Fig. 54.—Illustrating the moon's rotation.Fig. 54.—Illustrating the moon's rotation.
99.Cause of librations.—That the moon should librate is by no means so remarkable a fact as that it should at all times turn very nearly the same face toward the earth. This latter fact can have but one meaning: the moon revolves about an axis as does the earth, but the time required for this revolution is just equal to the time required to make a revolution in its orbit. Place two coins upon a table with their heads turned toward the north, as inFig. 54, and move the smaller one around the larger in such a way that its face shall always look away from the larger one. In making one revolution in its orbit the head on this small coin will be successively directed toward every point of the compass, and when it returns to its initial position the small coin will have made just one revolution about an axis perpendicular to the plane of its orbit. In no other way can it be made to face always awayfrom the figure at the center of its orbit while moving around it.
We are now in a position to understand the moon's librations, for, if the small coin at any time moves faster or slower in its orbit than it turns about its axis, a new side will be turned toward the center, and the same may happen if the central coin itself shifts into a new position. This is what happens to the moon, for its orbital motion, like that of Mercury (Fig. 17), is alternately fast and slow, and in addition to this there are present other minor influences, such as the fact that its rotation axis is not exactly perpendicular to the plane of its orbit; in addition to this the observer upon the earth is daily carried by its rotation from one point of view to another, etc., so that it is only in a general way that the rotation upon the axis and motion in the orbit keep pace with each other. In a general way a cable keeps a ship anchored in the same place, although wind and waves may cause it to "librate" about the anchor.
How the moon came to have this exact equality between its times of revolution and rotation constitutes a chapter of its history upon which we shall not now enter; but the equality having once been established, the mechanism by which it is preserved is simple enough.
The attraction of the earth for the moon has very slightly pulled the latter out of shape (§ 42), so that the particular diameter, which points toward the earth, is a little longer than any other, and thus serves as a handle which the earth lays hold of and pulls down into its lowest possible position—i. e., the position in which it points toward the center of the earth. Just how long this handle is, remains unknown, but it may be shown from the law of gravitation that less than a hundred yards of elongation would suffice for the work it has to do.
100.The moon as a world.—Thus far we have considered the moon as a satellite of the earth, dependent upon the earth, and interesting chiefly because of its relation to it.But the moon is something more than this; it is a world in itself, very different from the earth, although not wholly unlike it. The most characteristic feature of the earth's surface is its division into land and water, and nothing of this kind can be found upon the moon. It is true that the first generation of astronomers who studied the moon with telescopes fancied that the large dark patches shown inFig. 55were bodies of water, and named them oceans, seas, lakes, and ponds, and to the present day we keep those names, although it is long since recognized that these parts of the moon's surface are as dry as any other. Their dark appearance indicates a different kind of material from that composing the lighter parts of the moon, material with a different albedo, just as upon the earth we have light-colored and dark-colored rocks, marble and slate, which seen from the moon must present similar contrasts of brightness. Although these dark patches are almost the only features distinguishable with the unaided eye, it is far otherwise in the telescope or the photograph, especially along the ragged edge where great numbers of rings can be seen, which are apparently depressions in the moon and are called craters. These we find in great number all over the moon, but, as the figure shows, they are seen to the best advantage near theterminator—i. e., the dividing line between day and night, since the long shadows cast here by the rising or setting sun bring out the details of the surface better than elsewhere. Carefully examineFig. 55with reference to these features.
Fig. 55.—The moon at first and last quarter. Lick Observatory photographs.Fig. 55.—The moon at first and last quarter. Lick Observatory photographs.
Another feature which exists upon both earth and moon, although far less common there than here, is illustrated in the chain of mountains visible near the terminator, a little above the center of the moon in both parts ofFig. 55. This particular range of mountains, which is called the Lunar Apennines, is by far the most prominent one upon the moon, although others, the Alps and Caucasus, exist. But for the most part the lunar mountainsstand alone, each by itself, instead of being grouped into ranges, as on the earth. Note in the figure that some of the lunar mountains stretch out into the night side of the moon, their peaks projecting up into the sunlight, and thus becoming visible, while the lowlands are buried in the shadow.
