THE LICK OBSERVATORY, MOUNT HAMILTON, CAL.THE LICK OBSERVATORY, MOUNT HAMILTON, CAL.
In general each planet works ceaselessly upon the orbit of every other, changing its size and shape and position, backward and forward in accordance with the law of gravitation, and it is a question of serious moment how far this process may extend. If the diameter of the earth's orbit were very much increased or diminished by the perturbing action of the other planets, the amount of heat received from the sun would be correspondingly changed, and theearth, perhaps, be rendered unfit for the support of life. The tipping of the plane of the earth's orbit into a new position might also produce serious consequences; but the great French mathematician of a century ago, Laplace, succeeded in proving from the law of gravitation that although both of these changes are actually in progress they can not, at least for millions of years, go far enough to prove of serious consequence, and the same is true for all the other planets, unless here and there an asteroid may prove an exception to the rule.
The precession (Chapter V) is a striking illustration of a perturbation of slightly different character from the above, and another is found in connection with the plane of the moon's orbit. It will be remembered that the moon in its motion among the stars never goes far from the ecliptic, but in a complete circuit of the heavens crosses it twice, once in going from south to north and once in the opposite direction. The points at which it crosses the ecliptic are called thenodes, and under the perturbing influence of the sun these nodes move westward along the ecliptic about twenty degrees per year, an extraordinarily rapid perturbation, and one of great consequence in the theory of eclipses.
Fig. 22.—A planet subject to great perturbations by Jupiter.Fig. 22.—A planet subject to great perturbations by Jupiter.
40.Weighing the planets.—Although these perturbations can not be considered dangerous, they are interesting since they furnish a method for weighing the planets which produce them. From the law of gravitation we learn that the ability of a planet to produce perturbations depends directly upon its mass, since the forceFwhich it exerts contains this mass,m', as a factor. So, too, the divisorr2in the expression for the force shows that the distance between the disturbing and disturbed bodies is a matter of great consequence, for the smaller the distance the greater the force. When, therefore, the mass of a planet such as Jupiter is to be determined from the perturbations it produces, it is customary to select some such opportunity asis presented inFig. 22, where one of the small planets, called asteroids, is represented as moving in a very eccentric orbit, which at one point approaches close to the orbit of Jupiter, and at another place comes near to the orbit of the earth. For the most part Jupiter will not exert any very great disturbing influence upon a planet moving in such an orbit as this, since it is only at rare intervals that the asteroid and Jupiter approach so close to each other, as is shown in the figure. The time during which the asteroid is little affected by the attraction of Jupiter is used to study the motion given to it by the sun's attraction—that is, to determine carefully the undisturbed orbit in which it moves; but there comes a time at which the asteroid passes close to Jupiter, as shown in the figure, and the orbital motion which the sun imparts to it will then be greatly disturbed, and when the planet next comes round to the part of its orbit near the earth the effect of these disturbances upon its apparent position in the sky will be exaggerated by its close proximity to the earth. If now the astronomer observes the actual position of the asteroid in the sky, its right ascension and declination, and compares these with the position assigned to the planet by the law of gravitation when the attraction of Jupiter is ignored, the differences between the observed right ascensions and declinations and those computed upon the theory of undisturbed motion will measure the influence that Jupiter has had upon the asteroid, and the amount by which Jupiter has shifted it, compared with the amount by which the sun has moved it—that is, with the motion in its orbit—furnishesthe mass of Jupiter expressed as a fractional part of the mass of the sun.
There has been determined in this manner the mass of every planet in the solar system which is large enough to produce any appreciable perturbation, and all these masses prove to be exceedingly small fractions of the mass of the sun, as may be seen from the following table, in which is given opposite the name of each planet the number by which the mass of the sun must be divided in order to get the mass of the planet:
Mercury7,000,000 (?)Venus408,000Earth329,000Mars3,093,500Jupiter1,047.4Saturn3,502Uranus22,800Neptune19,700
It is to be especially noted that the mass given for each planet includes the mass of all the satellites which attend it, since their influence was felt in the perturbations from which the mass was derived. Thus the mass assigned to the earth is the combined mass of earth and moon.
