Magnitude (astronomy)

“ Decimals express all intermediate graduations of magnitude. Astronomers carry the telescopic magnitudes much farther, till a magnitude beyond the twentieth is reached, preserving in every case the ratio of two and one-half for each magnitude in relation to that numerically next to it. ”

“ A third-magnitude star is on the average twice as far away as one of the first magnitude, a fifth-magnitude star four times as far off, etc., each additional two magnitudes doubling the average distance of the stars, at least down to the eighth magnitude and possibly farther, although beyond this limit we have no certain knowledge. ”

“ The distances even of the few stars found to have measurable parallaxes are on a scale entirely beyond the powers of the human mind to conceive. In the attempt both to realize them distinctly, and to express them conveniently, a new unit of length, itself of bewildering magnitude, has originated. This is what we may call the light-journey of one year. The subtle vibrations of the ether, propagated on all sides from the surface of luminous bodies, travel at the rate of 186,300 miles a second, or (in round numbers) six billions of miles a year. ”

“ The development of this new branch requires great additions to this mass, the product of perhaps centuries of work on the older lines of the science. To the statistician of the stars, catalogues of spectra, magnitude, position and proper motions are of the same importance that census tables are to the student of humanity. The measurement of the speed with which the individual stars are moving towards or from our system is a work of such magnitude that what has yet been done is scarcely more than a beginning. ”

“ They are exhibited only by those of the ninth magnitude, or fainter; for with them sets in a significant crowding upon its condensed parts, attended by a scarcity over its comparative vacuities. Counts by magnitudes have, besides, made it clear that the stars, in portions of the sky removed from the Milky Way, thin out notably before the eleventh magnitude is reached; so that, outside the galactic zone, the stellar system is easily fathomed. ”

“ Pointing two similar telescopes upon two unequal stars, he equalised them to the eye by stopping down the aperture of the instrument directed towards the brighter object. Assuming each to emit the same quantity of light, their respective distances would then be inversely as the diameters of the reflecting surfaces by which they were brought to the same level of apparent lustre. But the enormous real diversities of stellar size and brightness render this plan of action wholly illusory. Even for average estimates, proper motion is apparently a safer criterion of distance than magnitude. ”

“ 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. ”

“ But when we pass beyond the tenth magnitude to those vast numbers of faint stars only to be seen in the best or the largest telescopes, there appears to be a sudden change in the ratio of increased numbers per magnitude. ”

“ The real magnitude, therefore, is a constant quantity; but the apparent magnitude varies continually with the distance, real or imaginary; and therefore, if we always judged of the dimensions of an object from its apparent magnitude, every thing around us would, in this respect, be undergoing very sensible variations, which might lead us into strange and serious mistakes. A fly, near 212 enough to the eye, might appear under an angle as great as an elephant at the distance of twenty feet, and the one be mistaken for the other. ”

“ 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 ”

“ It therefore appears that a weight which on the earth weighed a ton and a half would, if raised 240,000 miles, weigh less than a pound. But even at this vast distance we are not to halt; imagine that we retreat still further and further; the strain shown by the balance will ever decrease, but it will still exist, no matter how far we go. Astronomy appears to teach us that the attraction of gravitation can extend, with suitably enfeebled intensity, across the most profound gulfs of space. ”

“ Consequently the length that we arrive at by measurement is the “proper” length, that is to say, the length as estimated by an observer who shares the motion of the body. We never, in ordinary life, have to tackle the problem of [Pg 65] measuring a body which is in continual motion. And even if we did, the velocities of visible bodies on the earth are so small relatively to the earth that the anomalies dealt with by the theory of relativity would not appear. But in astronomy, or in the investigation of atomic structure, we are faced with problems which cannot be tackled in this way. ”

“ Light, travelling with its enormous velocity, requires on an average considerably over ten years to traverse the distance between our Solar System and Stars of the first magnitude, but the dimensions of the Milky Way are built up on such a huge scale that to traverse the whole stratum would require us to pass about 500 stars, separated from each other by this same tremendous interval ”

“ In the preceding chapters we have dealt with the gigantic bodies which form the chief objects in what we know as the solar system. We have studied mighty planets measuring thousands of miles in diameter, and we have followed the movements of comets whose dimensions are often to be told by millions of miles. Once, indeed, in a previous chapter we have made a descent to objects much lower in the scale of magnitude, and we have examined that numerous class of small bodies which we call the minor planets. ”

“ And as the calculation from light-ratios only includes stars just visible in the largest telescopes, and does not include all those proved to exist by photography, we have in this case a demonstration that the numbers of the stars below the tenth and down to the seventeenth magnitude diminish rapidly. ”

