time, their whole number is probably many thousands. Comets so circumstanced, can only become visible by the rare coincidence of a total eclipse of the Sun-a coincidence which happened, as related by Seneca, 60 years before Christ, when a large comet was actually observed very near the Sun. But M. Arago reasons in the following manner, with respect to the number of comets :The number of ascertained comets, which, at their least distances, pass within the orbit of Mercury, is thirty. Assuming that the comets are uniformly distributed throughout the solar system, there will be 117,649 times as many comets included within the orbit of Uranus, as there are within the orbit of Mercury. But as there are 30 within the orbit of Mercury, there must be 8,529,470 within the orbit of Uranus! 552. Of 97 comets whose elements have been calculated by astronomers, 24 passed between the Sun and the orbit of Mercury: 33 between the orbits of Mercury and Venus; 21 between the orbits of Venus and the Earth; 15 between the orbits of Ceres and Jupiter. 49 of these comets move from east to west, and 49 in the opposite direction. The total number of distinct comets, whose paths during the visible part of their course had been ascertained, up to the year 1855, was about one hundred and fifty. 553. What regions these bodies visit, when they pass beyond the limits of our view; upon what errands they come, when they again revisit the central parts of our system; what is the difference between their physical constitution and that of the Sun and planets; and what important ends they are destined to accomplish in the economy of the Universe, are inquiries which naturally arise in the mind, but which surpass the limited powers of the human understanding at present to determine. 554. Such is the celestial system with which our Earth was associated at its creation, distinct from the rest of the starry hosts. Whatever may be the comparative antiquity of our globe, and the myriads of radiant bodies which nightly gem the immense vault above us, it is most reasonable to conclude, that the Sun, Earth, and planets differ little in the date of their origin. This, fact, at least, seems to be philosophically certain, that all the bodies which compose our solar system must have been placed at one and the same time in that arrangement, and in those positions in which we now behold them; because all maintain their present stations, and motions, and distances, by their mutual action on each other. Neither could it be where it 552. Phenomenon 60 years before Christ? M. Arago's reasoning and conclusion? Perihelion distances of various comets? Directions in longitude? Number whose paths have been ascertained? 558. What inquiries awakened by the visits of cometary bodies? 554. Remarks respecting the date of the solar system? that the whole system was created at once? What supposed proof is, nor move as it does, nor appear as we see it, unless they were all co-existent. The presence of each is essential to the system-the Sun to them, they to the Sun, and all to each other. This fact is a strong indication that their formation was simultaneous. CHAPTER X. OF THE FORCES BY WHICH THE PLANETS ARE RETAINED IN THEIR ORBITS. 555. HAVING described the real and apparent motions of the bodies which compose the solar system, it may be interesting next to show, that these motions, however varied or complex they may seem, all result from one simple principle, or law, namely, the LAW OF UNIVERSAL GRAVITATION. By gravitation is meant, that universal law of attraction, by which every particle of matter in the system has a tendency to every other particle. This attraction, or tendency of bodies towards each other, is in proportion to the quantity of matter they contain. The Earth, being immensely large in comparison with all other substances in its vicinity, destroys the effect of this attraction between smaller bodies, by bringing them all to itself. It is said, that Sir Isaac Newton, when he was drawing to a close the demonstration of the great truth, that gravity is the cause which keeps the heavenly bodies in their orbits, was so much agitated with the magnitude and importance of the discovery he was about to make, that he was unable to proceed, and desired a friend to finish what the intensity of his feelings did not allow him to do. 556. The attraction of gravitation is reciprocal. All bodies not only attract other bodies, but are themselves attracted, and both according to their respective quantities of matter. The Sun, the largest body in our system, attracts the Earth and all the other planets, while they in turn attract the Sun. The 555. Subject of this chapter? What is meant by gravitation? Upon what does the amount of this attraction depend? Influence of the Earth? Anecdote of Newton? 556. Is attraction reciprocal? What illustration cited? Ways in which attraction Earth, also, attracts the Moon, and she in turn attracts the Earth. A ball, thrown upwards from the Earth, is brought again to its surface; the Earth's attraction not only counterbalancing that of the ball, but also producing a motion of the ball towards itself. This disposition, or tendency towards the Earth, is manifested in whatever falls, whether it be a pebble from the hand, an apple from a tree, or an avalanche from a mountain. All terrestial bodies, not excepting the waters of the ocean, gravitate towards the center of the Earth, and it is by the same power that animals on all parts of the globe stand with their feet pointing to its center. 557. The power of terrestial gravitation is greatest at the Earth's surface, whence it decreases both upwards and downwards; but not both ways in the same proportion. It decreases upwards as the square of the distance from the Earth's center increases; so that at a distance from the center equal to twice the semi-diameter of the Earth, the gravitating force would be only one-fourth of what it is at the surface. But below the surface, it decreases in the direct ratio of the distance from the center; so that at a distance of half a semi-diameter from the center, the gravitating force is but half of what it is at the surface. Weight and Gravity, in this case, are synonymous terms. We say a piece of lead weighs a pound, or 16 ounces; but if by any means it could be raised 4000 miles above the surface of the Earth, which is about the distance of the surface from the center, and consequently equal to two semi-diameters of the Earth above its center, it would weigh only one-fourth of a pound, or four ounces; and if the same weight could be raised to an elevation of 12,000 miles above the surface, or four semi-diameters above the center of the Earth, it would there weigh only one-sixteenth of a pound, or one ounce.. 