. Astronomy for high schools and colleges . of the sun from the geometricalcentre of the orbit (or, as they supposed, the distance ofthe earth from the centre of the suns orbit)—twice asgreat as it really was. An immediate consequence of these facts of observa-tion is Keplers second law of planetary motion, that theradii vectores drawn from the sun to a planet revolvinground it, sweep over equal areas in equal times. Sup-pose, in Fig. 51, that S represents the 23osition of the sun,and that the earth, or a planet, in a unit of time, say aday or a week, moves from P, to P^. At another partof its
. Astronomy for high schools and colleges . of the sun from the geometricalcentre of the orbit (or, as they supposed, the distance ofthe earth from the centre of the suns orbit)—twice asgreat as it really was. An immediate consequence of these facts of observa-tion is Keplers second law of planetary motion, that theradii vectores drawn from the sun to a planet revolvinground it, sweep over equal areas in equal times. Sup-pose, in Fig. 51, that S represents the 23osition of the sun,and that the earth, or a planet, in a unit of time, say aday or a week, moves from P, to P^. At another partof its orbit it moves from P to P^ in the same time,and at a third part from P^ to P,. Then the areasSP,P,, SPP,, SP,P, will all be equal. A littlegeometrical consideration will, in fact, make it clear thatthe areas of the triangles are equal when the angles at 8are inversely as the square of the radii vectores, SP, etc., 124 ASTRONOMY, since the expression for the area of a triangle in whicli theangle at S is very small is ^ angle S X ^ i^^*. Fig. 51.—law of abeas. In the time of Keplek the means of measuring thesuns angular diameter were so imperfect that the preced-ing method of determining the path of the earth aroundthe sun could not be applied. It was by a study of themotions of the planet Mars, as observed by Ttcho Brahe,that Kepler was led to his celebrated laws of planetarymotion. He found that no possible motion of Mars in atruly circular orbit, however eccentric, would represent theobservations. After long and laborious calculations, andthe trial and rejection of a great number of hypotheses,he was led to the conclusion that the planet Mars movedin an ellipse, having the sun in one focus. As the analo-gies of nature led to the inference that all the planets,the earth included, moved ia curves of the same class,and according to the same law, he was led to enunciatethe first two of his celebrated laws of planetary motion,which were as follow : * More exactly if we consid
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