914 



ASTRONOMY. 



[UEPLRB'S LAVS. 



being turned nearly lwy toward* the earth. The 

 |. point of it* orbit, at which 



Man will appear most 

 1,'ihbout, will be at M 

 <Ki',-. 04) ; at the point* 

 M' and M', when at op- 

 poaition and conjunction, 

 its illuminated hemi- 

 sphere will be wholly 

 turned towards the earth. 

 Tin- diminution of its 

 disc from a complete 

 rin-le is, however, very 

 sensible ; and a small 

 table of its defective illu- 

 mination is given in the 

 Xiiutical Almanac for 

 every month in the year. 

 It is wholly insensible in Jupiter and Saturn ; and to re- 

 duce the observation of the limb to the centre, it is only 

 requisite to apply the semi-diameter. 



KEPLER'S LAWS. Copernicus, in explaining the ap- 

 parent motions of the planets in the heavens, confined 

 himself, it will be seen, to circular motion, and all the 

 planets were supposed to revolve round the sun, as a 

 centre in circular orbits, which he considered the most 

 natural of any. It has already, however, been seen that 

 the sun's motion in its orbit is not equable ; nor will it 

 be explained by supposing the earth to revolve in a circle, 

 of which the sun is placed eccentrically to the orbit, and 

 that it can only be accounted for by supposing that our 

 planet moves in an ellipse, of which the sun is placed in 

 one of the foci, whilst rejecting all the other cumbrous 

 hypotheses of the Ptolemaic system. In order to explain 

 the various inequalities caused by this elliptic motion, 

 Copernicus was forced to retain the supposition of epi- 

 cycle and eccentric. The observations of Tycho Brake, 

 in the hands of the immortal Kepler, however, threw off 

 this hut obstruction, and discovered not only the true 

 figure of the orbits of the planets, but likewise other won- 

 derful laws in relation to them. 



In examining the orbit of Mars, he endeavoured to 

 determine the eccentricity in respect to the sun, sup- 

 posing it to be a circle, in the following manner : 

 Supposing that D (Fig. 65) was the point round which 



Fig. M. 



; and he thought that Tycho's observations 

 n>i','ht be in error by that, or even a quantity of 2'. 

 When compared with observations of the planet out of 

 opposition, it, however, became apparent that this 01 !>i: 

 would not answer, the errors of longitude sometimes 

 amounting to 8', which he was persuaded could not be 

 due to the observation of Tycho. He was consequently 

 lad to doubt if the observations could be satisfied by any 

 circular hypothesis, and further computation served to 

 confirm kia doubts. Supposing S to be the sun (Fig. GO), 

 K..W. 



the motion of the planet was uniform, C the centre of 

 the circle, and 8 the position of the sun, M, M'. M", M", 

 being four places of Mars at opposition, he endeavoured 

 to determine the angles A D M*, A S M", in such a 

 manner that the four points, M, M', M", M", were 

 situated on the circumference of the circle with the 

 centre C. By assuming the distance S D, and the two 

 ogles, A D M", and A S M", he calculated, trigonome- 

 tricallv; all the other parts of the figure, in order to 

 determine if the four angles at S made up 360, and the 

 point*, S, C, and D, on the same straight line. After 

 evenly mont laborious trials, he at length arrived at one 

 which agreed so well with observation, that out of twelve 

 opposition*, none of them differed more than 1' 47* in 



M, Mars, and T and T', two positions of the earth, when 

 Mars returned to the same part of its orbit, whilst the 

 earth was at T, he determined by observation the angle 

 M T S, and when at T, the angle M T' S. The distances 

 T S, T 8 being known, and the angle T S T, the side T T', 

 and the angles S T T' and S T T will be known, and 

 consequently the angles M T T' and M 1" T. The side 

 M T may be found in the triangle M T T', and finally 

 the side M S in the triangle M T S, or the distance of 

 Mars from the sun. By this method Kepler determined 

 the distance M S, at perihelion and aphelion, the former 

 of which ho found to be 138500, and the latter 166780 ; 

 the mean distance being 152610 ; that of the earth being 

 supposed to be 100000. In the same manner Kepler 

 determined three other distances of Mars, from observa- 

 tion at different parts of his orbit, which he found to bo 

 166255 j 163100 ; 147760. But by calculating these dis- 

 tances on the supposition that the mean distance was 

 152640, and the eccentricity 14140, the distances were 

 found to be respectively 166605; 163883; 148539. 

 Whence the errors were found to be 350, 783, and 789. 

 The true distances of Mars from the sun were, therefore, 

 shorter than those calculated ; and as the line of apsides 

 and the perihelion and aphelion distance were truly 

 known, it followed that the orbit was of an oval form ; 

 and the ellipse being the simplest of all ovals, he found 

 that this was the true curve. By examining Mars at 

 many other parts of its orbit, he found that it agreed 

 closely with this supposition. Thus the first law of Kepler 

 was discovered by infinite labour and sagacity, viz., that 

 the planets revolve about the mn in elliptic orbits, the sun 

 being situated in one of the foci. 



The second great law of Kepler was likewise discovered 

 by him from observation, by comparing the velocity of 

 the planets in their orbit with their distances from the 

 sun, or rather the areas of the sectors, and the arcs 

 included between the radii vectores bounding them. He 

 found that when at their apsides, the velocity of their 

 motion was inversely as their distances from the sun, or 

 that the planets describe equal areas in equal times at those 

 points ; and he was of opinion that this was true at all 

 parU of the orbit, although he could not prove such to 

 be the case. This, however, has since been proved to bo 

 a necessary law, and to follow consequently from the 

 doctrine of universal gravitation. 



The third great law of Kepler connects the distances 

 of the planets from the sun, with the time in which they 

 make a complete revolution about that luminary. The 

 further a planet is removed from the sun, the slower he 

 found its motion on comparing it with the absolute 

 motion of the earth. The distance of Saturn from the 

 sun being nine and a-half times that of the earth ; 

 consequently if their rates of motion wore alike, the 