“ The number of stars on any “given area of the Milky Way is about twice as great as in an equal area of any other region.” (2) This ratio does not increase for faint stars down to the 12th magnitude. (3) “The Milky Way covers about one-third of the sky and contains about half of the stars.” (4) There are about 10,000 stars of magnitude 6·6 or brighter, 100,000 down to magnitude 8·7, one million to magnitude 11, and two millions to magnitude 11·9. It is estimated that there are about 18 millions of stars down to the 15th magnitude visible in a telescope of 15 inches aperture. ”

“ Again, it shows that as the planets move in circular orbits about the central earth, they ought at all times to appear of the same magnitude; while, on the contrary, we observe their apparent magnitudes in the heavens to be very variable ”

“ There is abundant evidence of the application of this force in relation to our earth, as we shall see later on.
The universality of the Attraction of Gravitation is a fact that has been proved in a thousand ways, and a thousand times. All stars and suns, and all planets, satellites and comets and nebulae are subject to this universal law. Astronomy teaches us that its power extends across the vast abysses of space, and that stars situated at distances that cannot possibly be measured, are subject to this world-wide law. ”

“ It is thus seen that the number of stars increases with enormous rapidity as the smaller magnitudes come into question, and, according to Newcomb, there is no evidence of any falling off in the ratio of increase up to the tenth magnitude. ”

“ This method has been followed by Argelander, Behrmann, Heis, and Houzeau, but in the photometric catalogues of Harvard, Oxford, and Potsdam the magnitudes are measured in decimals of a degree. This has been found necessary for greater accuracy, as the heavens contain stars of all degrees of brightness.
The term “magnitude” means the ratio between the light of a star of a given magnitude and that of another exactly one magnitude fainter. This ratio has been variously estimated by different astronomers, and ranges from 2.155, found by Johnson in 1851, to 3.06, assumed by Pierce in 1878. ”

“ We have, first of all, to define the magnitude and form of the earth, its mean density, the constant of aberration of light expressing the relation between the earth’s mean velocity in space and the velocity of light. From the earth, as our observatory, we then proceed to lay down the mean distances of the sun, and of the planets from the same centre; all the elements of the planetary orbits, the magnitudes, densities, masses, periods of axial rotation of the several planets are by degrees determined with growing accuracy. The same labours must be gone through for the satellites. ”

“ It must be just as easy to tell a fourth magnitude star, for instance, from a fifth magnitude as from a third, and there must be as little doubt in distinguishing between the fifth and sixth magnitudes as between the third and second. The numbers expressing magnitudes, then, must actually represent a scale of equal differences as measured by the sensibility of the eye. ”

“ If now we were able to start a new scale of magnitude, it would be easy to say that a star just visible with an inch aperture on a fine night shall be called a ninth magnitude star, and fix a certain number of ninth magnitude stars for reference, so that 381the errors induced by hazy nights and variable eyes might be eliminated. ”

“ Our first task is a description of the world independent of the motion of the observer. The question of the elimination of his gauge of magnitude belongs to a later development of the theory discussed in Chapter xi. Let us draw a square on a sheet of paper, making the sides equal, to the best of our knowledge. We have seen that an aviator flying at 161,000 miles a second in the direction , would judge that the sides , had contracted to half their length, so that for him the figure would be an oblong. ”

“ The mathematical type of relativity is the one we have already had occasion to mention when discussing mathematical space and time. It implies that a distance in space, even after the space has been referred to the observer’s frame, has a purely relative magnitude; so that two distances in space may be congruent or unequal according to our measuring conventions. Even after we have decided upon our measuring conventions, the magnitude of a spatial distance can only be expressed by the magnitude of our measuring rod ”

“ The inaccurate mass of that planet, as previously known by months of computation based upon years and years of observation, was immediately discarded [78] in favor of the new mass derived from the distance and period of the outer satellite by only a few minutes' calculation.
In weighing the planets, astronomers always use the sun as the unit. What then is the sun's own weight? Obviously the law of gravitation answers this question, if we compare the sun's attraction with the earth's at equal distances. ”

“ We also see that the light given by the stars of any magnitude is twice as much as that of the stars two magnitudes higher in the scale, so that we can easily calculate what additional light we ought to receive from each additional magnitude if they continue to increase in numbers below the tenth as they do above that magnitude. ”

“ Few are the branches of astronomy that have not been modified by photography and the spectroscope. It has become a measuring tool of the first order of accuracy; measuring the speed of stars and nebulæ toward and from us; measuring the rotational speed of sun and planets, corona and Saturnian ring; measuring the distances of whole classes of stars from the solar system; measuring afresh even the distance of the sun—the yardstick of our immediate universe ”

“ 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. ”

“ As the star retreats farther and farther, the potency of the attraction will decrease; but, owing to the velocity of the star being over twenty-five miles a second, the attraction can never overcome the velocity; so that the star seems destined to escape. This calculation is of course founded on our assumption as to the total mass of the stars and other bodies which form our sidereal system. That estimate was founded on a liberal, indeed, a very liberal interpretation of the evidence which our telescopes have afforded. ”