Popular Science Monthly/Volume 14/January 1879/Astronomical Magnitudes and Distances
| ASTRONOMICAL MAGNITUDES AND DISTANCES. |
By Professor H. S. CARHART.
THE magnitudes and distances considered in physical astronomy are so immense that we cannot hope to reach even a faint conception of them except by illustration and comparison. If even then, with our best effort, we fail to measure up to the magnificent dimensions of the universe, the attempt will at least enlarge our intellectual conceptions, and lead us out mentally into a broader place.
The results reached by modern astronomy, respecting the dimensions and distances of the heavenly bodies, are based on two lines, the radius (or semi-diameter) of the earth and the radius of its orbit; the former is accurately known, the latter approximately. In modern times the highest refinements of engineering skill have been applied to the measurement of base-lines, which furnish through triangulation arcs of a meridian. So thoroughly has this work been done that, in the opinion of Prof. Young, the error in the ascertained length of the earth's equatorial radius cannot exceed 200 feet. This radius forms our base-line for broader operations. The equatorial, horizontal parallax of the moon, or the angle subtended at the moon by the earth's equatorial radius, is found to have an average value of 57' 2". Hence by plane trigonometry the moon's mean distance is 238,885 miles, or nearly ten times the circumference of the earth. Light, with a velocity of 186,500 miles a second, travels from the earth to the moon and back again in two and a half seconds, thus producing that faint illumination of the dark portion of the new moon turned toward us. Knowing the moon's distance, the measurement of its apparent diameter in minutes of arc furnishes immediately its absolute diameter in miles.
So, then, this queen of the night, once supposed to be a kind of lantern, fed by exhalations from the ocean, is a body 149 as large as the earth. It is our nearest celestial neighbor—in fact, a little out-lying, condensed nebulosity; and if we had a weather-station on the lunar mountain Tycho, connected by telegraph with Washington, General Myer would receive the lunar weather-reports in fifteen seconds by electricity.
Aristarchus, in the third century before the Christian era, attempted to use the moon's distance to compute the greater distance of the sun; but the method failed, and astronomers were compelled to fall back on the radius of the earth as a base-line for a still grander triangulation. The parallax of Mars, at opposition, gave us the first approximation to the sun's distance; then the transit of Venus furnished a nearer estimate; latterly, Le Verrier, who found Neptune by figures, has also determined the distance of the sun by means of planetary perturbations; still a fourth method combines the retardation of the eclipses of Jupiter's first satellite with the velocity of light, as determined by terrestrial measurement, and so measures off the millions of miles between us and the source of almost all our energy. These four methods, notably the last two, give us 92,360,000 miles as a near approximation to this long-sought distance. We have thus reduced this space by 3,000,000 miles, or about 132 of the entire amount. Across this interval the radiant energy of the sun dashes in eight minutes thirteen seconds. Thermal electricity, which might be presumed to exist at the sun in great quantity, would traverse the distance in one hour thirty-six minutes. Sensation travels along our nerves at the slow rate of about 150 feet a second. Imagine an infant with an arm long enough to reach the sun. It would have to live 102 years to know that it had burned its band in the solar fires. Counting three a second day and night, it would require an entire year to count the miles intervening between us and the sun; and to count the distance in feet, at the same rate, would consume 5,280 years, or nearly as much time as has elapsed since the introduction of man upon the earth, according to Biblical chronology.
The sun's distance being ascertained, its absolute diameter is determined from the apparent by the process applied to the moon, A near approximation to the sun's radius is 430,680 miles. Imagine the earth at the sun's centre: its surface would appear as far distant as does now the celestial vault, and the moon's orbit would fall nearly 200,000 miles within the surface, or little more than half-way from the centre out, A locomotive at thirty miles an hour would run from centre to surface in 1.63 years. Jules Verne got his traveler around the world in eighty days; at the same rate it would take him twenty-four years to make the circuit of the sun. Its volume is 1,334,000 times the earth's; but its mass, on account of its less density, is only 323,386 times as great. We say only, because the ratio of masses is so much less than that of volumes. But when we reflect that the spectroscope shows at least many terrestrial elements present in the sun, and that the sun contains enough of such substantial stuff as Mother Earth consists of to make more than 300,000 like her, we are prepared to admit that the ratio between the masses even is large enough for all practical purposes.
