134 THE EVOLUTION OF 



be either an ellipse or some other of the conic sections, 

 and each star must be in a focus of the orbit that the 

 other describes relatively to it. 



It is very important to realize clearly the nature of 

 this motion. If we imagine a body, free to move and 

 initially at rest, to be continually attracted towards a 

 fixed centre, it will clearly move directly towards it, and, 

 if the fixed centre is that of an attracting body, a collision 

 is inevitable. If, however, the attracted body has an 

 independent motion that is not directly towards or away 

 from the centre of attraction, it will not move directly 

 towards the centre of attraction, but it will pass round it in 

 a conic section, and if, in addition, its independent motion 

 is not excessive, the particular conic section traced will 

 be either an ellipse or a circle, which last may indeed be 

 regarded as an ellipse in which the longest and shortest 

 diameters have become equal. This movement is almost 

 exactly followed in the revolutions of the planets round 

 the Sun. 



So far we have assumed the centre of attraction to be 

 fixed, but force is a mutual influence exerted between two 

 bodies, and, in accordance with Newton's third law of 

 motion, whatever force one body exerts upon another, 

 this other must exert an equal and opposite force upon 

 the first. Hence the two components of a double star exert 

 equal forces of attraction upon each other, and both must 

 move in consequence. The general solution of this 

 problem is that the two bodies must describe similar 

 conic sections round a certain point between them that 

 is a focus of each orbit. This point is the centre of mass 

 of the pair. If the speeds of the bodies are not excessive 

 both orbits are either ellipses or circles. These laws 

 were first established by Newton towards the end of the 

 seventeenth century. 



