244 OUTLINES OF NATURAL PHILOSOPHY. 



SECT. II. 



OF THE FORCES WHICH DISTURB THE ELLIPTICAL 

 MOTION OF THE PLANETS. 



VV HEN there are only two bodies that gravitate to 

 one another, with forces inversely as the squares 

 of their distances, it appears from the last section 

 that they move in conic sections, and describe, 

 about their common centre of gravity, equal areas 

 in equal times, that centre either remaining at 

 rest, or moving uniformly in a straight line. But 

 if there are three bodies, the action of any one on 

 the other two, changes the nature of their orbits, 

 so that the determination of their motions be- 

 comes a problem of great difficulty, distinguish- 

 ed by the name of THE PROBLEM OF THE THREE 

 BODIES. 



The solution of this problem, in its utmost generali- 

 ty, is not within the power of the mathematical 

 sciences, as they now exist. Under certain limita- 

 tions, however, and such as are quite consistent 

 with the condition of the heavenly bodies, it ad- 

 mits of being resolved. These limitations are, 

 that the force which one of the bodies exerts on the 

 other two, is, either from the smallness of that 

 body, or its great distance, very inconsiderable, in 



respect 