41.Discovery of Neptune.—The most famous example of perturbations is found in connection with the discovery, in the year 1846, of Neptune, the outermost planet of the solar system. For many years the motion of Uranus, his next neighbor, had proved a puzzle to astronomers. In accordance with Kepler's first law this planet should move in an ellipse having the sun at one of its foci, but no ellipse could be found which exactly fitted its observed path among the stars, although, to be sure, the misfit was not very pronounced. Astronomers surmised that the small deviations of Uranus from the best path which theory combined with observation could assign, were due to perturbations in itsmotion caused by an unknown planet more remote from the sun—a thing easy to conjecture but hard to prove, and harder still to find the unknown disturber. But almost simultaneously two young men, Adams in England and Le Verrier in France, attacked the problem quite independently of each other, and carried it to a successful solution, showing that if the irregularities in the motion of Uranus were indeed caused by an unknown planet, then that planet must, in September, 1846, be in the direction of the constellation Aquarius; and there it was found on September 23d by the astronomers of the Berlin Observatory whom Le Verrier had invited to search for it, and found within a degree of the exact point which the law of gravitation in his hands had assigned to it.
This working backward from the perturbations experienced by Uranus to the cause which produced them is justly regarded as one of the greatest scientific achievements of the human intellect, and it is worthy of note that we are approaching the time at which it may be repeated, for Neptune now behaves much as did Uranus three quarters of a century ago, and the most plausible explanation which can be offered for these anomalies in its path is that the bounds of the solar system must be again enlarged to include another disturbing planet.
42.The shape of a planet.—There is an effect of gravitation not yet touched upon, which is of considerable interest and wide application in astronomy—viz., its influence in determining the shape of the heavenly bodies. The earth is a globe because every part of it is drawn toward the center by the attraction of the other parts, and if this attraction on its surface were everywhere of equal force the material of the earth would be crushed by it into a truly spherical form, no matter what may have been the shape in which it was originally made. But such is not the real condition of the earth, for its diurnal rotation develops in every particle of its body a force which is sometimes calledcentrifugal,but which is really nothing more than the inertia of its particles, which tend at every moment to keep unchanged the direction of their motion and which thus resist the attraction that pulls them into a circular path marked out by the earth's rotation, just as a stone tied at the end of a string and swung swiftly in a circle pulls upon the string and opposes the constraint which keeps it moving in a circle. A few experiments with such a stone will show that the faster it goes the harder does it pull upon the string, and the same is true of each particle of the earth, the swiftly moving ones near the equator having a greater centrifugal force than the slow ones near the poles. At the equator the centrifugal force is directly opposed to the force of gravity, and in effect diminishes it, so that, comparatively, there is an excess of gravity at the poles which compresses the earth along its axis and causes it to bulge out at the equator until a balance is thus restored. As we have learned from the study of geography, in the case of the earth, this compression amounts to about 27 miles, but in the larger planets, Jupiter and Saturn, it is much greater, amounting to several thousand miles.
But rotation is not the only influence that tends to pull a planet out of shape. The attraction which the earth exerts upon the moon is stronger on the near side and weaker on the far side of our satellite than at its center, and this difference of attraction tends to warp the moon, as is illustrated inFig. 23where1,2, and3represent pieces of iron of equal mass placed in line on a table near a horseshoe magnet,H. Each piece of iron is attracted by the magnet and is held back by a weight to which it is fastened by means of a cord running over a pulley,P, at the edge of the table. These weights are all to be supposed equally heavy and each of them pulls upon its piece of iron with a force just sufficient to balance the attraction of the magnet for the middle piece, No.2. It is clear that under this arrangement No.2will moveneither to the right nor to the left, since the forces exerted upon it by the magnet and the weight just balance each other. Upon No.1, however, the magnet pulls harder than upon No.2, because it is nearer and its pull therefore more than balances the force exerted by the weight, so that No.1will be pulled away from No.2and will stretch the elastic cords, which are represented by the lines joining1and2, until their tension, together with the force exerted by the weight, just balances the attraction of the magnet. For No.3, the force exerted by the magnet is less than that of the weight, and it will also be pulled away from No.2until its elastic cords are stretched to the proper tension. The net result is that the three blocks which, without the magnet's influence, would be held close together by the elastic cords, are pulled apart by this outside force as far as the resistance of the cords will permit.
