The Elements of Astronomy, Physical and Geometrical, Volume 1

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J. Nicholson and sold, 1715 - Astronomy
 

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Page 138 - ... the squares of the periodic times are as the cubes of the distances from the common centre, the centripetal forces will be inversely as the squares of the distances.
Page 247 - Month, is the i ath of the fame according to the New. As the Form of the Year in different Nations is various, fo alfo is the Beginning of it.
Page 79 - If a body revolves in an ellipse (including the special case of a circle), it is required to find the law of the centripetal force tending to the focus of the ellipse.
Page xii - Because the weights of the planets towards the sun are reciprocally as the squares of their distances from the...
Page 137 - Let us now go on to the other planets. Because the revolutions of the primary planets about the sun and of the secondary about Jupiter and Saturn are phenomena of the same kind with the revolution of the moon about the earth, and because it has been moreover demonstrated that the centripetal forces of the primary planets are directed towards the centre of the sun and those of the secondary towards the centres of Jupiter and...
Page 7 - ... therefore prefer the latter, taking account of its variation by the effect of precession, and restoring it, by calculation at every instant, to a fixed position. Now, to determine the situation of the ellipse described by a planet with respect to this plane, three elements require to be known : — 1st, the inclination of the plane of the planet's orbit to the plane of the ecliptic ; 2dly, the line in which these two planes intersect each other, which of necessity passes through the sun, and...
Page 50 - COR. 1. Therefore, since those arcs are as the velocities of the bodies, the centripetal forces are in a ratio compounded of the duplicate ratio of the velocities directly, and of the simple ratio of the radii inversely. COR. 2. And since the periodic times are in a ratio compounded of the ratio of the radii directly and the ratio of the velocities inversely, the centripetal forces are in a ratio compounded of the ratio of the radii directly and the...
Page 41 - ... of forces. PROPOSITION III. THEOREM III. Every body, that by a radius drawn to the centre of another body, howsoever moved, describes areas about that centre proportional to the times, is urged by a force compounded of the centripetal force tending to that other body, and of all the accelerative force by which that other body is impelled.
Page 6 - ... between 16° and 1°. 2976. Line of nodes. — The inclination is not enough to determine the position of the plane of the orbit, for it is evident that an infinite variety of different planes may be inclined at the same angle to the ecliptic. If, however, the direction of the line of intersection of the plane of the orbit with the plane of the ecliptic (which line must always pass through the centre of the sun) be also defined, the position of the plane of the orbit will be determined. This...
Page xi - And by comparing these weights of the planets, and the intervals of the tones produced by the weights, with the interval of the spheres; and...

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