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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.
On the Connection of the Physical Sciences - Page 381
by Mary Somerville - 1846 - 460 pages

New American Practical Navigator, Volume 1

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....

A Philosophical and Mathematical Dictionary: Containing an ..., Volume 2

Charles Hutton - Astronomy - 1815 - 686 pages
...their periods round him ; the great law of which is, that the squares of the periodic times are always proportional to the cubes of their mean distances from the sun. , The periods, both tropical and sidereal, with the proportions of the mean distances of the several planets,...

An Introduction to Astronomy ...

John Bonnycastle - Astronomy - 1816 - 490 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 - 720 pages
...the 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 - 170 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 - 666 pages
...conic 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...

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

Hervey Wilbur - Astronomy - 1834 - 172 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,...

On the Connexion of the Physical Sciences

Mary Somerville - Astronomy - 1835 - 532 pages
...appear to move in hyperbolas, like fig. 8. The third law is, that the squares of the periodic times of the planets are proportional to the cubes of their...that number multiplied by itself, and the cube of a number is that number twice multiplied by itself. For example, the squares of the numbers 2, 3, 4,...