Stellar parallax

“ The annual parallax can only be determined for near stars, nearer than, say, 5 siriometers. The direct picking out of these stars is not possible. The astronomers have therefore attacked the problem in the following way. The near stars must, on account of their proximity, be relatively brighter than other stars and secondly possess greater proper motions than those. Therefore parallax observations are essentially limited to (1) bright stars, (2) stars with great proper motions. Hence the selected attributes of the stars are m and μ. ”

“ Some of the things for which he is best known were results of those accidents that happen only to the indefatigable enthusiast. Such was the discovery of Uranus, which led to funds being provided for constructing his 40-feet telescope, after which, in 1786, he settled at Slough. In the same way, while trying to detect the annual parallax of the stars, he failed in that quest, but discovered binary systems of stars revolving in ellipses round each other; just as Bradley’s attack on stellar parallax failed, but led to the discovery of aberration, nutation, and the true velocity of light. ”

“ The failure of such astronomers as Bradley to get the parallax of any one star was enough to shew the hopelessness of this general undertaking, and, although Herschel did make an attack on the parallax problem (§ 263) , he saw that the question of stellar distribution in space, if to be answered at all, required some simpler if less reliable method capable of application on a large scale.
Accordingly he devised (1784) his method of star-gauging. The most superficial view of the sky shews that the stars visible to the naked eye are very unequally distributed on the celestial sphere ”

“ Only spurious star-parallaxes had claimed the attention of astronomers until F. W. Bessel announced, in December 1838, the perspective yearly shifting of 61 Cygni in an ellipse with a mean radius of about one-third of a second. Thomas Henderson (1798–1844) had indeed measured Stellar parallax.the larger displacements of α Centauri at the Cape in 1832–1833, but delayed until 1839 to publish his result. Out of several hundred stars since then examined, seventy or eighty have yielded fairly accurate, though very small parallaxes. ”

“ In some cases we see the nebulosity edgewise, or along the equatorial planes of the stellar vortices; in others we look down the poles, and the nebulosities are circular, and there is an endless variety in the shape and intensity of this light. But the universe seems full of motion, and we are not justified in supposing, because a star shows no such light, that it is without rotation. The parallax of the nearest star is only one second, the whole lenticular mass of light which surrounds our sun would therefore only subtend an angle of a single second at the nearest fixed star. ”

“ Not till Herschel was that discovered; not till this extraordinary aberration was allowed for could it be discovered. The effect observed by Bradley and Molyneux must manifestly be only an apparent motion: it was absurd to suppose a real stellar motion regulating itself according to the position of the earth. Parallax could not do it, for that would displace stars relatively among each other—it would not move similarly a set of neighbouring stars. ”

“ Arguing from these statistics some astronomers have put forward the theory that the stars in space are divided into two classes, which are not in reality closely related. The one class consists of intensely luminous stars and the other of feeble stars, with little or no transition between the two classes. If the parallax stars are arranged according to their apparent proper motion, or even according to their absolute proper motion, a similar bipartition is revealed in their frequency distribution. ”

“ Sublime as the Idea is, this assumption proves ineffectual, for the apparent places of the fixed stars are not sensibly changed by the earth's annual revolution; and with the aid derived from the refinements of modern astronomy and the most perfect instruments, it is still a matter of doubt whether a sensible parallax has been detected, even in the nearest of these remote suns. If a fixed star had the parallax of one second, its distance from the sun would be 20500000 millions of miles. ”

“ It will be noticed that such motions do not depend entirely upon the actual speed of the stars themselves, but that some of the apparent movement arises indirectly from the speed of our own sun. The part in a proper motion which can be ascribed to the movement of our solar system through space is clearly a displacement in the nature of a parallax—Sir William Herschel called it "Systematic Parallax"; so that knowing the distance which we move over in a certain lapse of time, we are able to hazard a guess at the distances of a good many of the stars. ”

“ For bodies of the solar system, parallax is the difference in the direction of the body due to the displacement of the observer from the center of the earth, and is called geocentric parallax, varying with the body’s altitude and distance from the earth. The geocentric parallel when a body is in the horizon is called horizontal parallax, as contrasted with the parallax at any altitude, called parallax in altitude. Parallax of the moon is called lunar parallax. In marine navigation it is customary to apply a parallax correction to sextant altitudes of the sun, moon, Venus, and Mars. ”

“ As we have seen in the chapter on the parallaxes, it is quite possible that there may be a number of stars with a measurable parallax whose proximity we have never suspected on account of the smallness of the proper motion. We can only say that the nearer a star is to the system the more likely its proximity is to be detected, so that we are much surer of the completeness of our list of large parallaxes than of small ones. ”

“ Bradley was engaged in making observations to determine if possible the parallax of some of the fixed stars. Parallax means the apparent relative shift of bodies due to a change in the observer's position. It is parallax which we observe when travelling by rail and looking out of window at the distant landscape. Things at different distances are left behind at different apparent rates, and accordingly they seem to move relatively to each other. The most distant objects are least affected ”

“ If it should ever be demonstrated that the individuals composing these star-rows have all an identical parallax, or, in other words, are all at the same distance from us, so much additional strength would be given to the argument that they owe their origin to a nebula which resembled in shape the figure that they mark out. But the inherent probability that the stars concerned in such cases really do have practically the same parallax is so great that actual measurement could hardly make it stronger. ”

