Astronomical unit

“ If equal portions of space really held equal numbers of stars, it is obvious that the number of stars visible in any particular direction would be strictly proportional to the range of the system in that direction, apparent accumulation being produced by real extent. The process of "gauging the heavens," accordingly, consisted in counting the stars in successive telescopic fields, and calculating thence the depths of space necessary to contain them. The result of 3,400 such operations was the plan of the Galaxy familiar to every reader of an astronomical text-book. ”

“ The semi-diameter of the earth's orbit is our standard measure for the universe. It is the great fundamental datum of astronomy—the unit of space, any error in the estimation of which is multiplied and repeated in a thousand different ways, both in the planetary and sidereal systems. Hence its determination was called by Airy "the noblest problem in astronomy." It is also one of the most difficult. The quantities dealt with are so minute that their sure grasp tasks all the resources of modern science. ”

“ For, when the right Ascension and Declination of any star is known, from astronomical tables, the telescope may be immediately adjusted to point to it, which will infallibly prevent his mistaking one star for another. In this way, likewise, the precise position of the planet Mercury, Uranus, Vesta, Juno, Ceres, Pallas—a small comet, a nebula, a double star, or any other celestial body not easily distinguishable by the naked eye, may be readily pointed out, when its right Ascension and Declination are known to a near approximation. ”

“ The measure of the Moon's distance involves no principle more abstruse than the measure of the distance of a tree on the opposite bank of a river. The principles of construction of the best Astronomical instruments are as simple and as closely referred to matters of common school-education and familiar experience, as are those of the common globes, the steam-engine, or the turning-lathe ”

“ No star of even the 20th magnitude has ever been seen by any telescope. Even on the best photographic plates it is doubtful that any stars much below the 18th magnitude are visible. To show a star of the 20th magnitude—if such stars exist—would require a telescope of 144 inches or 12 feet in aperture. ”

“ In glancing from side to side of the sun's disk, the eye ranges over a distance of more than 860,000 miles—not a mere ideal distance, or an expanse of empty space, but a distance filled by an actual and, so to speak, tangible body, whose diameter is of that stupendous magnitude. One sees at a glance, then, the enormous scale on which these spots are formed. The earth placed beside them would be but a speck, and yet they are mere pits in the surface of the sun, filled perhaps with partially cooled metallic vapors, which have been cast up from the interior, and are settling back again. ”

“ At certain times some of them approach near enough to the earth to merit the attention of those astronomers who are specially interested in determining the dimensions of the solar system. The observations are of such a nature that they can be made with considerable precision; they can also be multiplied to any extent that may be desired. Some of these little bodies have consequently a great astronomical future, inasmuch as they seem destined to indicate the true distance from the earth to the sun more accurately than Venus or than Mars. ”

“ Probably the greatest need of stellar astronomy at the present day, in order to make sure that our theoretical deductions are starting on the right lines, is some means of measuring the apparent angular diameter of stars. ”

“ It is customary to divide the stars into classes, called magnitudes, according 220to their apparent brightness. By a system of photometry, or light-measurement, they are grouped into stars of the first, second, third, etc., magnitude. With the naked eye no stars fainter than the sixth magnitude are visible, but very powerful telescopes may show them down to the eighteenth magnitude. Each magnitude is about two and a half times brighter than the next magnitude below in the scale. A first-magnitude star is about one hundred times brighter than one of the sixth magnitude. ”

“ The galactic system is composed of a countless number of stars, spreading out on all sides along a very extended plane. These stars, which are very unevenly distributed, show a decided tendency to cluster together into individual groups of different sizes and forms, separated by comparatively vacant spaces. This layer where the stars congregate in such vast numbers may be conceived as a very irregular flat disk, sending many branches in various directions, and having a diameter eight or ten times its thickness. ”

“ These components will be expressed in one component (u0) parallel to the galactic plane, and one component (v0) perpendicular to it. If the distance (r) is known we are able to convert these components into components of the linear velocity perpendicular to the line of sight (U and V) .
III. The intensity of the light of the stars is expressed in magnitudes. We may distinguish between the apparent magnitude (m) and the absolute magnitude (M) , the latter being equal to the value of the apparent magnitude supposing the star to be situated at a distance of one siriometer. ”

“ Stars which have bright lines in their spectra (§ 312) form another link connecting nebulae with stars. A good many converging lines of evidence thus point to a greater variety in the arrangement, size, and structure of the bodies with which the telescope makes us acquainted than seemed probable when sidereal astronomy was first seriously studied; they also indicate the probability that these bodies should be regarded as belonging to a single system, even if it be of almost inconceivable complexity, rather than to a number of perfectly distinct systems of a simpler type. ”

“ Sir John Herschel says, “A glorious cluster of immense magnitude, being at least 2 fields in extent every way. The stars are 8, 9, 10, and 11th magnitudes, but chiefly 10th magnitude, of which there must be at least 200. It is the most brilliant object of the kind I have ever seen” ... “has several [Pg 210] elegant double stars, and many orange-coloured stars.” [369] This should form a fine object in even a comparatively small telescope, and may be recommended to observers in the southern hemisphere. A telescope of 3-inches aperture should show it well. ”

“ But there is obviously no limit to the labours of astronomers; not only are millions of distant stars awaiting their first measurements, but those already registered require endless scrutiny as regards their movements in the three dimensions of space, their periods of revolution, their333 changes of brilliance and colour. It is obvious that though astronomical numbers are conventionally called constant, they are probably in all cases subject to more or less rapid variation. ”