Fig. 23.—Tide-raising forces.Fig. 23.—Tide-raising forces.
An entirely analogous set of forces produces a similar effect upon the shape of the moon. The elastic cords ofFig. 23stand for the attraction of gravitation by which all the parts of the moon are bound together. The magnet represents the earth pulling with unequal force upon different parts of the moon. The weights are the inertia of the moon in its orbital motion which, as we have seen in aprevious section, upon the whole just balances the earth's attraction and keeps the moon from falling into it. The effect of these forces is to stretch out the moon along a line pointing toward the earth, just as the blocks were stretched out along the line of the magnet, and to make this diameter of the moon slightly but permanently longer than the others.
Fig. 24.—The tides.Fig. 24.—The tides.
The tides.—Similarly the moon and the sun attract opposite sides of the earth with different forces and feebly tend to pull it out of shape. But here a new element comes into play: the earth turns so rapidly upon its axis that its solid parts have no time in which to yield sensibly to the strains, which shift rapidly from one diameter to another as different parts of the earth are turned toward the moon, and it is chiefly the waters of the sea which respond to the distorting effect of the sun's and moon's attraction. These are heaped up on opposite sides of the earth so as to produce a slight elongation of its diameter, andFig. 24shows how by the earth's rotation this swelling of the waters is swept out from under the moon and is pulled back by the moon until it finally takes up some such position as that shown in the figure where the effect of the earth's rotation in carrying it one way is just balanced by the moon's attraction urging it back on line with the moon. This heaping up of the waters is called atide. IfIin the figure represents a little island in the sea the waters which surround it will of course accompany it in its diurnal rotation about the earth's axis, but whenever the island comes back to thepositionI, the waters will swell up as a part of the tidal wave and will encroach upon the land in what is called high tide or flood tide. So too when they reachI'', half a day later, they will again rise in flood tide, and midway between these points, atI', the waters must subside, giving low or ebb tide.
The height of the tide raised by the moon in the open sea is only a very few feet, and the tide raised by the sun is even less, but along the coast of a continent, in bays and angles of the shore, it often happens that a broad but low tidal wave is forced into a narrow corner, and then the rise of the water may be many feet, especially when the solar tide and the lunar tide come in together, as they do twice in every month, at new and full moon. Why do they come together at these times instead of some other?
Small as are these tidal effects, it is worth noting that they may in certain cases be very much greater—e. g., if the moon were as massive as is the sun its tidal effect would be some millions of times greater than it now is and would suffice to grind the earth into fragments. Although the earth escapes this fate, some other bodies are not so fortunate, and we shall see in later chapters some evidence of their disintegration.
43.The scope of the law of gravitation.—In all the domain of physical science there is no other law so famous as the Newtonian law of gravitation; none other that has been so dwelt upon, studied, and elaborated by astronomers and mathematicians, and perhaps none that can be considered so indisputably proved. Over and over again mathematical analysis, based upon this law, has pointed out conclusions which, though hitherto unsuspected, have afterward been found true, as when Newton himself derived as a corollary from this law that the earth ought to be flattened at the poles—a thing not known at that time, and not proved by actual measurement until long afterward. It is, in fact, this capacity for predicting the unknown and for explainingin minutest detail the complicated phenomena of the heavens and the earth that constitutes the real proof of the law of gravitation, and it is therefore worth while to note that at the present time there are a very few points at which the law fails to furnish a satisfactory account of things observed. Chief among these is the case of the planet Mercury, the long diameter of whose orbit is slowly turning around in a way for which the law of gravitation as yet furnishes no explanation. Whether this is because the law itself is inaccurate or incomplete, or whether it only marks a case in which astronomers have not yet properly applied the law and traced out its consequences, we do not know; but whether it be the one or the other, this and other similar cases show that even here, in its most perfect chapter, astronomy still remains an incomplete science.
