 | Nautical astronomy - 1977 - 1412 pages
...sweeps over equal areas in equal intervals of time. 3. The squares of the sidereal periods of any two planets are proportional to the cubes of their mean distances from the sun. In 1687 Isaac Newton stated three "laws of motion," which he believed were applicable to the planets.... | |
 | New Church gen. confer - 1855 - 590 pages
...present planetary orbits ; and he gives a formula which brings out the same results as Kepler's law, that the squares of the periodic times of the planets are proportional to the cubes of their respective distances, There is also another motion which he points out, which is at present not seen.... | |
 | Encyclopedias and dictionaries - 1823 - 894 pages
...some relation existed between them. After many attempts continued for 17 years, he at last discovered that the squares of the periodic times of the planets are proportional to the cubes of the greater axis of their orbits. CHAP. IV. Of the Orbit j of the Comets. OF all the celestial bodies,... | |
 | Mary Somerville - Astronomy - 1831 - 710 pages
...the orbits of the planets and comets are conic sections, having the sun in one of their foci. iii. That the squares of the periodic times of the planets...to the cubes of their mean distances from the sun. 310. It has been shown, that if the law of the force which acts on a moving body be known, the curve... | |
 | Mary Somerville - Celestial mechanics - 1831 - 720 pages
...indefinitely small time dt, is J cdt ; hence the law of Kepler gives whence (85) But, by Kepler's third law, the. squares of the periodic times of the planets...to the cubes of their mean distances from the sun ; therefore T' = *" a\ k being the same for all the planets. Hence c == but 2a (1 — e*) is 2SV, the... | |
 | Mary Somerville - Physical science - 1834 - 390 pages
...orbits of the planets and comets are conic sections, having the sun in one of their foci ; and third, that the squares of the periodic times of the planets...to the cubes of their mean distances from the sun. These laws extend also to the satellites. Latent heat. Caloric existing in all bodies, which is not... | |
 | Western Literary Institute and College of Professional Teachers - Education - 1837 - 286 pages
...the thought conveyed by it, any more than it would lead him to the knowledge of the Keplerian law, that the squares of the periodic times of the planets...proportional to the cubes of their mean distances from the sun's centre! ' These are subsequent efforts. A child of four years of age can say, "God exists," but... | |
 | William Augustus Norton - Astronomy - 1839 - 530 pages
...is an ellipse, of which the sun occupies one of the foci. 3. The squares of the times of revolution of the planets are proportional to the cubes of their mean distances from the sun, or of the semi-major axes of their orbits. These laws are known by the denomination of Kepler's Laws.... | |
 | John Gummere - Astronomy - 1842 - 516 pages
...round the sun and their mean distances from him, Kepler discovered that the squares of the periodical times of the planets are proportional to the cubes of their mean distances from him. 155. To find the position of the line of the apsides of the solar orbit. Let B and D, Fig. 24,... | |
 | John Stuart Mill - Knowledge, Theory of - 1843 - 654 pages
...other the opposite angles are equal, is true of all such lines and angles, by whatever cause produced. That the squares of the periodic times of the planets are proportional to the cubes of their distances from the sun, is an uniformity derived from the laws of the causes which produce the planetary... | |
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The squares of the periods of revolution of any two planets are proportional to the cubes of their mean distances from the sun. 
