108 NEWTON S 



its parabolic motion combined with the advance of the 

 centre of gravity. The moon in this way describes thirteen 

 cycloidal curves in a year, and all of them concave towards 

 the sun. 



It appears then, that the orbits of the system composed 

 of our earth and its satellite, must be considered as traced, 

 not by either of these bodies but by their centre of gravity. 

 While neither body describes an ellipse round the sun, but 

 both revolve round each other and round their centre of 

 gravity, that centre itself describes an elliptical line a line 

 which would be a perfect ellipse if no disturbances of an 

 other kind than those which we have been considering in 

 terfered to alter the form of the orbit. To these disturbances 

 we now proceed. 



ii. While the primary planets and their satellites are 

 influencing each other and while the whole motion of each 

 subordinate system round the sun, the common centre, is 

 the elliptical orbit described by the centre of gravity of 

 each such system, there are disturbing forces exerted on 

 each planet by the rest, and on the motions of satellites by 

 the action of the sun also; so that many sensible deviations 

 take place from the motions, and from the orbits, which 

 those bodies, both primary planets and satellites, would 

 have, if they moved round the common centre undisturbed ; 

 that is, if they described elliptical orbits round the sun 

 by his attraction, without any other force acting on them, 

 except that attraction of the sun on each planet, and 

 the attraction of each planet on its satellites. If no such 

 disturbances existed, and the only forces that acted were 

 the mutual actions of the primary and satellites on each 

 other, and of the sun on the common centre of gravity of 

 the primary and satellites, the centre would describe an 

 ellipse round the sun, and the primary and satellites 

 would describe ellipses round each other and round that 