44.The size of the earth.—The student is presumed to have learned, in his study of geography, that the earth is a globe about 8,000 miles in diameter and, without dwelling upon the "proofs" which are commonly given for these statements, we proceed to consider the principles upon which the measurement of the earth's size and shape are based.
Fig. 25.—Measuring the size of the earth.Fig. 25.—Measuring the size of the earth.
InFig. 25the circle represents a meridian section of the earth;P P'is the axis about which it rotates, and the dotted lines represent a beam of light coming from a star in the plane of the meridian, and so distant that the dotted lines are all practically parallel to each other. The several radii drawn through the points1,2,3, represent the direction of the vertical at these points, and the angles which these radii produced, make with the rays of starlight are each equal to the angular distance of the star from the zenith of the place at the moment the star crosses the meridian. We have already seen, inChapter II, how these angles may be measured, and it is apparent from the figure that the difference between any two of these angles—e. g.,the angles at1and2—is equal to the angle at the center,O, between the points1and2. By measuring these angular distances of the star from the zenith, the astronomer finds the angles at the center of the earth between the stations1,2,3, etc., at which his observations are made. If the meridian were a perfect circle the change of zenith distance of the star, as one traveled along a meridian from the equator to the pole, would be perfectly uniform—the same number of degrees for each hundred miles traveled—and observations made in many parts of the earth show that this is very nearly true, but that, on the whole, as we approach the pole it is necessary to travel a little greater distance than is required for a given change in the angle at the equator. The earth is, in fact, flattened at the poles to the amount of about 27 miles in the length of its diameter, and by this amount, as well as by smaller variations due to mountains and valleys, the shape of the earth differs from a perfect sphere. These astronomical measurements of the curvature of the earth's surface furnish by far the most satisfactory proof that it is very approximately a sphere, and furnish as its equatorial diameter 7,926 miles.
Neglecting thecompression, as it is called, i. e., the 27 miles by which the equatorial diameter exceeds the polar, the size of the earth may easily be found by measuring the distance1-2along the surface and by combining with this the angle1 O 2obtained through measuring the meridian altitudes of any star as seen from1and2. Draw on paper an angle equal to the measured difference of altitude and find how far you must go from its vertex in order to have the distance between the sides, measured along an arc of a circle, equal to the measured distance between1and2. This distance from the vertex will be the earth's radius.
Exercise 19.—Measure the diameter of the earth by the method given above. In order that this may be done satisfactorily, the two stations at which observations are made must be separated by a considerable distance—i. e.,200 miles. They need not be on the same meridian, but if they are on different meridians in place of the actual distance between them, there must be used the projection of that distance upon the meridian—i. e., the north and south part of the distance.
By co-operation between schools in the Northern and Southern States, using a good map to obtain the required distances, the diameter of the earth may be measured with the plumb-line apparatus described inChapter IIand determined within a small percentage of its true value.
45.The mass of the earth.—We have seen inChapter IVthe possibility of determining the masses of the planets as fractional parts of the sun's mass, but nothing was there shown, or could be shown, about measuring these masses after the common fashion in kilogrammes or tons. To do this we must first get the mass of the earth in tons or kilogrammes, and while the principles involved in this determination are simple enough, their actual application is delicate and difficult.
Fig. 26.—Illustrating the principles involved in weighing the earth.Fig. 26.—Illustrating the principles involved in weighing the earth.
InFig. 26we suppose a long plumb line to be suspended above the surface of the earth and to be attracted toward the center of the earth,C, by a force whose intensity is (Chapter IV)
F=kmE/R2,
whereEdenotes the mass of the earth, which is to be determined by experiment, andRis the radius of the earth, 3,963 miles. If there is no disturbing influence present,the plumb line will point directly downward, but if a massive ball of lead or other heavy substance is placed at one side,1, it will attract the plumb line with a force equal to
f=kmB/r2,
whereris the distance of its center from the plumb bob andBis its mass which we may suppose, for illustration, to be a ton. In consequence of this attraction the plumb line will be pulled a little to one side, as shown by the dotted line, and if we represent bylthe length of the plumb line and bydthe distance between the original and the disturbed positions of the plumb bob we may write the proportion
F:f::l:d;
and introducing the values ofFandfgiven above, and solving forEthe proportion thus transformed, we find
E=B·l/d· (R/r)2.