A subordinate feature of the moon's surface is the system ofrayswhich seem to radiate like spokes from some of the larger craters, extending over hill and valley sometimes for hundreds of miles. A suggestion of these rays may be seen inFig. 55, extending from the great crater Copernicus a little southwest of the end of the Apennines, but their most perfect development is to be seen at the time of full moon around the crater Tycho, which lies near the south pole of the moon. Look for them with an opera glass.
Another and even less conspicuous feature is furnished by the rills, which, under favorable conditions of illumination, appear like long cracks on the moon's surface, perhaps analogous to the cañons of our Western country.
101.The map of the moon.—Fig. 55furnishes a fairly good map of a limited portion of the moon near the terminator, but at the edges little or no detail can be seen. This is always true; the whole of the moon can not be seen to advantage at any one time, and to remedy this we need to construct from many photographs or drawings a map which shall represent the several parts of the moon as they appear at their best.Fig. 56shows such a map photographed from a relief model of the moon, and representing the principal features of the lunar surface in a way they can never be seen simultaneously. Perhaps its most striking feature is the shape of the craters, which are shown round in the central parts of the map and oval at the edges, with their long diameters parallel to the moon's edge. This is, of course, an effect of the curvature of the moon's surface, for we look very obliquely at the edge portions, and thus see their formationsmuch foreshortened in the direction of the moon's radius.
Fig. 56.—Relief map of the moon's surface.—After Nasmyth and Carpenter.Fig. 56.—Relief map of the moon's surface.—AfterNasmythandCarpenter.
The north and south poles of the moon are at the top and bottom of the map respectively, and a mere inspection of the regions around them will show how much more rugged is the southern hemisphere of the moon than the northern. It furnishes, too, some indication of how numerous are the lunar craters, and how in crowded regions they overlap one another.
The student should pick out upon the map those features which he has learned to know in the photograph (Fig. 55)—the Apennines, Copernicus, and the continuation of the Apennines, extending into the dark part of the moon.
Fig. 57.—Mare Imbrium. Photographed by G. W. Ritchey.Fig. 57.—Mare Imbrium. Photographed byG. W. Ritchey.
102.Size of the lunar features.—We may measure distances here in the same way as upon a terrestrial map, remembering that near the edges the scale of the map is very much distorted parallel to the moon's diameter, and measurements must not be taken in this direction, but may be taken parallel to the edge. Measuring with a millimeter scale, we find on the map for the diameter of the crater Copernicus, 2.1 millimeters. To turn this into the diameter of the real Copernicus in miles, we measure upon the same map the diameter of the moon, 79.7 millimeters, and then have the proportion—
Diameter of Copernicus in miles : 2,163 :: 2.1 : 79.7,
Fig. 58.—Mare Crisium. Lick Observatory photographs.Fig. 58.—Mare Crisium. Lick Observatory photographs.
which when solved gives 57 miles. The real diameter of Copernicus is a trifle over 56 miles. At the eastern edge of the moon, opposite the Apennines, is a large oval spot called the Mare Crisium (Latin,ma-re= sea). Measure itslength. The large crater to the northwest of the Apennines is called Archimedes. Measure its diameter both in the map and in the photograph (Fig. 55), and see how the two results agree. The true diameter of this crater, east and west, is very approximately 50 miles. The great smooth surface to the west of Archimedes is the Mare Imbrium. Is it larger or smaller than Lake Superior?Fig. 57is from a photograph of the Mare Imbrium, and the amount of detail here shown at the bottom of the sea is a sufficient indication that, in this case at least, the water has been drawn off, if indeed any was ever present.
Fig. 58is a representation of the Mare Crisium at a time when night was beginning to encroach upon its eastern border, and it serves well to show the rugged character of the ring-shaped wall which incloses this area.
With these pictures of the smoother parts of the moon's surface we may compareFig. 59, which shows a region near the north pole of the moon, andFig. 60, giving an early morning view of Archimedes and the Apennines. Note how long and sharp are the shadows.
Fig. 59.—Illustrating the rugged character of the moon's surface.—Nasmyth and Carpenter.Fig. 59.—Illustrating the rugged character of the moon's surface.—NasmythandCarpenter.
