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A NEW INVESTIGATION OF KEPLER^S PROBLEM, 



BY F. T. SCHUBERT. 



Communicated Ausaust 13* 1817 



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HIS famous Problem has the same relation to that part 



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of Astronomy, commonly called theoreticalf which the Problem 

 of three bodies has to the physical part of Astronomy. It con- 

 tains, in nncBf the laws of Kepler, or the whole theory of that 

 part of the science, which explains the true motions of the celes- 

 tial bodies, in the same manner, as the Problem of three bodies 

 comprehends the Newtonian theory of gravitation. After it is 

 theoretically resolved, it is still, in jpraxi, subjected to so many 

 difficulties, arising from the complicated calculation it requires, 

 that every attempt to render it more simple, will be favourably re- 



ceived by astrc 

 of this Proble 



ers. It is true, we have already many solutions 

 but after a full consideration of the subject, I 



am of opinion, that the only method strictly mathematical is that, 



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used by Laplace in his XmxAOYidlyfovk fMecaninue Celeste, torn. 



p. 170. et sea. J 



straight course, and 



may stop or advance, whenever we please ; whereas the other 



-methods lead us with difficulty through bye-paths, and oblige us 



to determine, in the very beginning of the computation, the degree 



of accuracy which we mean to attain, so that, afterwards, it is not 



in our power to bring the calculus to a higher degree of accuracy, 



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