Vast and incomprehensible as we have found our distance from the sun to be, we have still to contemplate far greater reaches within the limits of the solar system. Jupiter holds on its silent course 5210 as far away from the sun as the earth, and therefore receives only 127 the intensity of solar radiant energy. Saturn is nearly twice as far distant as Jupiter; Uranus more than twice as far as Saturn; while Neptune glimmers at thirty times the earth's distance with light that has consumed eight and a quarter hours in flashing twice across this vast abyss since leaving the sun. At that distant boundary the light and heat of the sun have only 1900 the intensity that we enjoy, while its apparent diameter, observed from that position, would shrink to 64", or little more than the greatest apparent diameter of Venus. We modestly lay claim to this small corner of the universe, denominated the solar system, and assert our right to possession by calling it ours. What is the area of this plane bounded by Neptune's orbit, with which the planes of the other planetary orbits nearly coincide? What is the space swept by the radius-vector of this planetary child of Adams's and Le Verrier's calculations? Since circles are as the squares of their radii, this area is 900 times that comprised within the earth's orbit. Breaking this unit up into smaller ones, we find it contains twenty-six billions, five hundred millions of millions of square miles; or, with reference to the earth's entire surface, the ratio between it and the area of its orbit is 13,520,000. But Neptune's orbit exceeds this 900 times!
Conceive this orbit immersed in the universal ether, like an immense ring mapped out on the surface of still water. A pebble dropped at the centre of this ring would send its widening wavelets outward with a perfectly definite velocity. So a wave of light, emanating from the sun, with a length of no more than the 501000 part of an inch, is propagated through this universal ether with such rapidity that in four hours and nine minutes it describes the entire area comprised within Neptune's path around the sun.
Across this vast interval quivers, too, in some mysterious way, that universal influence that we call gravitation. But at that outlying point, where Neptune holds on its silent course, it no longer exercises that dominant sway that characterizes it at the earth. The earth moves through 18.4 miles of its orbit every second, and is deflected from a straight line by the sun during that interval a little less than 12100 of an inch (0.11598 inch), Neptune travels 3.35 miles a second, and is deflected from a straight line during the same time only about 13100000 of an inch (0.000129 inch); yet by that slight pull the sun asserts its mastery, and brings Neptune round once in 164 years.
Vast as is this field of solar operations, we demand a still broader sphere for the exercise of our intellectual faculties. The successive eminences on which Astronomy has planted her appliances for more advanced operations stand related to each other as the terms, not of an arithmetical, but of a geometrical progression. Having settled the relative distances of this rather unsocial family of planets, the next advance is on to the stars. From the measurement of a base-line a few miles in extent, the astronomer essays, with undaunted hardihood, to fathom by triangulation the depths of space. The dog bays at the moon, the child stretches out its tiny hand to pluck the stars from the sky, and the astronomer applies his measuring-rod along the vibrating lines of light so far into immensity that blazing suns, exceeding in brightness the mid-day splendor of our own, dwindle to the luminous points of twinkling stars.
When Copernicus, the Polish astronomer, sought to extricate astronomy from the hopeless complexity into which it had become entangled by cycles, epicycles, and eccentric positions, and proclaimed the heliocentric system, his opponents objected that the earth's axis, produced to the celestial sphere, with its successive positions day after day parallel to each other, should be seen to describe a circle in the heavens as the earth sweeps round through its orbit of nearly 600,000,000 miles in length. Copernicus replied that it does describe such a circle; but the stars, by reference to which it can alone be mapped out, are so distant that the circle of almost 100,000,000 miles' radius there dwindles to a point and vanishes by perspective. To reverse the line of sight, let us suppose ourselves transported to the pole-star and looking back upon the orbit of the earth. So vast is the distance that this elliptical orbit contracts almost to the infinitesimal dimensions of a point; for, at that distant station, the earth's orbital diameter subtends an angle of only 0.182", or twice the angle called the parallax of the star. Such is the distance that the astronomer has successfully attempted to measure, starting with a primary triangle based on a determined line of only a few miles in length.
The nearest fixed star is Alpha Centauri, with a parallax of 0.928", corresponding to a distance of 20,518,000 millions of miles. Light, traveling at the rate of 186,500 miles a second, requires 3.5 years to reach us from this nearest star. So the solar system, with its immense distances, is yet alone in the universe of stars; and our central luminary is separated so far from other suns that the distance to its outmost planet is almost a vanishing quantity in comparison with the distance to its nearest starry neighbors. We gaze upon the glittering heavens at night, and wrap in thought a canopy of shining stars about our earth as if it were an ornamented mantle; but could we take our station on a silent planet circling round some other starry sun, our sun would take its place as only one among the mazes of the stars.
How brilliantly Sirius shines with pure white light in the evening sky! Yet the earth has circled seventeen times round the sun since the light that the eye gathers to an image of the Dog-star left that glorious orb. Patiently the astronomer centres that little circle around which the pole-star sheds its guiding light, that he may adjust his instrument to parallelism with the axis of a revolving world. But since that light left its source at the pole-star, a child has grown through youth to manhood, and in his hair the gray of silver lines has begun to develop under the cares of six-and-thirty years. And these are only our nearest neighbors among the stars!
