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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.
The Encyclopedia Americana: A Library of Universal Knowledge - Page 374
1919

American Practical Navigator, Volume 1

Nautical astronomy - 1977
...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....

An Introduction to Astronomy ...

John Bonnycastle - Astronomy - 1816 - 428 pages
...that the squares of the times in which any two planets complete their revolutions in their orbits, are proportional to the cubes of their mean distances from the sun. To illustrate this rule by an example : Venus, for instance, revolves round the sun in 224 days, and...

Mechanism of the Heavens

Mary Somerville - Celestial mechanics - 1831 - 621 pages
...law of Kepler gives whence (85) But, by Kepler's third law, the. squares of the periodic times of the planets are proportional 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...

Elements of Astronomy: Descriptive and Physical ...

Hervey Wilbur - Astronomy - 1831 - 144 pages
...the squares of the periods, in which any two pla* nets complete their revolutions in their orbits, are proportional to. the cubes of their mean distances from the Sun. \ This proportion requires illustration. Let the period of tha Earth's revolution, be called 12 months,...

On the Connexion of the Physical Sciences

Mary Somerville - Physical sciences - 1834 - 458 pages
...sections, having the sun in one of their foci ; and third, that the squares of the periodic times of the planets are proportional 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 sensible,...

The Connection of the Physical Sciences

Mary Somerville - Physical science - 1834 - 356 pages
...sections, having the sun in one of their foci ; and third, that the squares of the periodic times of the planets are proportional 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 sensible,...

Elements of Astronomy, Descriptive and Physical: In which the General ...

Hervey Wilbur - Astronomy - 1834 - 144 pages
...that the squares of the periods, in which any two planets complete their revolutions in their orbits, are proportional to the cubes of their mean distances from the Sun. This proportion requires illustration. Let the period of the Earth's revolution, be called 12 months,...

Transactions of the Annual Meetings of the Western Literary ..., Volume 6

...would lead him to the knowledge of the Keplerian law, that the squares of the periodic times of the planets are 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...