In this equation the mass of the ball,B, the length of the plumb line,l, the distance between the center of the ball and the center of the plumb bob,r, and the radius of the earth,R, can all be measured directly, andd, the amount by which the plumb bob is pulled to one side by the ball, is readily found by shifting the ball over to the other side, at2, and measuring with a microscope how far the plumb bob moves. This distance will, of course, be equal to2 d.
By methods involving these principles, but applied in a manner more complicated as well as more precise, the mass of the earth is found to be, in tons, 6,642 × 1018—i. e., 6,642 followed by 18 ciphers, or in kilogrammes 60,258 × 1020. The earth's atmosphere makes up about a millionth part of this mass.
If the length of the plumb line were 100 feet, the weight of the ball a ton, and the distance between the twopositions of the ball,1and2, six feet, how many inches,d, would the plumb bob be pulled out of place?
Find from the mass of the earth and the data of§ 40the mass of the sun in tons. Find also the mass of Mars. The computation can be very greatly abridged by the use of logarithms.
46.Precession.—That the earth is isolated in space and has no support upon which to rest, is sufficiently shown by the fact that the stars are visible upon every side of it, and no support can be seen stretching out toward them. We must then consider the earth to be a globe traveling freely about the sun in a circuit which it completes once every year, and rotating once in every twenty-four hours about an axis which remains at all seasons directed very nearly toward the star Polaris. The student should be able to show from his own observations of the sun that, with reference to the stars, the direction of the sun from the earth changes about a degree a day. Does this prove that the earth revolves about the sun?
But it is only in appearance that the pole maintains its fixed position among the stars. If photographs are taken year after year, after the manner ofExercise 7, it will be found that slowly the pole is moving (nearly) toward Polaris, and making this star describe a smaller and smaller circle in its diurnal path, while stars on the other side of the pole (in right ascension 12h.) become more distant from it and describe larger circles in their diurnal motion; but the process takes place so slowly that the space of a lifetime is required for the motion of the pole to equal the angular diameter of the full moon.
Spin a top and note how its rapid whirl about its axis corresponds to the earth's diurnal rotation. When the axis about which the top spins is truly vertical the top "sleeps"; but if the axis is tipped ever so little away from the vertical it begins to wobble, so that if we imagine the axis prolonged out to the sky and provided with a pencil point asa marker, this would trace a circle around the zenith, along which the pole of the top would move, and a little observation will show that the more the top is tipped from the vertical the larger does this circle become and the more rapidly does the wobbling take place. Were it not for the spinning of the top about its axis, it would promptly fall over when tipped from the vertical position, but the spin combines with the force which pulls the top over and produces the wobbling motion. Spin the top in opposite directions, with the hands of a watch and contrary to the hands of a watch, and note the effect which is produced upon the wobbling.
The earth presents many points of resemblance to the top. Its diurnal rotation is the spin about the axis. This axis is tipped 23.5° away from the perpendicular to its orbit (obliquity of the ecliptic) just as the axis of the top is tipped away from the vertical line. In consequence of its rapid spin, the body of the earth bulges out at the equator (27 miles), and the sun and moon, by virtue of their attraction (seeChapter IV), lay hold of this protuberance and pull it down toward the plane of the earth's orbit, so that if it were not for the spin this force would straighten the axis up and set it perpendicular to the orbit plane. But here, as in the case of the top, the spin and the tipping force combine to produce a wobble which is called precession, and whose effect we recognize in the shifting position of the pole among the stars. The motion of precession is very much slower than the wobbling of the top, since the tipping force for the earth is relatively very small, and a period of nearly 26,000 years is required for a complete circuit of the pole about its center of motion. Friction ultimately stops both the spin and the wobble of the top, but this influence seems wholly absent in the case of the earth, and both rotation and precession go on unchanged from century to century, save for certain minor forces which for a time change the direction or rate of the precessionalmotion, first in one way and then in another, without in the long run producing any results of consequence.