For every star visible to the naked eye under the most favorable circumstances the great Washington telescope shows from 5,000 to 8,000 more. According to the best authorities, the first six magnitudes contain 5,904 stars. Only half of these can be seen above the horizon at once; and the sixth magnitude comprises 4,424. These can be seen distinctly only on very favorable nights; so that for ordinary observation only 740 stars are visible at any moment above the horizon. There are only twenty stars of the first magnitude, that is, of the first degree of brightness. It is demonstrable that Sirius is a hundred and sixty times as bright intrinsically as our sun. From a comparison of Sirius with the moon, and the moon with the sun, it is found that sunlight is 6,000 million times brighter than that of Sirius. But since Sirius is 1,000,000 times more distant than our sun, if brought as near us, the intensity of its light would be increased in the ratio of the square of 1,000,000 or 1,000,000 millions. This quantity, divided by 6,000 millions, would show Sirius to be at least a hundred and sixty times as bright intrinsically as our sun.
It is fair, however, to suppose that the chief cause of difference of brightness of stars is difference of distance. If so, we then have the means of approximating to the distance of even telescopic stars. Herschel estimated that stars of the first order emit, on an average, light one hundred times as intense as those of the sixth; hence the latter must be at ten times the distance, the intensity of light varying inversely as the square of the distance. Sirius is 98,000,000 of millions of miles from us; stars of the sixth magnitude are therefore about 1,000 millions of millions distant, and their light reaches us only after a flight of 169 or 170 years.
The space-penetrating power of a telescope depends upon the ratio between its aperture and the pupil of the eye. Herschel estimated that his four-foot reflector penetrated 194 times as far as the naked eye; and, as the faintest stars visible to the naked eye are ten times as distant as the brightest, it follows that the faintest stars visible in the field of Herschel's telescope are 1,940 times as distant as Sirius or Alpha Lyræ. In other words, Sirius would still be visible if removed to about 2,000 times its present distance. With Lord Rosse's six-foot reflector Sirius would still be visible at 3,000 times its present distance. If, therefore, this brightest star in the heavens should suddenly shoot away from us with the velocity of light, it would remain visible to the naked eye twice 170 years, since 170 years would be consumed in its flight and 170 more in the return of the light; and with Lord Rosse's telescope it could be traced 100,000 years longer (twice 3,000 times 170 years). This is the lowest estimate, too, for Sirius is many times brighter than the average star of the first magnitude. If intrinsically only four times as bright, it could still be seen by the telescope so infinitely far into space that light from it could reach us only after the lapse of 100,000 years.
But we need not pause even at these distant telescopic suns. Beyond the stars that merely dot with points of light the telescopic field of view, hovering on the outskirts of this inconceivable space swept by the far-fathoming line of telescopic vision, are discerned faintly-defined masses too distant to be resolved into stars, whose hazy light is gathered from congeries of suns, the individual blazing brightness of which is reduced in our view to the fleecy films of unresolvable nebulæ. Even imagination tires in winging its way to these star-clusters, so far removed from us that each one may be called another universe of God. From them nothing comes to us but the faint, palpitating throb of an ethereal wave; no tidings cross that gulf save what flew throughout the universe when He who made these systems first said, "Let there be light." And, if thought falters and figures fail in the presence of these infinitudes of distance, no less do they when the dimensions of these nebulous fields are contemplated. The nearest star, viewed with a power of 6,000 diameters, shows no proper disk, and is still only a brilliant point. Its diameter, though perhaps greater than that of our own sun, is still at least 6,000 times too small to come within the limits of unaided vision. But many nebulaæ, though almost infinitely farther removed, are still of extent sufficient to more than fill the telescopic field. Who, then, can estimate their absolute dimensions?
Such, then, are the magnitudes and distances which the godlike human intellect has undertaken to determine. And still art vies with science to fashion lenses that shall gather at their focus still more and more of that luminous intelligence that discloses to the mind of man the secrets of the outside universe. But as the space-penetrating power of the telescope is increased, and the bright spots of light are resolved into groups of brilliant stars, more nebulous haze comes up from the deep distance, indicating that the visual ray is not yet long enough to fathom the mighty depths. There is still haze behind, independent of those nebulæ shown to be gaseous by the spectroscope. The telescopic ray has not yet shot entirely through the mighty distance, leaving only the deep, dark heavens beyond as the background of the brilliant picture. The words uttered by David spring to our lips with fuller meaning when we look out upon the glorious heavens illumined by the concentrated light of these latter days: "When I consider thy heavens, the work of thy fingers, the moon and the stars which thou hast ordained; what is man, that thou art mindful of him? or the son of man, that thou visitest him?"
