| James M'Intire - Astronomy - 1850 - 326 pages
...periodic times of the planets and their mean distances from the sun. From these comparisons he found **that the squares of the periodic times are proportional to the cubes of** their mean distances, or to the cubes of the semi-major axes of their elliptic orbits. This law prevails... | |
| Robert Grant - Astronomy - 1852 - 637 pages
...second, that a line joining the planet and the sun sweeps over equal areas in equal times; the third, **that the squares of the periodic times are proportional to the cubes of the mean distances from the sun.** Kepler was conducted to the first and second of these laws by researches on the motion of the planet... | |
| 1856
...foci. 2. That the areas included between two radii vectores are as the times of describing the arcs. 3. **That the squares of the periodic times are proportional to the cubes of the** distances. It must not be supposed that it was mere chance that led to these discoveries. His previous... | |
| Cambridge univ, exam. papers - 1856
...ellipses about a common centre, and the centripetal force varies inversely as the square of the distance ; **the squares of the periodic times are proportional to the cubes of the** major axes. A particle moves in an ellipse about the centre of force in the focus S : when the particle... | |
| Carl Friedrich Gauss - Orbits - 1857 - 326 pages
...motion -^t J~—--, from which it is apparent, that for difa* . ferent bodies revolving about the sun, **the squares of the periodic times are proportional to the cubes of the mean distances,** so far as the masses of the bodies, or rather the inequality of their masses, can be neglected. 8.... | |
| E. D. Bourdillon - Education and state - 1859
...focus. 10. If any number of bodies move in ellipses about a common centre of force, which is the focus, **the squares of the periodic times are proportional to the cubes of the** major axis. 1 1 . The arc of a cycloid measure from the vertex to any point equals twice the chord... | |
| Ormsby MacKnight Mitchel - Astronomy - 1860 - 376 pages
...planetary orbit, or will it increase or decrease the length of the major axis? Kepler's third law tells us **that the squares of the periodic times are proportional to the cubes of the** major axes, and from this relation it is manifest that any change in the elliptic velocity of a planet... | |
| Astronomy - 1860
...planetary orbit, or will it increase or decrease the length of the major axis? Kepler's third law tells us **that the squares of the periodic times are proportional to the cubes of the** major axes, and from this relation it is manifest that any change in the elliptic velocity of a planet... | |
| George Robarts Smalley - 1862
...plane proportional to the time. (2) The orbits are ellipses having the sun in one of their foci. (3) **The squares of the periodic times are proportional to the cubes of the mean distances from the Sun.** 3. Deductions from Kepler's Laws, From Law (1) — the force which acts upon the bodies tends always... | |
| Sir Isaac Newton - Curves, Plane - 1863 - 288 pages
...planet to the Sun's center 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. These laws were discovered by Kepler from observations made on the planet Mars, and stated... | |
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