Sphere (astronomy)

“ If an observer looks at the stars on any clear night he sees an apparently innumerable [1] host of them, which seem to lie on a portion of a spherical surface, of which he is the centre. This spherical surface is commonly spoken of as the sky, and is known to astronomy as the celestial sphere. The visible part of this sphere is bounded by the earth, so that only half can be seen at once; but only the slightest effort of the imagination is required to think of the other half as lying below the earth, and containing other stars, as well as the sun. ”

“ We may therefore, in all questions relating only to the directions of the stars, replace the angle between the directions of two stars by the arc joining the corresponding points on the celestial sphere, or, in other words, by the distance between these points on the celestial sphere. But such arcs on a sphere are easier both to estimate by eye and to treat geometrically than angles, and the use of the celestial sphere is therefore of great value, apart from its historical origin. ”

“ When you have thus made a sphere for yourself, or, with an artificial globe before you, if you have access to one, proceed to point out on it the various arcs of azimuth and altitude, right ascension and declination, terrestrial and celestial latitude and longitude,—these last being referred to the equator on the earth, and to the ecliptic in the heavens.
When the circles of the sphere are well learned, we may advantageously employ projections of them in various illustrations. By the projection of the sphere is meant a representation of all its parts on a plane. ”

“ If the earth is a perfect sphere, then its attraction on any other body is exactly the same as if its mass were all concentrated at its centre (§ 182) , and so also the attraction on it of any other body such as the sun or moon is equivalent to a single force passing through the centre o of the earth; but this is no longer true if the earth is not spherical. ”

“ Since all the diurnal circles are parallel to the equator, consequently, they would all, like the equator [83] be perpendicular to the horizon. Such a view of the heavenly bodies is called a right sphere, which may be thus defined: a right sphere is one in which all the daily revolutions of the stars are in circles perpendicular to the horizon. ”

“ In the lapse of one of our days, the light would have filled a sphere around the star having a diameter more than one hundred and fifty times the distance of the sun from the earth, and more than five times the dimensions of the whole solar system. Continuing its course and enlarging its sphere day after day, the sight presented to us would have been that of a gradually expanding nebulous mass—a globe of faint light continually increasing in size with the velocity of light. ”

“ Moreover modern astronomers, as well as ancient, find it convenient for very many purposes to make use of this sphere, though it has no material existence, as a means of representing the directions in which the heavenly bodies are seen and their motions. ”

“ By methods, the history and description of which we have not here sufficient space to give, it has been proved that the earth is, in form, a globe, or more strictly an ellipsoid, slightly drawn in at the poles and swollen round the equator. The polar diameter is 7899 miles, and the equatorial diameter 7926 miles, the difference amounting to only 27 miles. Thus, for ordinary purposes, we may regard the earth as being a true sphere. ”

“ According to Ptolemy’s scheme, the eighth sphere formed the outermost boundary of the universe; but later astronomers added to this system two other spheres—a ninth, called the Crystalline, which caused Precession of the Equinoxes; and a tenth, called the Primum Mobile, or First Moved, which brought about the alternation of day and night, by carrying all the other spheres round the Earth once in every twenty-four hours. ”

“ If we consider, that the Earth is not a perfect sphere, but an oblate spheroid, having its Axis shorter than its Equatoreal diameter; and that the Sun and Moon are constantly acting obliquely upon the greater quantity of matter about the Equator, pulling it, as it were, towards a nearer and nearer co-incidence with the Ecliptic ”

“ If a heavy body, as for example, a sphere of metal be suspended by a string from a point A, Figure 66, vertically above N, the North Pole of the earth, and allowed to hang freely, the motion of the earth about its axis ANS will twist the string, and so cause the sphere to rotate about its vertical diameter. If, now, the sphere be drawn aside to a point B and allowed to drop gently, it will begin to vibrate in the plane NAB, and as the rotation communicated to the sphere does not tend to withdraw it from that plane, it will continue constantly to move in it. ”

“ If this star-sprent sphere were made to revolve once in twenty-four hours, all the stars would successively Page 60 pass in review. How easily we could measure distances between stars, from a certain fixed meridian, or the equator! How easily we could tell when any particular star would culminate! It is as easy to take all these measurements when our earthly observatory is steadily revolved within the sphere of circumambient stars. Stars can be mapped as readily as the streets of a great city. ”

“ To an observer at either Pole, the Horizon and Equinoctial are coincident; and the Sun and Stars seem to move parallel to the Horizon: therefore, such an observer is said to have a Parallel position of the Sphere. To an observer any where between the Poles and Equator, the Parallels described by the Sun and Stars are cut obliquely by the Horizon, and therefore he is said to have an Oblique position of the Sphere. To an observer any where on the Equator, the Parallels of Motion, described by the Sun and Stars are cut perpendicularly, or at Right angles, 45by the Horizon ”

“ If we know so little about the existence of gravitation in the space accessible to our telescopes, what are we to say of those distant regions of space to which our view can never penetrate? Let a vast sphere be described of such mighty dimensions that it embraces not only all the objects visible to the unaided eye, not only all the objects visible in our most powerful telescopes, but even every object that the most fertile imagination can conceive, what relation must this stupendous sphere bear to the whole of space? ”

“ It was believed that the planets and stars were set in a series of concentric orbs or spheres, each so perfectly transparent that bodies in the outer ones were visible through all the intervening ones. The drawing shows the order of the spheres and the system of the universe according to Ptolemy. The earth is in the center enclosed by the sphere of the moon, beyond are the concentric spheres of Mercury, Venus, the sun, Mars, Jupiter and Saturn. Outside of all are the crystalline heavens and the abode of the blessed. ”

“ Even if the spheres were more or less flattened about the poles of their axes, as is the case with all the planets which we have been able carefully to measure, as well as with the sun, provided the axes of rotation were precisely parallel to each other, the mutual attraction of the masses would cause no disturbance of the spheres. The same would be the case if the polar axis of one sphere stood precisely at right angles to that of the other. ”

“ But as the bodies of the solar system are nearly spherical, they will all act upon one another and upon bodies placed on their surface, as if they were so many centres of attraction; and therefore we obtain the law of gravity, that one sphere will act upon another sphere with a force directly proportional to the quantity of matter, and inversely as the square of the distance between the centres of the spheres. ”

“ Occasionally the brilliant spheres that hung, spinning in mid-air, darted suddenly toward the larger globe in the center. When one of the smaller spheres neared it, the central ball emitted a peculiar high-pitched hum. The globes, combined with the darting lights, gave me the impression that they must be used by the Jovians for some astronomical purpose. The big sphere, I thought, must represent the home planet of the grotesque beings. ”