103.The moon's atmosphere.—Upon the earth the sun casts no shadows so sharp and black as those ofFig. 60, because his rays are here scattered and reflected in all directionsby the dust and vapors of the atmosphere (§ 51), so that the place from which direct sunlight is cut off is at least partially illumined by this reflected light. The shadows ofFig. 60show that upon the moon it must be otherwise, and suggest that if the moon has any atmosphere whatever, its density must be utterly insignificant in comparison with that of the earth. In its motion around the earth the moon frequently eclipses stars (occultsis the technical word), and if the moon had an atmosphere such as is shown inFig. 61, the light from the starAmust shine through this atmosphere just before the moon's advancing body cuts it off, and it must be refracted by the atmosphere so that the star would appear in a slightly different direction (nearer toB) than before. The earth's atmosphere refracts the starlight under such circumstances by more than a degree, but no one has been able to find in the case of the moon any effect of this kind amounting to even a fraction of a second of arc. While this hardly justifies the statement sometimes made that the moon has no atmosphere, we shall be entirely safe in saying that if it has one at all its density is less than a thousandth part of that of the earth's atmosphere. Quite in keeping with this absence of an atmosphere is the fact that clouds never float over the surface of the moon.Its features always stand out hard and clear, without any of that haze and softness of outline which our atmosphere introduces into all terrestrial landscapes.
Fig. 60.—Archimedes and Apennines. Nasmyth and Carpenter.Fig. 60.—Archimedes and Apennines.NasmythandCarpenter.
104.Height of the lunar mountains.—Attention has already been called to the detached mountain peaks, which inFig. 55prolong the range of Apennines into the lunar night. These are the beginnings of the Caucasus mountains, and from the photograph we may measure as follows the height to which they rise above the surrounding level of the moon:Fig. 62represents a part of the lunar surface along the boundary line between night and day, the horizontal line at the top of the figure representing a level ray of sunlight which just touches the moon atTand barely illuminates the top of the mountain,M, whose height,h, is to be determined. If we letRstand for the radius of the moon andsfor the distance,T M, we shall have in the right-angled triangleM T C,
R2+s2= (R+h)2,
and we need only to measures—that is, the distance from the terminator to the detached mountain peak—to make this equation determineh, sinceRis already known, being half the diameter of the moon—1,081 miles. Practically it is more convenient to use instead of this equation anotherform, which the student who is expert in algebra may show to be very nearly equivalent to it:
h(miles)=s2/ 2163,orh(feet)=2.44s2.
Fig. 61.—Occultations and the moon's atmosphere.Fig. 61.—Occultations and the moon's atmosphere.
The distancesmust be expressed in miles in all of these equations. InFig. 55the distance from the terminator to the first detached peak of the Caucasus mountains is 1.7 millimeters = 52 miles, from which we find the height of the mountain to be 1.25 miles, or 6,600 feet.
Fig. 62.—Determining the height of a lunar mountain.Fig. 62.—Determining the height of a lunar mountain.
Two things, however, need to be borne in mind in this connection. On the earth we measure the heights of mountainsabove sea level, while on the moon there is no sea, and our 6,600 feet is simply the height of the mountain top above the level of that particular point in the terminator, from which we measure its distance. So too it is evident from the appearance of things, that the sunlight, instead of just touching the top of the particular mountain whose height we have measured, really extends some little distance down from its summit, and the 6,600 feet is therefore the elevation of the lowest point on the mountains to which the sunlight reaches. The peak itselfmay be several hundred feet higher, and our photograph must be taken at the exact moment when this peak appears in the lunar morning or disappears in the evening if we are to measure the altitude of the mountain's summit. Measure the height of the most northern visible mountain of the Caucasus range. This is one of the outlying spurs of the great mountain Calippus, whose principal peak, 19,000 feet high, is shown inFig. 55as the brightest part of the Caucasus range.
The highest peak of the lunar Apennines, Huyghens, has an altitude of 18,000 feet, and the Leibnitz and Doerfel Mountains, near the south pole of the moon, reach an altitude 50 per cent greater than this, and are probably the highest peaks on the moon. This falls very little short of the highest mountain on the earth, although the moon is much smaller than the earth, and these mountains are considerably higher than anything on the western continent of the earth.