The center of motion, about which the pole travels in a small circle having an angular radius of 23.5°, is at that point of the heavens toward which a perpendicular to the plane of the earth's orbit points, and may be found on the star map in right ascension 18h. 0m. and declination 66.5°.
Exercise 20.—Find this point on the map, and draw as well as you can the path of the pole about it. The motion of the pole along its path is toward the constellation Cepheus. Mark the position of the pole along this path at intervals of 1,000 years, and refer to these positions in dealing with some of the following questions:
Does the wobbling of the top occur in the same direction as the motion of precession? Do the tipping forces applied to the earth and top act in the same direction? What will be the polar star 12,000 years hence? The Great Pyramid of Egypt is thought to have been used as an observatory when Alpha Draconis was the bright star nearest the pole. How long ago was that?
The motion of the pole of course carries the equator and the equinoxes with it, and thus slowly changes the right ascensions and declinations of all the stars. On this account it is frequently called the precession of the equinoxes, and this motion of the equinox, slow though it is, is a matter of some consequence in connection with chronology and the length of the year.
Will the precession ever bring back the right ascensions and declinations to be again what they now are?
In what direction is the pole moving with respect to the Big Dipper? Will its motion ever bring it exactly to Polaris? How far away from Polaris will the precession carry the pole? What other bright stars will be brought near the pole by the precession?
47.The warming of the earth.—Winter and summer alike the day is on the average warmer than the night, and it iseasy to see that this surplus of heat comes from the sun by day and is lost by night through radiation into the void which surrounds the earth; just as the heat contained in a mass of molten iron is radiated away and the iron cooled when it is taken out from the furnace and placed amid colder surroundings. The earth's loss of heat by radiation goes on ceaselessly day and night, and were it not for the influx of solar heat this radiation would steadily diminish the temperature toward what is called the "absolute zero"—i. e., a state in which all heat has been taken away and beyond which there can be no greater degree of cold. This must not be confounded with the zero temperatures shown by our thermometers, since it lies nearly 500° below the zero of the Fahrenheit scale (-273° Centigrade), a temperature which by comparison makes the coldest winter weather seem warm, although the ordinary thermometer may register many degrees below its zero. The heat radiated by the sun into the surrounding space on every side of it is another example of the same cooling process, a hot body giving up its heat to the colder space about it, and it is the minute fraction of this heat poured out by the sun, and in small part intercepted by the earth, which warms the latter and produces what we call weather, climate, the seasons, etc.
Observe the fluctuations, the ebb and flow, which are inherent in this process. From sunset to sunrise there is nothing to compensate the steady outflow of heat, and air and ground grow steadily colder, but with the sunrise there comes an influx of solar heat, feeble at first because it strikes the earth's surface very obliquely, but becoming more and more efficient as the sun rises higher in the sky. But as the air and the ground grow warm during the morning hours they part more and more readily and rapidly with their store of heat, just as a steam pipe or a cup of coffee radiates heat more rapidly when very hot. The warmest hour of the day is reached when these opposing tendencies of income and expenditure of heat are just balanced; andbarring such disturbing factors as wind and clouds, the gain in temperature usually extends to the time—an hour or two beyond noon—at which the diminishing altitude of the sun renders his rays less efficient, when radiation gains the upper hand and the temperature becomes for a short time stationary, and then commences to fall steadily until the next sunrise.
We have here an example of what is called a periodic change—i. e., one which, within a definite and uniform period (24 hours), oscillates from a minimum up to a maximum temperature and then back again to a minimum, repeating substantially the same variation day after day. But it must be understood that minor causes not taken into account above, such as winds, water, etc., produce other fluctuations from day to day which sometimes obscure or even obliterate the diurnal variation of temperature caused by the sun.
Expose the back of your hand to the sun, holding the hand in such a position that the sunlight strikes perpendicularly upon it; then turn the hand so that the light falls quite obliquely upon it and note how much more vigorous is the warming effect of the sun in the first position than in the second. It is chiefly this difference of angle that makes the sun's warmth more effective when he is high up in the sky than when he is near the horizon, and more effective in summer than in winter.
