...referred to the famous law of Kepler, which declares that for planets moving around the same primary the squares of the periodic times are proportional to the cubes of the mean distances. This principle will answer every question regarding the periodic time which the Moon would have it'...

...sweeps over equal areas in equal times. (3) The squares of the times of revolution of all the planets are proportional to the cubes of the mean distances from the sun. These laws apply equally wejl to the motions of satellites round their primary planets. The first law has...

...ellipses be described under a central force which varies inversely as the square of the distance, then the squares of the periodic times are proportional to the cubes of the major axes ; to * Kigaud, pp. 16-20; Edleston, Cotes Correspondence, p. 207; see also Brewster, vol....

...that a straight line drawn from the planet to the sun passes over equal areas in equal times. Third. That the squares of the periodic times are proportional to the cubes of the mean distances. Kepler, who is one of the chief founders of modern astronomy, deduced these laws governing planetary...

...comparison of the different powers of the numbers which express these distances and times, and he found that the squares of the periodic times are proportional to the cubes of the mean distances from the sun. He considered this the most important of all, and demonstrated it for all the planets then known. It...

...planet to the sun's centre are, in the same orbit, proportional to the time of describing them. III. That the squares of the periodic times are proportional to the cubes of the major axes. 219. Kepler's laws, although not rigidly true, are sufficiently near to the truth to have...

...describes equal areas in equal times. 2. The planets describe ellipses having the sun at a focus. 3. The squares of the periodic times are proportional to the cubes of the mean "distances. Kepler was not possessed of correct notions regarding the nature of motion and force, but we have seen...

...every point that a straight line drawn from it to the sun passes over equal areas in equal times. III. The squares of the periodic times are proportional to the cubes of the mean distances.1 1 Ball's " Astronomy." This proves beyond doubt the law and order of the planets. We had...

...describing a complete ellipse 2 x area of the ellipse Thus 2' 3 oc a 3 . Kepler's Third Law is;— The squares of the periodic times are proportional to the cubes of the major axes. It is to be inferred that the accelerations of all the different planets are such as would...

...proportion." The mathematical expression for Kepler's Third Law is that in the case of the planets " the squares of the periodic times are proportional to the cubes of the mean distances." Newton's grand generalisation, which is absolutely exact and universal, requires that the united mass...