The vagueness of outline of the terminator makes it difficult to measure from it with precision, and somewhat more accurate determinations of the heights of lunar mountains can be obtained by measuring the length of the shadows which they cast, and the depths of craters may also be measured by means of the shadows which fall into them.
105.Craters.—Fig. 63shows a typical lunar crater, and conveys a good idea of the ruggedness of the lunar landscape. Compare the appearance of this crater with the following generalizations, which are based upon the accurate measurement of many such:
A. A crater is a real depression in the surface of the moon, surrounded usually by an elevated ring which rises above the general level of the region outside, while the bottom of the crater is about an equal distance below that level.
B. Craters are shallow, their diameters ranging fromfive times to more than fifty times their depth. Archimedes, whose diameter we found to be 50 miles, has an average depth of about 4,000 feet below the crest of its surrounding wall, and is relatively a shallow crater.
Fig. 63.—A typical lunar crater.—Nasmyth and Carpenter.Fig. 63.—A typical lunar crater.—NasmythandCarpenter.
C. Craters frequently have one or more hills rising within them which, however, rarely, if ever, reach up to the level of the surrounding wall.
D. Whatever may have been the mode of their formation, the craters can not have been produced by scooping out material from the center and piling it up to make the wall, for in three cases out of four the volume of the excavation is greater than the volume of material contained in the wall.
106.Moon and earth.—We have gone far enough now to appreciate both the likeness and the unlikeness of the moon and earth. They may fairly enough be likened to offspring of the same parent who have followed very different careers, and in the fullness of time find themselves in very different circumstances. The most serious point of difference in these circumstances is the atmosphere, which gives to the earth a wealth of phenomena altogether lackingin the moon. Clouds, wind, rain, snow, dew, frost, and hail are all dependent upon the atmosphere and can not be found where it is not. There can be nothing upon the moon at all like that great group of changes which we call weather, and the unruffled aspect of the moon's face contrasts sharply with the succession of cloud and sunshine which the earth would present if seen from the moon.
The atmosphere is the chief agent in the propagation of sound, and without it the moon must be wrapped in silence more absolute than can be found upon the surface of the earth. So, too, the absence of an atmosphere shows that there can be no water or other liquid upon the moon, for if so it would immediately evaporate and produce a gaseous envelope which we have seen does not exist. With air and water absent there can be of course no vegetation or life of any kind upon the moon, and we are compelled to regard it as an arid desert, utterly waste.
107.Temperature of the moon.—A characteristic feature of terrestrial deserts, which is possessed in exaggerated degree by the moon, is the great extremes of temperature to which they and it are subject. Owing to its slow rotation about its axis, a point on the moon receives the solar radiation uninterruptedly for more than a fortnight, and that too unmitigated by any cloud or vaporous covering. Then for a like period it is turned away from the sun and allowed to cool off, radiating into interplanetary space without hindrance its accumulated store of heat. It is easy to see that the range of temperature between day and night must be much greater under these circumstances than it is with us where shorter days and clouded skies render day and night more nearly alike, to say nothing of the ocean whose waters serve as a great balance wheel for equalizing temperatures. Just how hot or how cold the moon becomes is hard to determine, and very different estimates are to be found in the books. Perhaps the most reliable of these are furnished by the recent researches of Professor Very, whoseexperiments lead him to conclude that "its rocky surface at midday, in latitudes where the sun is high, is probably hotter than boiling water and only the most terrible of earth's deserts, where the burning sands blister the skin, and men, beasts, and birds drop dead, can approach a noontide on the cloudless surface of our satellite. Only the extreme polar latitudes of the moon can have an endurable temperature by day, to say nothing of the night, when we should have to become troglodytes to preserve ourselves from such intense cold."
While the night temperature of the moon, even very soon after sunset, sinks to something like 200° below zero on the centigrade scale, or 320° below zero on the Fahrenheit scale, the lowest known temperature upon the earth, according to General Greely, is 90° Fahr. below zero, recorded in Siberia in January, 1885.
