LECTUBE II. 



ACCELERATIONS OF THE MOON RELATIVE TO THE EARTH. 



WHEN three bodies move under their mutual attraction, their motions 

 are unknown to us except in the cases when they are approximately 

 elliptical ; but this restriction includes almost all the most important cases 

 in the Solar System. 



If one body of the system is greatly predominant and if the lesser 

 bodies are not close together, the centre of gravity of the greater body may 

 be taken as a common focus around which the others move in approximate 

 ellipses. Or again, if two bodies lie close together, their relative motion 

 may be approximately the same as though they were isolated, although the 

 system contains a third greatly predominant body ; for their relative motion 

 is affected by the difference of the attractions of the central body upon 

 them and not by the absolute value of those attractions. 



The Sun and Planets are an example of the first kind ; the Earth, 

 Moon and Sun of the second. The Earth and Moon describe orbits round 

 the Sun which are approximately ellipses, and the Moon might be regarded 

 as one of the planets ; but this point of view would not be a simple 

 one ; the disturbing action of the Earth would be too great, though it 

 is never so great as the direct attraction of the Sun, that is to say, 

 never great enough to make the Moon's path convex to the Sun. The 

 more convenient method is to refer the motion of the Moon to the 

 Earth, and counting only the difference of the attractions of the 

 Sun upon the Earth and upon the Moon, to find how this distorts 

 the otherwise elliptical relative orbit. This is the method of the Lunar 

 Theory. 



The position of the Sun must be referred to the same origin ; but 

 since the Earth describes an ellipse about the Sun which is disturbed by 



