| Sir Richard Gregory - Geomorphology - 1893 - 277 pages
...sweeps over equal areas in equal times. (3) The squares of the times of revolution of all the planets **are proportional to the cubes of the mean distances from the sun. These** laws apply equally wejl to the motions of satellites round their primary planets. The first law has... | |
| W. W. ROUSE BALL - 1893
...ellipses be described under a central force which varies inversely as the square of the distance, then **the squares of the periodic times are proportional to the cubes of the** major axes ; to * Kigaud, pp. 16-20; Edleston, Cotes Correspondence, p. 207; see also Brewster, vol.... | |
| 1896
...that a straight line drawn from the planet to the sun passes over equal areas in equal times. Third. **That the squares of the periodic times are proportional to the cubes of the mean distances.** Kepler, who is one of the chief founders of modern astronomy, deduced these laws governing planetary... | |
| John Clark Ridpath - 1897
...comparison of the different powers of the numbers which express these distances and times, and he found **that the squares of the periodic times are proportional to the cubes of the mean distances from the sun.** He considered this the most important of all, and demonstrated it for all the planets then known. It... | |
| Sir Isaac Newton, Percival Frost - Curves, Plane - 1900 - 292 pages
...planet to the sun's centre are, in the same orbit, proportional to the time of describing them. III. **That the squares of the periodic times are proportional to the cubes of the** major axes. 219. Kepler's laws, although not rigidly true, are sufficiently near to the truth to have... | |
| William Woolsey Johnson - Mechanics - 1901 - 434 pages
...describes equal areas in equal times. 2. The planets describe ellipses having the sun at a focus. 3. **The squares of the periodic times are proportional to the cubes of the mean "distances.** Kepler was not possessed of correct notions regarding the nature of motion and force, but we have seen... | |
| Edward Macomb Duff, Thomas Gilchrist Allen - Bible and spiritualism - 1902 - 396 pages
...every point that a straight line drawn from it to the sun passes over equal areas in equal times. III. **The squares of the periodic times are proportional to the cubes of the mean** distances.1 1 Ball's " Astronomy." This proves beyond doubt the law and order of the planets. We had... | |
| John Cox - Mechanics - 1904 - 332 pages
...describing a complete ellipse 2 x area of the ellipse Thus 2' 3 oc a 3 . Kepler's Third Law is;— **The squares of the periodic times are proportional to the cubes of the** major axes. It is to be inferred that the accelerations of all the different planets are such as would... | |
| English periodicals - 1903
...proportion." The mathematical expression for Kepler's Third Law is that in the case of the planets " **the squares of the periodic times are proportional to the cubes of the mean distances."** Newton's grand generalisation, which is absolutely exact and universal, requires that the united mass... | |
| J.H. JEANS, M.A. - 1907
...earth. 5. Assuming that the planets describe circles round the sun with different periodic times, such **that the squares of the periodic times are proportional to the cubes of the** radii of the circles, show that the accelerations of the planets are inversely proportional to the... | |
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