Winter and summer are not markedly different upon the moon, since its rotation axis is nearly perpendicular to the plane of the earth's orbit about the sun, and the sun never goes far north or south of the moon's equator. The month is the one cycle within which all seasonal changes in its physical condition appear to run their complete course.
108.Changes in the moon.—It is evidently idle to look for any such changes in the condition of the moon's surface as with us mark the progress of the seasons or the spread of civilization over the wilderness. But minor changes there may be, and it would seem that the violent oscillations of temperature from day to night ought to have some effect in breaking down and crumbling the sharp peaks and crags which are there so common and so pronounced. For a century past astronomers have searched carefully for changes of this kind—the filling up of some crater or the fall of a mountain peak; but while some things of this kind have been reported from time to time, the evidence in their behalf has not been altogether conclusive. At the present time it is an open question whetherchanges of this sort large enough to be seen from the earth are in progress. A crater much less than a mile wide can be seen in the telescope, but it is not easy to tell whether so minute an object has changed in size or shape during a year or a decade, and even if changes are seen they may be apparent rather than real.Fig. 64contains two views of the crater Archimedes, taken under a morning and an afternoon sun respectively, and shows a very pronounced difference between the two which proceeds solely from a difference of illumination. In the presence of such large fictitious changes astronomers are slow to accept smaller ones as real.
Fig. 64.—Archimedes in the lunar morning and afternoon.—Weinek.Fig. 64.—Archimedes in the lunar morning and afternoon.—Weinek.
It is this absence of change that is responsible for the rugged and sharp-cut features of the moon which continue substantially as they were made, while upon the earth rain and frost are continually wearing down the mountains and spreading their substance upon the lowland in an unending process of smoothing off the roughnesses of its surface. Upon the moon this process is almost if not wholly wanting, and the moon abides to-day much more like its primitive condition than is the earth.
109.The moon's influence upon the earth.—There is a widespread popular belief that in many ways the moon exercisesa considerable influence upon terrestrial affairs: that it affects the weather for good or ill, that crops must be planted and harvested, pigs must be killed, and timber cut at the right time of the moon, etc. Our common word lunatic means moonstruck—i. e., one upon whom the moon has shone while sleeping. There is not the slightest scientific basis for any of these beliefs, and astronomers everywhere class them with tales of witchcraft, magic, and popular delusion. For the most part the moon's influence upon the earth is limited to the light which it sends and the effect of its gravitation, chiefly exhibited in the ocean tides. We receive from the moon a very small amount of second-hand solar heat and there is also a trifling magnetic influence, but neither of these last effects comes within the range of ordinary observation, and we shall not go far wrong in saying that, save the moonlight and the tides, every supposed lunar influence upon the earth is either fictitious or too small to be readily detected.
110.Dependence of the earth upon the sun.—There is no better introduction to the study of the sun than Byron's Ode to Darkness, beginning with the lines—
"I dreamed a dreamThat was not all a dream.The bright sun was extinguished,"
"I dreamed a dreamThat was not all a dream.The bright sun was extinguished,"
and proceeding to depict in vivid words the consequences of this extinction. The most matter-of-fact language of science agrees with the words of the poet in declaring the earth's dependence upon the sun for all those varied forms of energy which make it a fit abode for living beings. The winds blow and the rivers run; the crops grow, are gathered and consumed, by virtue of the solar energy. Factory, locomotive, beast, bird, and the human body furnish types of machines run by energy derived from the sun; and the student will find it an instructive exercise to search for kinds of terrestrial energy which are not derived either directly or indirectly from the sun. There are a few such, but they are neither numerous nor important.
111.The sun's distance from the earth.—To the astronomer the sun presents problems of the highest consequence and apparently of very diverse character, but all tending toward the same goal: the framing of a mechanical explanation of the sun considered as a machine; what it is, and how it does its work. In the forefront of these problems stand those numerical determinations of distance, size,mass, density, etc., which we have already encountered in connection with the moon, but which must here be dealt with in a different manner, because the immensely greater distance of the sun makes impossible the resort to any such simple method as the triangle used for determining the moon's distance. It would be like determining the distance of a steeple a mile away by observing its direction first from one eye, then from the other; too short a base for the triangle. In one respect, however, we stand upon a better footing than in the case of the moon, for the mass of the earth has already been found (Chapter IV) as a fractional part of the sun's mass, and we have only to invert the fraction in order to find that the sun's mass is 329,000 times that of the earth and moon combined, or 333,000 times that of the earth alone.