We have seen inChapter IIIthat the sun's motion among the stars takes place along a path which carries it alternately north and south of the equator to a distance of 23.5°, and the stars show by their earlier risings and later settings, as we pass from the equator toward the north pole of the heavens, that as the sun moves northward from the equator, each day in the northern hemisphere will become a little longer, each night a little shorter, and every day the sun will rise higher toward the zenith until this process culminates toward the end of June, whenthe sun begins to move southward, bringing shorter days and smaller altitudes until the Christmas season, when again it is reversed and the sun moves northward. We have here another periodic variation, which runs its complete course in a period of a year, and it is easy to see that this variation must have a marked effect on the warming of the earth, the long days and great altitudes of summer producing the greater warmth of that season, while the shorter days and lower altitudes of December, by diminishing the daily supply of solar heat, bring on the winter's cold. The succession of the seasons, winter following summer and summer winter, is caused by the varying altitude of the sun, and this in turn is due to the obliquity of the ecliptic, or, what is the same thing, the amount by which the axis of the earth is tipped from being perpendicular to the plane of its orbit, and the seasons are simply a periodic change in the warming of the earth, quite comparable with the diurnal change but of longer period.
It is evident that the period within which the succession of winter and summer is completed, the year, as we commonly call it, must equal the time required by the sun to go from the vernal equinox around to the vernal equinox again, since this furnishes a complete cycle of the sun's motions north and south from the equator. On account of the westward motion of the equinox (precession) this is not quite the same as the time required for a complete revolution of the earth in its orbit, but is a little shorter (20m. 23s.), since the equinox moves back to meet the sun.
48.Relation of the sun to climate.—It is clear that both the northern and southern hemispheres of the earth must have substantially the same kind of seasons, since the motion of the sun north and south affects both alike; but when the sun is north of the equator and warming our hemisphere most effectively, his light falls more obliquely upon the other hemisphere, the days there are short andwinter reigns at the time we are enjoying summer, while six months later the conditions are reversed.
In those parts of the earth near the equator—the torrid zone—there is no such marked change from cold to warm as we experience, because, as the sun never gets more than 23.5° away from the celestial equator, on every day of the year he mounts high in the tropic skies, always coming within 23.5° of the zenith, and usually closer than this, so that there is no such periodic change in the heat supply as is experienced in higher latitudes, and within the tropics the temperature is therefore both higher and more uniform than in our latitude.
In the frigid zones, on the contrary, the sun never rises high in the sky; at the poles his greatest altitude is only 23.5°, and during the winter season he does not rise at all, so that the temperature is here low the whole year round, and during the winter season, when for weeks or months at a time the supply of solar light is entirely cut off, the temperature falls to a degree unknown in more favored climes.
If the obliquity of the ecliptic were made 10° greater, what would be the effect upon the seasons in the temperate zones? What if it were made 10° less?
Does the precession of the equinoxes have any effect upon the seasons or upon the climate of different parts of the earth?
If the axis of the earth pointed toward Arcturus instead of Polaris, would the seasons be any different from what they are now?
49.The atmosphere.—Although we live upon its surface, we are not outside the earth, but at the bottom of a sea of air which forms the earth's outermost layer and extends above our heads to a height of many miles. The study of most of the phenomena of the atmosphere belongs to that branch of physics called meteorology, but there are a few matters which fairly come within our consideration of the earth as a planet.We can not see the stars save as we look through this atmosphere, and the light which comes through it is bent and oftentimes distorted so as to present serious obstacles to any accurate telescopic study of the heavenly bodies. Frequently this disturbance is visible to the naked eye, and the stars are said to twinkle—i. e., to quiver and change color many times per second, solely in consequence of a disturbed condition of the air and not from anything which goes on in the star. This effect is more marked low down in the sky than near the zenith, and it is worth noting that the planets show very little of it because the light they send to the earth comes from a disk of sensible area, while a star, being much smaller and farther from the earth, has its disk reduced practically to a mere point whose light is more easily affected by local disturbances in the atmosphere than is the broader beam which comes from the planets' disk.
