 | Peter Nicholson - 1825 - 1046 pages
...section, if the projectile force does not exceed a certain limit, will become an ellipse. The t laid law, that the squares of the periodic times are as the cubes of the distances, is a property which belongs to the bodies describing elliptic orbits under the conditions... | |
 | 1832 - 698 pages
...: that the planets move in elliptical orbiis ; that equal areas are described in equal times ; and that the squares of the periodic times, are as the cubes of their distances. At the same time that Kepler was thus laying the foundation of physical astronomy,... | |
 | Mary Somerville - 1831 - 710 pages
...they make the two satellites fall through in a second ; hence F: F' ::«_ :a'_, or " T1' T,* ' but the squares of the periodic times are as the cubes of the mean distances ; hence TZ • 7*8 •• n3 • nt* . i . it .. a . a , whence F : F' ::— : • 325. As the eartli... | |
 | John Martin Frederick Wright - 1831 - 282 pages
...an equiangular spiral might be described. 18. In different elliptic orbits, having a common focus, the squares of the periodic times are as the cubes of the major axes. ST. JOHN'S COLLEGE, 1824. 1 - DEFINE what is meant by the terms " limit " and " limiting... | |
 | William Whewell - 1832 - 286 pages
...means of Prop. 4. Cor 7- of the Introduction. It was discovered by Kepler, and is called his third Law, that the squares of the periodic times are as the cubes of the mean distances from the sun. From this it follows, Introd. Prop. 4. Cor. 6, that the forces are inversely as the distances... | |
 | James Renwick - 1832 - 584 pages
...whence Va:ca: :r^R'; and as the timas are inversely as the velocities, T3 : P : : R' : r', (89) or the squares of the periodic times, are as the cubes of the radii. 66. Having thus investigated the circumstances of motion, in those lines and curves that will... | |
 | 1840 - 526 pages
...swept by each radius vector in a given lime is a constant quantity for the same planet, and lastly, that the squares of the periodic times are as the cubes of the mean distance, have supplied means for a much more accurate determination of the sun's parallax. Assuming... | |
 | B. Powell - 1834 - 420 pages
...; the periodic times in which those orbits are completed; and establishes the remarkable relation, that the squares of the periodic times are, as the cubes of the major axes, the halves of which are the mean distances, as a dynamical consequence from a law of force... | |
 | 1834 - 578 pages
...follows. The semi-axis major is known, the periodic time being known ; for, by Kepler's third law, the squares of the periodic times are as the cubes of the major axis : the periodic time of the earth is known, and its semi-axis major. Now, the semi-axis major... | |
 | 1834 - 574 pages
...follows. The semi-axis major is known, the periodic lime being known ; for, by Kepler's third law, the squares of the periodic times are as the cubes of the major axis : the periodic time of the earth is known, and its semi-axis major. Now, the semi-axis major... | |
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... 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. 
