LECTUBE XVI. 



MOTION IN AN ORBIT OF ANY INCLINATION, (continued). 



To satisfy the equation at the end of Lecture XV, assume 



r = a[l+A l coa2(6- 0') + A, cos 20 + A, cos 20' + A 4 cos 2 (0 + 0')], 



neglecting the square of the disturbing force and the eccentricity ; thus in 

 the small terms we write 



d0_ ,_ , dff = , 



a> dt ~ n ' a ' dt~ 



Hence 



- = n -a [(2 - 2m) 2 A 1 cos 2(0- 0') + 4A cos 20 + 4mM 3 cos 20' 



+ (2 + 2m)- A t cos 2(0 + 0')] ; 

 substitute in the equation 



,cPr 



therefore 



H* = fj.a [1 + A, cos 2(0- 0') + A, cos 20 + A 3 cos 20' + A t cos 2(0 + 



- mVa 4 {1 + cos 2 ((9 - 0')} cos 4 1 + {cos 20 + cos 20'} 2 cos 3 1 sin 2 | 



- nV [(2 - 2m) 2 ^ cos 2 (0 - ^) + 4^ 2 cos 20 + 4m 2 ^ 3 cos 20' 



+ (2 + 2m) 2 A 4 cos 2 (0 + 0')J. 



