2½ times as much as at aphelion, and the time which it occupies in passing from perihelion to aphelion is only six weeks, its entire year being equal to 88 of our days. Being situated so much nearer the sun than the earth is, Mercury is never visible to us except in the morning or the evening sky, and then not very far from the sun. Its diameter is about 3000 miles, but its mass is not certainly known from lack of knowledge of its mean density. This lack of knowledge is due to the fact that Mercury has no satellite. When a planet has a satellite it is easy to calculate its density from its measured diameter combined with the orbital speed of its satellite. Certain considerations have led some to believe that the mean density of Mercury may be very great, perhaps as great as that of lead, or of the metal mercury itself. Not knowing the mass, we cannot say exactly what the weight of bodies on Mercury is. We are also virtually ignorant of the condition of the surface of this planet, the telescope revealing very little detail, but it is generally thought that it bears a considerable resemblance to the surface of the moon. There is another way in which Mercury is remarkably like the moon. The latter, as we have seen, always keeps the same side turned toward the earth, which is the same thing as saying that it turns once on its axis, while going once around the earth. So Mercury keeps always the same side toward the sun, making one rotation on its axis in the course of one revolution in its orbit. Consequently, one side of Mercury is continually in the sunlight, while the opposite side is continually buried in night. There must, however, be regions along the border between these two sides, where the sun does rise and set once in the course of one of Mercury's years. This arises from the eccentricity of the orbit, and the consequent variations in the orbital velocity of the planet, which cause now a little of one edge and now a little of the other edge of the dark hemisphere to come within the line of sunlight. (The same thing occurs with the moon, though to a less degree owing to the smaller eccentricity of the moon's orbit, which, however, is sufficient to enable us to see at one time a short distance round one side of the moon and at another time a short distance round the opposite side.) This phenomenon is known as libration. Mercury apparently possesses an atmosphere, but we know nothing certain concerning its density.

The next planet, in the order of distance from the sun, is Venus, whose average distance is 67,200,000 miles. The orbit of Venus is remarkable for its small eccentricity, so that the difference between its greatest and least distances from the sun is less than a million miles. The period, or year, of Venus is 225 of our days. Owing to her situation closer to the sun, she gets nearly twice as much light and heat as the earth gets. In size Venus is remarkably like the earth, her diameter being 7713 miles, which differs by only 205 miles from the mean diameter of the earth. Her axis is nearly perpendicular to the plane of her orbit. Her globe is a more perfect sphere than that of the earth, being very little flattened at the poles or swollen at the equator. Although Venus, like Mercury, has no satellite, her mean density has been calculated by other means, and is found to be 0.89 that of the earth. From this, in connection with her measured diameter, it is easy to deduce her mass, and the force of gravity on her surface. The latter comes out at about 0.85 that of the earth, i. e. a body weighing 100 pounds on the earth would weigh 85 pounds if removed to Venus. She possesses an atmosphere denser and more extensive than would theoretically have been expected—indicating, perhaps, a difference of constitution. Her atmosphere has been estimated to be twice as dense as ours, a great advantage, it may be remarked, from the point of view of aëronautics. But this dense and abundant atmosphere renders Venus a very difficult object for the telescope on account of the brilliance of its reflection. In consequence, we know but little of the surface of the planet.

One important result of this is that the question remains undecided whether Venus rotates on her axis at a rate closely corresponding with that of the earth, as some observers think, or whether, as others think, she, like Mercury, turns only once on her axis in going once round the sun. The importance of the question in its bearing on the habitability of Venus is apparent, for if she keeps one face always sunward, then on one side there is perpetual day and on the other perpetual night. On the other hand, if she has days and nights approximately equal in length to those of the earth, it may well be thought that she is habitable by beings not altogether unlike ourselves, because the force of gravity on her surface is not much less than on the earth, and her dense atmosphere, filled with clouds, might tend to shield her inhabitants from the effects of the greater amount of heat poured upon her by the sun. As her orbit is inside that of the earth, Venus, like Mercury, is only visible either in the evening or in the morning sky, but owing to her greater actual distance from the sun, her apparent distance from it in the sky is greater than that of Mercury.