“ The moon was assumed to have a tendency to fall towards the Earth, and the Earth and Moon together towards the Sun. The same relation was assumed to exist between all the smaller and larger luminaries in the firmament; and it soon became necessary to extend this assumption to infinity. The universe was parcelled out into systems—co-existent and illimitable. Suns, Planets, Satellites, and Comets were assumed to exist, infinite in number and boundless in extent ”

“ The two components, under the influence of powerful mutual gravitational attraction, must be revolving in a mighty orbit. Yet this vast orbit, as a whole, with the two great stars in it, must be approaching our part of the universe all the time. For the spectroscope shows the velocity of approach to increase and diminish, indeed, but it is always present. Here, then, is this great stellar system, having a four-day revolution of its own, and yet swinging rapidly through space in our direction. Nor is this all. One of the component stars must be nearly or quite dark ”

“ And how easie is it for Astronomers to assign what distance they please to the Planets, and defend them, when they have such a curious subterfuge as that of Refraction, wherein a very little variation will allow them liberty enough to place the Celestial Bodies at what distance they please.
If therefore we would come to any certainty in this point, we must go other wayes to work; and as I have here examined the height and refractive property of the Air by other wayes then are usual, so must we find the Parallax of the Planets by wayes not yet practiced ”

“ Let us, for simplicity, think of a star situated near the pole of the ecliptic, and thus appearing to revolve annually in a circle, whether we regard either the phenomenon of parallax or of aberration. As the earth revolves, so does the star appear to revolve; and thus to each place of the earth in its orbit corresponds a certain place of the star in its circle. If the movement arise from annual parallax, it is easy to see where the place of the star will be for any position of the earth. ”

“ It is worthy of note that the waves at the point H, whatever their real magnitude may be, are magnified and rendered more obstructive by the very instrument—the telescope—which is employed to make the objects beyond more plainly visible: and thus the phenomenon is often very strikingly observed—that while a powerful telescope will render the sails and rigging of a ship when beyond the point H, or the optical horizon, so distinct that the very ropes are easily distinguished, not the slightest portion of the hull can be seen. ”

“ Earth. this plane is found with great exactness from observations of the transits of Venus. So exact is the latter determination that, were there no weak point in the subsequent parts of the process, this method would give far the most certain result for the solar parallax. Its weak point is that the apparent motion of the node depends partly upon the motion of the ecliptic, which cannot be determined with equal precision. The derivation of the distance of the sun by it is of such interest from its simplicity that we shall show the computation. ”

“ This demonstrates that our sun with his stately retinue of planets, satellites, comets, and meteorites, all move in grand march toward the constellation Hercules. The entire universe is in motion. But these revelations of the micrometer are tame compared with its final achievement, the discovery of parallax. ”

“ For if a double star is binary, then the two members are approximately at the same distance from the earth and therefore equally affected by the earth’s motion, whereas for the purpose of finding the parallax it is essential that one should be much more remote than the other. ”

“ It will be only when the two bodies, coming from contrary directions, collide with equal momentum that the entire motion will be stopped. But in the case of stellar masses moving, as it were, at random in every direction this is a condition which will but rarely occur. Accordingly, in most cases the resulting stars will have more or less motion. In short, the stars should, according to the theory, be moving in all directions and with all varieties of velocity. ”

“ Another consideration has made these authors enlarge this distance a little more: for since the moon's diameter is rather more than a quarter of the earth's diameter, if the sun's parallax be supposed 15 seconds, the body of the moon would be larger than that of Mercury, viz. a secondary planet larger than a primary one, which seems repugnant to the regular proportion and symmetry of the mundane system. ”

“ The earth-flatteners form a considerable section of the paradoxical family. They experienced a practical rebuff, a few years since, which should to some degree have shaken their faith in the present chief of their order. To do this chief justice, he is probably far less confident about the flatness of the earth than any of his disciples. Under the assumed name of Parallax he visited most of the chief towns of England, propounding what he calls his system of zetetic astronomy. Why he should call himself Parallax it would be hard to say ”

“ Fig. 28. to be drawn six months later from the same stars, touching our earth's orbit on the other side, as R B T, such a line would not diverge sufficiently from a straight line for us to detect its divergence. Numerous vain attempts had been made, up to the year 1835, to detect and measure the angle of parallax by which we could rescue some one or more of the stars from the inconceivable depths of space, and ascertain their distance from us. We are ever impelled to triumph over what is declared to be unconquerable. There are peaks in the Alps no man has ever climbed. ”

“ Such collision may be long delayed; the dark star may be drawn in comet-like circuit about thousands of other stellar masses, and be hurtled on thousands of diverse parabolic or elliptical orbits, before it chances to collide—but that matters not: "billions are the units in the arithmetic of eternity," and sooner or later, we can hardly doubt, a collision must occur. Then without question the mutual impact must shatter both colliding bodies into vapor, or vapor combined with meteoric fragments; in short, into a veritable nebula, the matrix of future worlds. ”

“ For these, being immeasurably remote, will remain unchanged, within the limits of our powers of observation, and thus serve as points of reference for marking the apparent shifting of the brighter star we are actually considering.
We have merely to photograph the region at various seasons of the year. Careful examination of the photographs under the microscope will then enable us to measure the slightest dis [97] placement of the parallax star. From these measures, by a process of calculation, astronomers can then obtain the star's distance. It will not become known in miles ”