558. The same body, at the center of the Earth, being equally attracted in every direction, would be without weight; at 1000 miles from the center it would weigh one-fourth of a pound: at 2000 miles, one-half of a pound; at 3000 miles, three-fourths of a pound; and at 4000 miles, or at the surface, one pound. It is a universal law of attraction, that its power decreases as the square of the distance increases. The converse of this is also true, viz.: The power increases as the square of the distance decreases. Giving to this law the form of a practical rule, it will stand thus : The gravity of bodies above the surface of the Earth decreases in a duplicate ratio (or as the squares of their distances), in semidiameters of the Earth, from the Earth's center. That is, when manifests itself? 557. Where is the power of terrestrial gravitation greatest? How diminished? In what ratio as we ascend above the Earth? As we descend toward its center? Are weight and gravity the same? 558. What would be the weight of a body at the Earth's center? At 100 miles from the center? At 2000 miles? At 4000? What universal law? What rule based upon this law? What illustrations given? What rule the gravity is increasing, multiply the weight by the square of the distance; but when the gravity is decreasing, divide the weight by the square of the distance. Suppose a body weighs 40 pounds at 2000 miles above the Earth's surface, what would it weigh at the surface, estimating the Earth's semi-diameter at 4000 miles. From the center to the given height, is 11⁄2 semi-diameters; the square of 11⁄2, or 1.5 is 2.25, which, multiplied into the weight (40), gives 90 pounds, the answer. Suppose a body which weighs 256 pounds upon the surface of the Earth, be raised to the distance of the Moon (240,000 miles), what would be its weight? Thus, 4000)240,000(60 semi-diameters, the square of which is 3600. As the gravity in this case is decreasing, divide the weight by the square of the distance, and it will give 3600)256(1-16th of a pound, or 1 ounce. To find to what height a given weight must be raised to lose a certain portion of its weight. RULE. Divide the weight at the surface by the required weight, and extract the square root of the quotient. Ex. A boy weighs 100 pounds, how high must he be carried to weigh but 4 pounds? Thus, 100 divided by 4, gives 25, the square root of which is 5 semi-diameters, or 20,000 miles above the center. 559. Bodies of equal magnitude do not always contain equal quantities of matter; a ball of cork, of equal bulk with one of lead, contains less matter, because it is more porous. The Sun, though fourteen hundred thousand times larger than the Earth, being much less dense, contains a quantity of matter only 355,000 as great, and hence attracts the Earth with a force only 355,000 times greater than that with which the Earth attracts the Sun. The quantity of matter in the Sun is 780 times greater than that of all the planets and satellites belonging to the Solar System; consequently, their whole united force of attraction is 780 times less upon the Sun, than that of the Sun upon them. CENTER OF GRAVITY. 560. The Center of Gravity of a body, is that point in which its whole weight is concentrated, and upon which it would rest, if freely suspended. If two weights, one of ten pounds, the other of one pound, be connected together by a rod eleven feet long, nicely poised on a center, and then be thrown into a free rotary motion, the heaviest will move in a circle with a radius of one foot, and the lightest will describe a circle with a radius of ten feet; the center around which they move is their common center of gravity. (See the Figure.) to find what height a given weight must be raised to lose a certain portion of its weight? 559. Do bodies attract in proportion to their bulk? Why not? What illustrations? Quantity of matter in the Sun? 560. What is meant by the center of gravity? Illustration? How with the Sun and planets? How would it be if there was Thus the Sun and planets move around in an imaginary point as a center, always preserving an equilibrium. If there were but one body in the universe, provided it were of uniform density, the center of it would be the center of gravity towards which all the surrounding portions would uniformly tend, and they would thereby balance each other. Thus the center of gravity, and the body itself, would for ever remain at rest. It would neither move up nor down; there being no other body to draw it in any direction. In this case, the terms up and down would have no meaning, except as applied to the body itself, to express the direction of the surface from the center. 561. Were the Earth the only body revolving about the Sun, as the Sun's quantity of matter is 355,000 times as great as that of the Earth, the Sun would revolve in a circle equal only to the three hundred and fifty-five thousandth part of the Earth's distance from it; but as the planets in their several orbits vary their positions, the center of gravity is not always at the same distance from the Sun. The quantity of matter in the Sun so far exceeds that of all the planets together, that were they all on one side of him, he would never be more than his own diameter from the common center of gravity; the Sun is, therefore, justly considered as the center of the system. 562. The quantity of matter in the Earth being about 80 times as great as that of the Moon, their common center of gravity is 80 times nearer the former than the latter, which is about 3000 miles from the Earth's center. The secondary planets are governed by the same laws as their primaries, and both together move around a common center of gravity. Every system in the universe is supposed to revolve in like manner, around one common center. ATTRACTIVE AND PROJECTILE FORCES. 563. All simple motion is naturally rectilinear; that is, all bodies put in motion would continue to go forward in straight lines, as long as they met with no resistance or diverting force. On the other hand, the Sun, from his immense size, would, by the power of attraction, draw all the planets to him, if his attractive force were not counterbalanced by the primitive impulse of the planetary bodies to move in straight lines. 564. The attractive power of a body drawing another body but one body in the universe? 561. Suppose the Earth was the only body revolving around the Sun? Is the center of gravity always at the same distance from the Sun? Why not? How would it be if all the planets were on one side of him? 562. What is the amount of matter in the Earth as compared with the Moon? How with the secondary planets? With other systems in the universe? 563. What is the character of all simple motion? What illustrations given? 564 What is the attractive power called? |