...ones do round their centre the .Sun; viz. in such manner that, in the satellites of the same planet, the squares of the periodic times are proportional to the cubes of their distances from the primary planet. SATELLITE« of Jupiter, are four little moons, or secondary...

...do round their centre the sun ; viz, in ¡>ueh a maniirr that, in the satellites of the same planet, the squares of the periodic times are proportional to the cubes of their distances from the primary planet. For the physical cause of their motions, see GRAVITY. See...

...ones do round their centre the Sun ; viz. in such manner, that, in the satellites of the same planet, the squares of the periodic times are proportional to the cubes of their distances from the primary planet. SATELLITES of Jupiter, are four little moons, or secondary...

...ones do round their centre the Sun ; viz. in such manner, that, in the satellites of the same planet, the squares of the periodic times are proportional to the cubes of their distances from the primary planet. SATELLITES of Jupiter, are four little moons, or secondary...

...the mean distances. Farther, it is rigorously demonstrable, that when bodies circulate in such manner that the squares of the periodic times are proportional to the cubes of the distances, the central force which actuates them is in the inverse ratio of the square of the distance...

...proportional to the times ; 3. that in the movements of different planets round the same central body the squares of the periodic times are proportional to the cubes of the mean distances. The Rhodolphirie tables of the planetary movements, in constructing which he assisted Tycho, were published...

...section, if the projectile force does not exceed a certain limit, will become an ellipse. The tliird law, that the squares of the periodic times are proportional to the cubes of the distances, is a property which belongs to the bodies describing elliptic orbits, according to the conditions...

...sector S Pp by the time, t, and the sector varies as *Ja ; therefore Q varies as i^/07 253. Again, the squares of the periodic times are proportional to the cubes of the transverse axes. For let 6 be the less, </ the greater axis, and a the parameter ; then by conies ad...

...masses are respectively 0-265252 and 133412; and these numbers are in the same proportion as 1637029 (12 ciphers), and 823365 (18 ciphers). (39.) The three...were first explained from the theory by Newton, about AD 1680. (40. ) The last of these is not strictly true, unless we suppose that the central body is...

...areas constitute two of the three celebrated truths known by the name of Kepler's laws. The third, viz. that the squares of the periodic times are proportional to the cubes of the mean distances from the sun, was not discovered till twelve years after, although, before the publication of his '...