If we could rely implicitly upon this number we might make it determine for us the distance of the sun through the law of gravitation as follows: It was suggested in§ 38that Newton proved Kepler's three laws to be imperfect corollaries from the law of gravitation, requiring a little amendment to make them strictly correct, and below we give in the form of an equation Kepler's statement of the Third Law together with Newton's amendment of it. In these equations—
T= Periodic time of any planet;
a= One half the major axis of its orbit;
m= Its mass;
M= The mass of the sun;
k= The gravitation constant corresponding to the particular set of units in whichT,a,m, andMare expressed.
(Kepler)a3/T2=h; (Newton)a3/T2=k(M+m).
Kepler's idea was: For every planet which moves around the sun,a3divided byT2always gives the same quotient,h; and he did not concern himself with the significanceof this quotient further than to note that if the particularaandTwhich belong to any planet—e. g., the earth—be taken as the units of length and time, then the quotient will be 1. Newton, on the other hand, attached a meaning to the quotient, and showed that it is equal to the product obtained by multiplying the sum of the two masses, planet and sun, by a number which is always the same when we are dealing with the action of gravitation, whether it be between the sun and planet, or between moon and earth, or between the earth and a roast of beef in the butcher's scales, provided only that we use always the same units with which to measure times, distances, and masses.
Numerically, Newton's correction to Kepler's Third Law does not amount to much in the motion of the planets. Jupiter, which shows the greatest effect, makes the circuit of his orbit in 4,333 days instead of 4,335, which it would require if Kepler's law were strictly true. But in another respect the change is of the utmost importance, since it enables us to extend Kepler's law, which relates solely to the sun and its planets, to other attracting bodies, such as the earth, moon, and stars. Thus for the moon's motion around the earth we write—
(240,000)3/(27.32)2=k(1 + 1/81),
from which we may find that, with the units here employed, the earth's mass as the unit of mass, the mean solar day as the unit of time, and the mile as the unit of distance—
k= 1830 × 1010.
If we introduce this value ofkinto the corresponding equation, which represents the motion of the earth around the sun, we shall have—
a3/(365.25)2= 1830 × 1010(333,000 + 1),
where the large number in the parenthesis represents the number of times the mass of the sun is greater than the mass of the earth. We shall find by solving this equation thata, the mean distance of the sun from the earth, is very approximately 93,000,000 miles.
113.Another method of determining the sun's distance.—This will be best appreciated by a reference toFig. 17. It appears here that the earth makes its nearest approach to the orbit of Mars in the month of August, and if in any August Mars happens to be in opposition, its distance from the earth will be very much less than the distance of the sun from the earth, and may be measured by methods not unlike those which served for the moon. If now the orbits of Mars and the earth were circles having their centers at the sun this distance between them, which we may represent byD, would be the difference of the radii of these orbits—
D=a''-a',
where the accents '', ' represent Mars and the earth respectively. Kepler's Third Law furnishes the relation—
(a'')3/(T'')2= (a')3/(T')2;
and since the periodic times of the earth and Mars,T',T'', are known to a high degree of accuracy, these two equations are sufficient to determine the two unknown quantities,a',a''—i. e., the distance of the sun from Mars as well as from the earth. The first of these equations is, of course, not strictly true, on account of the elliptical shape of the orbits, but this can be allowed for easily enough.
In practice it is found better to apply this method of determining the sun's distance through observations of an asteroid rather than observations of Mars, and great interest has been aroused among astronomers by the discovery, in 1898, of an asteroid, or planet, Eros, which at times comes much closer to the earth than does Mars or any other heavenlybody except the moon, and which will at future oppositions furnish a more accurate determination of the sun's distance than any hitherto available. Observations for this purpose are being made at the present time (October, 1900).
