...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....

...founded on a series of the most accurate observations, he discovered, that the squares of the times in which any two planets complete their revolutions...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...

...series of the most accurate observations^ that the squares of the periods, in which any two pla* nets complete their revolutions in their orbits, are proportional...proportion requires illustration. Let the period of tha Earth's revolution, be called 12 months, and the period of Mercury's revolution, 3 months. By the...

...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...

...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...

...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...

...From Kepler's third law, we know that the squares of the periodical times of any two of the planets are proportional to the cubes of their mean distances from the sun. This law is independent of the eccentricities of the orbits; and the same relation would subsist between...

...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....

...the sun, pass over equal areas in equal times; and 3. The squares of their times of annual revolution are proportional to the cubes of their mean distances from the sun. By the second law, the planets move slowest when farthest from the sun ; as the radius vector, being...

...in making a revolution. Kepler discovered that the squares of the periodic times of any two planets are proportional to the cubes of their mean distances from the sun. Take, for example, the Earth and Mars, whose periods are 365.2504 and 686.9796 days, and whose distances...