HALLEYS COMET. 



Fig. 4. 



its direction c m' make an obtuse angle with the line c P, it will 

 retard it. 



This being understood, the disturbing action of a planet such 

 as Jupiter or Saturn on a comet such as Halley's may be easily 

 comprehended. In fig. 4, the orbit of the comet is represented at 

 A c P c" in its proper proportions, 

 A P being the major axis, P the place 

 of perihelion, A that of aphelion, 

 and s that of the focus in which the 

 sun is placed. The small circle de- 

 scribed round s represents in its 

 proper proportions the orbit of the 

 earth, whose distance is about twice 

 that of the comet when the latter is 

 at perihelion. The circle p p' p" re- 

 presents in its proper proportions 

 the orbit of Jupiter which, for illus- 

 tration, we shall consider as the 

 disturbing planet. 



It will be apparent on the mere 

 inspection of the diagram, that lines 

 drawn from the planet whatever be 

 its place, to any point whatever of 

 the comet's path between its aphe- 

 lion A, and the point m' where it 

 arrives at the orbit of the planet 

 in approaching the sun, will make 

 acute angles with the direction of 

 the comet's motion ; and that, con- 

 sequently, the comet will be accele- 

 rated by the action of the planet. 

 In like manner, it is apparent that 

 lines drawn from the planet what- 

 ever be its place, to any point 

 whatever of the comet's path between m and aphelion A, will 

 make obtuse angles with the direction of the comet's motion ; and, 

 consequently, the comet will be retarded by the action of the 

 planet, in departing from the sun, from m to A. 



In that part of the comet's path which lies within the planet's 

 orbit, the action of the planet alternately accelerates and retards 

 it, according to their relative position. If the planet be at p, 

 suppose p o drawn so as to be at right angles to the path of the 

 comet. Between m' and o the action of the planet at p will 

 accelerate the comet, and after the comet passes o it will retard 

 it. In like manner if the planet be at p", it will first retard 



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