Many other methods of measuring the sun's distance have been devised by astronomers, some of them extremely ingenious and interesting, but every one of them has its weak point—e. g., the determination of the mass of the earth in the first method given above and the measurement ofDin the second method, so that even the best results at present are uncertain to the extent of 200,000 miles or more, and astronomers, instead of relying upon any one method, must use all of them, and take an average of their results. According to Professor Harkness, this average value is 92,796,950 miles, and it seems certain that a line of this length drawn from the earth toward the sun would end somewhere within the body of the sun, but whether on the nearer or the farther side of the center, or exactly at it, no man knows.
114.Parallax and distance.—It is quite customary among astronomers to speak of the sun's parallax, instead of its distance from the earth, meaning by parallax its difference of direction as seen from the center and surface of the earth—i. e., the angle subtended at the sun by a radius of the earth placed at right angles to the line of sight. The greater the sun's distance the smaller will this angle be, and it therefore makes a substitute for the distance which has the advantage of being represented by a small number, 8".8, instead of a large one.
The books abound with illustrations intended to help the reader comprehend how great is a distance of 93,000,000 miles, but a single one of these must suffice here. To ride 100 miles a day 365 days in the year would be counted a good bicycling record, but the rider who started at the beginning of the Christian era and rode at that rate toward the sun from the year 1A. D.down to the present momentwould not yet have reached his destination, although his journey would be about three quarters done. He would have crossed the orbit of Venus about the time of Charlemagne, and that of Mercury soon after the discovery of America.
115.Size and density of the sun.—Knowing the distance of the sun, it is easy to find from the angle subtended by its diameter (32 minutes of arc) that the length of that diameter is 865,000 miles. We recall in this connection that the diameter of the moon'sorbitis only 480,000 miles, but little more than half the diameter of the sun, thus affording abundant room inside the sun, and to spare, for the moon to perform the monthly revolution about its orbit, as shown inFig. 65.
Fig. 65.—The sun's size.—Young.Fig. 65.—The sun's size.—Young.
In the same manner in which the density of the moon was found from its mass and diameter, the student may find from the mass and diameter of the sun given above that its mean density is 1.4 times that of water. This is about the same as the density of gravel or soft coal, andis just about one quarter of the average density of the earth.
We recall that the small density of the moon was accounted for by the diminished weight of objects upon it, but this explanation can not hold in the case of the sun, for not only is the density less but the force of gravity (weight) is there 28 times as great as upon the earth. The athlete who here weighs 175 pounds, if transported to the surface of the sun would weigh more than an elephant does here, and would find his bones break under his own weight if his muscles were strong enough to hold him upright. The tremendous pressure exerted by gravity at the surface of the sun must be surpassed below the surface, and as it does not pack the material together and make it dense, we are driven to one of two conclusions: Either the stuff of which the sun is made is altogether unlike that of the earth, not so readily compressed by pressure, or there is some opposing influence at work which more than balances the effect of gravity and makes the solar stuff much lighter than the terrestrial.
116.Material of which the sun is made.—As to the first of these alternatives, the spectroscope comes to our aid and shows in the sun's spectrum (Fig. 50) the characteristic line markedD, which we know always indicates the presence of sodium and identifies at least one terrestrial substance as present in the sun in considerable quantity. The lines markedCandFare produced by hydrogen, which is one of the constituents of water,Eshows calcium to be present in the sun,bmagnesium, etc. In this way it has been shown that about one half of our terrestrial elements, mainly the metallic ones, are present as gases on or near the sun's surface, but it must not be inferred that elements not found in this way are absent from the sun. They may be there, probably are there, but the spectroscopic proof of their presence is more difficult to obtain. Professor Rowland, who has been prominent in the study of the solarspectrum, says: "Were the whole earth heated to the temperature of the sun, its spectrum would probably resemble that of the sun very closely."
Some of the common terrestrial elements found in the sun are:
Aluminium.Calcium.Carbon.Copper.Hydrogen.Iron.Lead.Nickel.Potassium.Silicon.Silver.Sodium.Tin.Zinc.Oxygen (?)
