| Sir James Hopwood Jeans - Mechanics, Analytic - 1907 - 364 pages
...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... | |
| John Ellard Gore - Astronomy - 1907 - 342 pages
...many attempts, he at last arrived at the following result : the squares of the periods of revolution **are proportional to the cubes of the mean distances from the sun.** This is the famous third law of Kepler, and its truth has been abundantly verified by all subsequent... | |
| William Ralph Boyce Gibson, Augusta Klein - Logic - 1908 - 500 pages
...drawn from it to the sun passes over equal areas in equal times. To these Kepler added a third : 3. **The squares of the periodic times are proportional to the cubes of the mean distances from the sun** (the periodic time being the time which the planet requires for the completion of its orbit) — T2... | |
| William Ralph Boyce Gibson - Logic - 1908 - 500 pages
...drawn from it to the sun passes over equal areas in equal times. To these Kepler added a third : 3. **The squares of the periodic times are proportional to the cubes of the mean distances from the sun** (the periodic time being the time which the planet requires for the completion of its orbit) — T2... | |
| Hamilton Association for the Cultivation of Science, Literature and Art - Science - 1908
...the distance of all the others follows as a natural consequence of the discovery of Kepler's great **law, that : " The squares of the periodic times are...proportional to the cubes of the mean distances."** The task, therefore, is only to find out the scale upon which the solar fysteni has been formed, as... | |
| Federigo Enriques - Logic - 1914 - 392 pages
...The areas described by the radius vectors are proportional to the time taken in describing them. 3. **The squares of the periodic times are proportional to the cubes of the** major axes. The same laws apply to the relative motions of the satellites of Jupiter and of other planets,... | |
| Encyclopedias and dictionaries - 1919
...third, that the distances of the various planets are so related to the periods of their revolution **that the squares of the periodic times are proportional to the cubes of the mean distances from the sun.** From these laws Newton made the following deductions : He inferred from the second law that the planet... | |
| Paul Carus - Philosophy - 1920
...easily find that T is proportional to a3/2 or that T2 is proportional to a8. This expresses Kepler's **third law that the squares of the periodic times are proportional to the cubes of the** major axes ; and, in the fourth theorem of the tract of 1684, Newton proved this law of Kepler and... | |
| Walter William Bryant - 1920 - 62 pages
...exactly the sesquiplicate proportion of the mean distances of the orbits," or as generally given, " **the squares of the periodic times are proportional to the cubes of the mean distances."** Kepler was evidently transported with delight and wrote, " What I prophesied two and twenty years ago,... | |
| ARTHUR SULLIVAN GALE, CHARLES WILLIAM WATKEYS - 1920
...planetary motion states that for different planets the squares of the times of describing their orbits **are proportional to the cubes of the mean distances from the sun.** That is ^ = jy ELEMENTARY FUNCTIONS 15. If the distance of the earth from the sun changed from 93,000,000... | |
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