A sensible parallax of about one second has been ascertained in the case of the double star [ Alpha Centauri ] of the constellation of the Centaur, and one of the third of that amount for the double star, 61 Cygni; which gave reason to presume that the distance of the former might be about twenty thousand millions of miles, and the latter of much greater amount. If we suppose that similar intervals exist between all the stars, we shall readily see that the space occupied by even the comparatively small number visible to the naked eye, must be vast beyond all powers of conception.
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Let me give you a handle on that. Say the distance between the Earth and the sun is, oh, one centimeter. Mercury orbits the sun at a range of a toasty two millimeters. Jupiter is six centimeters out; the span of your outstretched arms, fingertip to fingertip, will just about encompass the orbit of Eris, which it’s taken me so many years to reach. Got that?
Well, on this scale, Proxima Centauri, our nearest star, is two and a half kilometers down the road. And we’re going to Tau Ceti, three times as far away as that.
If we suppose the distance of the fixed stars from the sun to be so great that the diameter of the earth's orbit viewed from them would not subtend a sensible angle, or which amounts to the same, that their annual is quite insensible; it will then follow that a line drawn from the earth in any part of its orbit to a fixed star, will always, as to sense, make the same angle with the plane of the ecliptic, and the place of the star, as seen from the earth, would be the same as seen from the sun placed in the focus of the ellipsis described by the earth in its annual revolution, which place may therefore be called its true or real place.
But if we further suppose that the velocity of the earth in its orbit bears any sensible proportion to the velocity with which light is propagated, it will thence follow that the fixed stars (though removed too far off to be subject to a parallax on account of distance) will nevertheless be liable to an aberration, or a kind of parallax, on account of the relative velocity between light and the earth in its annual motion.
For if we conceive, as before, the true place of any star to be that in which it would appear viewed from the sun, the visible place to a spectator moving along with the earth, will be always different from its true, the star perpetually appearing out of its true place more or less, according as the velocity of the earth in its orbit is greater or less; so that when the earth is in its perihelion, the star will appear farthest distant from its true place, and nearest to it when the earth is in its aphelion; and the apparent distance in the former case will be to that in the latter in the reciprocal proportion of the distances of the earth in its perihelion and its aphelion. When the earth is in any other part of its orbit, its velocity being always in the reciprocal proportion of the perpendicular let fall from the sun to the tangent of the ellipse at that point where the earth is, or in the direct proportion of the perpendicular let fall upon the same tangent from the other focus, it thence follows that the apparent distance of a star from its true place, will be always as the perpendicular let fall from the upper focus upon the tangent of the ellipse. And hence it will be found likewise, that (supposing a plane passing through the star parallel to the earth's orbit) the locus or visible place of the star on that plane will always be in the circumference of a circle, its true place being in that diameter of it which is parallel to the shorter axis of the earth's orbit, in a point that divides that diameter into two parts, bearing the same proportion to each other, as the greatest and least distances of the earth from the sun.
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Things don’t always look as they seem. Some stars, for example, look like bright pinholes, but when you get them pegged under a microscope for find you’re looking at a globular cluster-a million stars that, to us, presents as a single entity. On aless dramatic note there are triples, like Alpha Centauri, which up close turns out to be a double star and a red dwarf inclose proximity.There’s an indigenous tribe in Africa that tells of life coming from the second star in Alpha Centauri, the one no one can see without a high-powered observatory telescope. Come to think of it, the Greeks, the Aboriginals, and the Plains Indians all lived continents apart and all, independently, looked at the same septuplet knot of the Pleiades and believed them tobe seven young girls running away from something that threatened to hurt them.Make of it what you will.
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For common purposes we may without sensible error suppose the earth's motion equable and neglect the corrections, and then the rule for the parallax of will be this:
Sine lat. : rad. : : cotang. A : cotang. C, or rad : sine lat. : : tang. A : tang. C; then long. star <math>\mp</math> C = long. of λ.
Cosine C : cosine A : : semi transverse axis : z.
And cosine decl. cosine (ʘ - λ) :: z : x = parallax of right ascension.
But we would do well to meditate daily, rather as the religious do on their God, on the 9.5 trillion kilometres which comprise a single light year, or perhaps on the luminosity of the largest known star in our galaxy, Eta Carinae, 7,500 light years distant, 400 times the size of the sun and 4 million times as bright. We should punctuate our calendars with celebrations in honour of VY Canis Majoris, a red hypergiant in the constellation Canis Major, 5,000 light years from earth and 2,100 times bigger than our sun. Nightly – perhaps after the main news bulletin – we might observe a moment of silence in order to contemplate the 200 to 400 billion stars in our galaxy, the 100 billion galaxies and the 3 septillion stars in the universe. Whatever their value may be to science, the stars are in the end no less valuable to mankind as solutions to our megalomania, self-pity and anxiety. To answer our need to be repeatedly connected through our senses to ideas of transcendence, we should insist that a percentage of all prominently positioned television screens on public view be hooked up to live feeds from the transponders of our extraplanetary telescopes. We would then be able to ensure that our frustrations, our broken hearts, our hatred of those who haven’t called us and our regrets over opportunities that have passed us by would continuously be rubbed up against, and salved by, images of galaxies such as Messier 101, a spiral structure which sits towards the bottom left corner of the constellation Ursa Major, 23 million light years away, majestically unaware of everything we are and consolingly unaffected by all that tears us apart.
Whether the stars were all at the same distance, or whether they were scattered throughout infinite space, or whether they formed a finite system of vast but limited depth, were questions that could not be answered until towards the end of the eighteenth century. Until then, stellar astronomy was a field left to the unaided imagination.
How far away from the earth are those remotest of stars: they are beyond the reach of eye, or man's devices, or man's thought. What an absurdity is this motion (of spheres). He also argues for the extreme variability of the distance to the various heavenly bodies and states that situated "in thinnest aether, or in the most subtle fifth essence, or in vacuity - how shall the stars keep their places in the mighty swirl of these enormous spheres composed of a substance of which no one knows aught?
A standard of reference for the arrangement of the stars may be had by comparing their distribution to a certain properly modified equality of scattering. The equality which I propose does not require that the stars should be at equal distances from each other, nor is it necessary that all those of the same nominal magnitude should be equally distant from us.
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