Whatever differences of chemical structure may exist between the sun and the earth, it seems that we must regard these bodies as more like than unlike to each other in substance, and we are brought back to the second of our alternatives: there must be some influence opposing the force of gravity and making the substance of the sun light instead of heavy, and we need not seek far to find it in—
117.The heat of the sun.—That the sun is hot is too evident to require proof, and it is a familiar fact that heat expands most substances and makes them less dense. The sun's heat falling upon the earth expands it and diminishes its density in some small degree, and we have only to imagine this process of expansion continued until the earth's diameter becomes 58 per cent larger than it now is, to find the earth's density reduced to a level with that of the sun. Just how much the temperature of the earth must be raised to produce this amount of expansion we do not know, neither do we know accurately the temperature of the sun, but there can be no doubt that heat is the cause of the sun's low density and that the corresponding temperature is very high.
Before we inquire more closely into the sun's temperature,it will be well to draw a sharp distinction between the two terms heat and temperature, which are often used as if they meant the same thing. Heat is a form of energy which may be found in varying degree in every substance, whether warm or cold—a block of ice contains a considerable amount of heat—while temperature corresponds to our sensations of warm and cold, and measures the extent to which heat is concentrated in the body. It is the amount of heat per molecule of the body. A barrel of warm water contains more heat than the flame of a match, but its temperature is not so high. Bearing in mind this distinction, we seek to determine not the amount of heat contained in the sun but the sun's temperature, and this involves the same difficulty as does the question, What is the temperature of a locomotive? It is one thing in the fire box and another thing in the driving wheels, and still another at the headlight; and so with the sun, its temperature is certainly different in different parts—one thing at the center and another at the surface. Even those parts which we see are covered by a veil of gases which produce by absorption the dark lines of the solar spectrum, and seriously interfere both with the emission of energy from the sun and with our attempts at measuring the temperature of those parts of the surface from which that energy streams.
In view of these and other difficulties we need not be surprised that the wildest discordance has been found in estimates of the solar temperature made by different investigators, who have assigned to it values ranging from 1,400° C. to more than 5,000,000° C. Quite recently, however, improved methods and a better understanding of the problem have brought about a better agreement of results, and it now seems probable that the temperature of the visible surface of the sun lies somewhere between 5,000° and 10,000° C., say 15,000° of the Fahrenheit scale.
118.Determining the sun's temperature.—One ingenious method which has been used for determining this temperatureis based upon the principle stated above, that every object, whether warm or cold, contains heat and gives it off in the form of radiant energy. The radiation from a body whose temperature is lower than 500° C. is made up exclusively of energy whose wave length is greater than 7,600 tenth meters, and is therefore invisible to the eye, although a thermometer or even the human hand can often detect it as radiant heat. A brick wall in the summer sunshine gives off energy which can be felt as heat but can not be seen. When such a body is further heated it continues to send off the same kinds (wave lengths) of energy as before, but new and shorter waves are added to its radiation, and when it begins to emit energy of wave length 7,500 or 7,600 tenth meters, it also begins to shine with a dull-red light, which presently becomes brighter and less ruddy and changes to white as the temperature rises, and waves of still shorter length are thereby added to the radiation. We say, in common speech, the body becomes first red hot and then white hot, and we thus recognize in a general way that the kind or color of the radiation which a body gives off is an index to its temperature. The greater the proportion of energy of short wave lengths the higher is the temperature of the radiating body. In sunlight the maximum of brilliancy to the eye lies at or near the wave length, 5,600 tenth meters, but the greatest intensity of radiation of all kinds (light included) is estimated to fall somewhere between green and blue in the spectrum at or near the wave length 5,000 tenth meters, and if we can apply to this wave length Paschen's law—temperature reckoned in degrees centigrade from the absolute zero is always equal to the quotient obtained by dividing the number 27,000,000 by the wave length corresponding to maximum radiation—we shall find at once for the absolute temperature of the sun's surface 5,400° C.
Paschen's law has been shown to hold true, at least approximately, for lower temperatures and longer wavelengths than are here involved, but as it is not yet certain that it is strictly true and holds for all temperatures, too great reliance must not be attached to the numerical result furnished by it.