“ Let us attempt such a formula by taking at once, for our unit of division, the most minute space ever brought into visibility by the highest power of the microscope. Let our dividend on the other hand, be the utmost distance within which the telescope has ever detected the existence of a material entity. Denote the quotient by the letter x, and let r stand for the radius of the earth's orbit. ”

“ But smaller instruments reveal only the in-running star streams and the sprinkling of stellar points over the main aggregation, which cause it to sparkle like a cloud of diamond dust transfused with sunbeams. The appearance of flocking together that those uncountable thousands of stars present calls up at once a picture of our lone sun separated from its nearest stellar neighbor by a distance probably a hundred times as great as the entire diameter of the spherical space within which that multitude is congregated. ”

“ The sun and moon are about half a degree in apparent diameter, and the distance between the extreme stars in Orion’s belt, three degrees, which measures being made familiar to the eye, may be applied to other spaces of the heavens, and an approximate idea conveyed of the relative distances of objects in the sky.
From what has been stated above, it is evident that the magnitude of objects may be considered in different points of view. The true dimensions of an object, considered in itself, give what is called its real or absolute magnitude ”

“ Eighteen observatories scattered north and south of the equator divided the sky among them; and the outcome of their combined operations aimed at the production of a catalogue of at least 2,000,000 strictly determined stars, together with a colossal map in 22,000 sheets, showing stars to the fourteenth magnitude, in numbers difficult to estimate. (See Photography, Celestial.)
The arrangement of the stars in space can be usefully discussed only in connexion with their apparent light-power, or “magnitude.” Photometric catalogues, accordingly, form an indispensable part of stellar statistics ”

“ Even Jupiter and Venus, and the sun and moon, are sometimes calculated on this scale of stellar magnitude, numerically negative, of course, Venus sometimes being as bright as magnitude -4.3, and the sun -26.7.
Knowing thus the relation of sun, moon, and stars, and the number of the stars of different magnitudes, it is possible to estimate the total light from the stars. This interesting relation comes out this way: that the stars we cannot see with the naked eye give a greater total of light than those we can because of their vastly greater numbers. ”

“ We have a knowledge of the so-called extent of the stellar universe, which, whatever it may amount to in terms of ultimate reality, is not a mere description of location in a conventional and arbitrary mathematical space. ”

“ I direct one of the legs to the lower part of the sun, and the other to the upper part of the sun; I then know the apparent angular breadth of the sun; and from this I determine the proportion of the absolute diameter of the sun to the distance of the sun, and whatever distance I assume for the sun I must take the diameter proportionately to that distance. If the distance of the sun is one hundred millions of miles, the breadth of the sun (roughly speaking) must be one million; if the distance of the sun is fifty millions of miles, the diameter of the sun is half-a-million of miles. ”

“ But, viewed through the telescope, while the planets are seen to possess clearly appreciable diameters, the stars are still only mere luminous points. The most powerful of existing telescopes, that of Melbourne, which magnifies 8,000 times, gives us an image of one of our planets possessing an apparent diameter of several degrees. Jupiter, for instance, which, seen with the naked eye, appears as a star of the first magnitude, with a diameter of 45′′ at the most, will in this telescope have its diameter multiplied 8,000 times, and will be seen as if it occupied in the heavens an angle of 100°. ”

“ The paths of the planets and comets round the Sun, and of the satellites round their planets, are called their ORBITS.
Those stars which always appear in the same situation in relation to each other are called Fixed Stars. About 1000 can be seen at once by the naked eye, and by the help of the telescope many millions may be seen. Their sizes are little known, but probably some of them are many million times larger than the earth. They are not considered a part of our Solar System, but are supposed to be Suns of other systems, round which other planets revolve. ”

“ It accordingly appeared that a planet possessing the mass which he had assigned, and moving in the orbit which his calculations had indicated, must indeed exist, though no eye had ever beheld any such body. Here was, indeed, an astonishing result. The mathematician sitting at his desk, by studying the observations which had been supplied to him of one planet, is able to discover the existence of another planet, and even to assign the very position which it must occupy, ere ever the telescope is invoked for its discovery. ”

“ The apparent position of a star is generally denoted by its right ascension (α) and its declination (δ) . Taking into account the apparent distribution of the stars in space, it is, however, more practical to characterize the position of a star by its galactic longitude (l) and its galactic latitude (b) . Before defining these coordinates, which will be generally used in the following pages, it should be pointed out that we shall also generally give the coordinates α and δ of the stars in a particular manner. ”

“ We observe the star with the mural circle while the earth is in the position E'. We apply the corrections for precession, nutation, aberration, and refraction; and we shall know what the corrected position of that star should be half a year hence, as observed when the earth is at E'". Now, suppose we go to this second state of things, and when the earth is at E"', we observe the meridional zenith distance of the star, we correct it for refraction, precession, nutation, and aberration. ”

“ Its measurement has been one of the important problems of astronomy for centuries, ever since men recognized that the Copernican theory of our universe requires the determination of stellar distances for its complete demonstration.
If the earth is swinging around the sun once a year in a mighty path or orbit, there must be changes of its position in space comparable in size with the orbit itself. And the stars ought to shift their apparent places on the sky to correspond with these changes in the terrestrial observer's position. ”