Gravitation: An Elementary Explanation of the Principal Perturbations in the Solar System

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C. Knight, 1834 - Gravitation - 215 pages

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Page 29 - The third, viz. that the squares of the periodic times are proportional to the cubes of the mean distances...
Page 22 - In all our diagrams it is to be understood, that the planet, or satellite, moves through its orbit in the direction opposite to the motion of the hands of a watch. This is the direction in which all the planets and satellites would appear to move, if viewed from any place on the north side of the planes of their orbits. The time in which the planet moves from any one point of the orbit through the whole orbit, till it comes to the same point again, is called the planet's periodic time.
Page 14 - The planets describe ellipses which are very little flattened, and differ very little from circles. Three or four comets describe very long ellipses : and nearly all the others that have been observed are found to move in curves which cannot be distinguished from parabolas. There is reason to think that two or three comets which have been observed move in hyperbolas.
Page vii - The exercise of the mind in understanding a series of propositions, where the last conclusion is geometrically in close connexion with the first cause, is very different from that which it receives from putting in play the long train of machinery in a profound analytical process. The degrees of convictiOD in the two cases are very different.
Page 13 - S) ; and if no other force whatever but this attraction acts upon the body ; then the body will move in one of the following curves — a circle, an ellipse, a parabola, or a hyperbola. " In every case the curve will, at the point A, have the same direction as the line AB ; or (to use the language of mathematicians) AB will be a tangent to the curve at A.
Page 7 - The accuracy of astronomical observations is carried to a degree that can scarcely be imagined ; and by means of these we can every day compare the observed place of a planet with the place which was calculated beforehand, according to the law of gravitation. It is found that they agree so nearly as to leave no doubt of the truth of the law. The motion of Jupiter, for instance, is so perfectly calculated, that astronomers have computed ten years beforehand the time at which it will pass the meridian...
Page viii - ... conclusion is geometrically in close connexion with the first cause, is very different from that which it receives from putting in play the long train of machinery in a profound *. analytical process. The degrees of conviction in the two cases are very different. It is known to every one who has been engaged in the instruction of students at our Universities, that the results of the differential calculus are received by many, rather with the doubts of imperfect faith than with the confidence...
Page 20 - A, the sun's attraction (which is always directed to the sun) retards the planet hi its orbit, just as the force of gravity retards a ball which is bowled up a hill ; and when it has reached c, its velocity is extremely small ; and, therefore, though the sun's attraction at c is small, yet the deflection which it produces in the planet's motion is, (on account of the planet's slowness there) sufficient to make its path very much curved, and the planet approaches the sun, and goes over the same orbit...
Page 1 - Every particle of matter attract» every other particle. That is, if there were a single body alone, and at rest, then, if a second body were brought near it, the first body would immediately begin to move towards the second body. Just in the same manner, if a needle is at rest on a table, and if a magnet is brought near it, the needle immediately begins to move towards the magnet, and we say that the magnet attracts the needle. But magnetic attraction belongs only to certain bodies : whereas the...
Page 9 - ... will, at last, be turned into a motion in the opposite direction. We have yet to consider a case much more important for astronomy than either of these : Suppose that a body is projected in a direction transverse to, or crossing, the direction in which the force draws it, how will it move ? (14.) The simplest instance of this motion that we can imagine is the motion of a stone when it is thrown from the hand in a horizontal direction, or in a direction nearly horizontal. We all know that the...

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