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century, subsequently discovered the great law of gravity, viz.,that every particle of matter in the universe attracts everyother particle with a force which is proportional to the inversesquare of their distance apart, he showed that two other lawsof the planetary movements, which Kepler also discovered, aswell as the law to which we have just referred, were necessaryresults of gravitation. Let us, therefore, now state all threeof these important laws in as accurate and simple language aspossible.
Kepler ’s first law is : The planets rotate round the Sun inellipses, each of rchich has the centre of the Sun as its focus.
If we speak somewhat more accurately, we may say, thatthe common centre of gravity of the Sun and any particularplanet is the focus about which (so far as those two bodies areconcerned) they both describe an ellipse;—the planet a largeellipse, the Sun a small one. It is, however, also true, thatthe orbit of an}’ planet relatively to the Sun (apart from anyperturbations caused by the attraction of the other planets), isan ellipse as stated by Kepler , although the Sun is alwaysmoving round about the common centre of gravity of itself andall the planets, from which the average distance of its centre isabout half-a-million of miles.
Kepler ’s second law is :—The velocity of each planet isgreatest when it is nearest to the Sun, and less when furtheraway, and in exactly such a proportion as involves the follow-ing rule :—
The area formed by the curved path of any planet, in anygiven time, and the straight lines joining its places at the endand the beginning of that time to the Sun, is always proportionalto the time in question, or always the same, in the same length oftime, for any given planet.
This is illustrated by Fig. XXXY., in •which the areassml, see, sxy, are supposed to be described, each in the sameinterval of time, around the Sun (s) ; and, consequently (bythe above law), to be equal to one another; the actual por-tions of the curved path, viz., ml, fe, xy, described by theplanet, decreasing in length as its velocity diminishes with its.increase of distance from s.