...of the sun is one of the foci, 3°. The squares of the times of revolution of the different planets are proportional to the cubes of their mean distances from the sun, or the semi-major axes of their orbits. These laws relate only to the center of inertia of each planet,...

...of the sun is one of the foci, 3°. The squares of the times of revolution of the different planets are proportional to the cubes of their mean distances from the sun, or the semi-major axes of their orbits. These laws relate only to the center of inertia of each planet,...

...thus moving fastest when nearest to the sun, 1 slowest when farthest from him. 3. The squares of their periodic times are proportional to the cubes of their mean distances from the sun. 8. It is with the latter of these laws alone that we are concerned at present, and its use in investigating...

...ellipses about a common centre, and the centripetal force varies inversely as the square of the distance ; the squares of the periodic times are proportional to the cubes of the major axes. A particle moves in an ellipse about the centre of force in the focus S : when the...

...That the areas included between two radii vectores are as the times of describing the arcs. 3. That the squares of the periodic times are proportional to the cubes of the distances. It must not be supposed that it was mere chance that led to these discoveries. His previous...

...the periodic times of the planets, that is, of the times of a complete revolution in their orbits, are proportional to the cubes of their mean distances from the sun ; in other words, that the square of the periodic time of one planet is to the square of the periodic...

...motion -^t J~—--, from which it is apparent, that for difa* . ferent bodies revolving about the sun, the squares of the periodic times are proportional to the cubes of the mean distances, so far as the masses of the bodies, or rather the inequality of their masses, can...

...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 the sun. 155. To find the position of the line of the apsides of the solar orbit. Let B and D, Fig. 24, on,...

...in one of their foci. 3°. The squares of the times of the revolutions of the planets about the sun, are proportional to the cubes of their mean distances from the sun. 184. From these laws, derived from observation, Newton deduced the law of universal gravitation. We...

...focus. 10. If any number of bodies move in ellipses about a common centre of force, which is the focus, the squares of the periodic times are proportional to the cubes of the major axis. 1 1 . The arc of a cycloid measure from the vertex to any point equals twice the chord...