50.Refraction.—At all times, whether the stars twinkle or not, their light is bent in its passage through the atmosphere, so that the stars appear to stand higher up in the sky than their true positions. This effect, which the astronomer calls refraction, must be allowed for in observations of the more precise class, although save at low altitudes its amount is a very small fraction of a degree, but near the horizon it is much exaggerated in amount and becomes easily visible to the naked eye by distorting the disks of the sun and moon from circles into ovals with their long diameters horizontal. The refraction lifts both upper and lower edge of the sun, but lifts the lower edge more than the upper, thus shortening the vertical diameter. SeeFig. 27, which shows not only this effect, but also the reflection of the sun from the curved surface of the sea, still further flattening the image. If the surface of the water were flat, the reflected image would have the same shape as the sun's disk, and its altered appearance is sometimes cited as a proof that the earth's surface is curved.
The total amount of the refraction at the horizon is a little more than half a degree, and since the diameters of the sun and moon subtend an angle of about half a degree, we have the remarkable result that in reality the whole disk of either sun or moon is below the horizon at the instant that the lower edge appears to touch the horizon and sunset or moonset begins. The same effect exists at sunrise, and as a consequence the duration of sunshine or of moonshine is on the average about six minutes longer each day than it would be if there were no atmosphere and no refraction. A partial offset to this benefit is found in the fact that the atmosphere absorbs the light of the heavenly bodies, so that stars appear much less bright when near the horizon than when they are higher up in the sky, and by reason of this absorption the setting sun can be looked at with the naked eye without the discomfort which its dazzling luster causes at noon.
Fig. 27.—Flattening of the sun's disk by refraction and by reflection from the surface of the sea.Fig. 27.—Flattening of the sun's disk by refraction and by reflection from the surface of the sea.
51.The twilight.—Another effect of the atmosphere, even more marked than the preceding, is the twilight. Asat sunrise the mountain top catches the rays of the coming sun before they reach the lowland, and at sunset it keeps them after they have faded from the regions below, so the particles of dust and vapor, which always float in the atmosphere, catch the sunlight and reflect it to the surface of the earth while the sun is still below the horizon, giving at the beginning and end of day that vague and diffuse light which we call twilight.
Fig. 28.—Twilight phenomena.Fig. 28.—Twilight phenomena.
Fig. 28shows a part of the earth surrounded by such a dust-laden atmosphere, which is illuminated on the left by the rays of the sun, but which, on the right of the figure, lies in the shadow cast by the earth. To an observer placed at1the sun is just setting, and all the atmosphere above him is illumined with its rays, which furnish a bright twilight. When, by the earth's rotation, this observer has been carried to2, all the region to the east of his zenith lies in the shadow, while to the west there is a part of the atmosphere from which there still comes a twilight, but now comparatively faint, because the lower part of the atmosphere about our observer lies in the shadow, and it is mainly its upper regions from which the light comes, and here the dust and moisture are much less abundant than in the lower strata. Still later, when the observer has been carried by the earth's rotation to the point3, every vestige of twilight will have vanished from his sky, because all of the illuminated part of the atmosphere is now below his horizon, which is represented by the line3 L. In the figure the sun is represented to be 78° below this horizon line at the end of twilight, but this is a gross exaggeration, made for the sake of clearness in the drawing—in fact, twilight is usually said to end when the sun is 18° below the horizon.
Let the student redrawFig. 28on a large scale, so that the points1and3shall be only 18° apart, as seen from the earth's center. He will find that the pointLis brought down much closer to the surface of the earth, and measuring the length of the line2 L, he should find for the "height of the atmosphere" about one-eightieth part of the radius of the earth—i. e., a little less than 50 miles. This, however, is not the true height of the atmosphere. The air extends far beyond this, but the particles of dust and vapor which are capable of sending sunlight down to the earth seem all to lie below this limit.
The student should not fail to watch the eastern sky after sunset, and see the shadow of the earth rise up and fill it while the twilight arch retreats steadily toward the west.