THE ELEMENTS OF THE ORBIT OF A SATELLITE. 
805 
Let 
111 : 
kn 
1 
(230) 
m is the ratio of the moment of momentum of the earth’s rotation to that of the 
orbital motion of moon and earth round their common centre of inertia. (The /x 
of my paper on “Precession” is equal to the reciprocal of in , where nt 0 is the value 
of in when t— 0.) 
By (121) and (112) we have, 
k 
a—rrt 
Now the ellipticity of the earth due to rotation; and as T=-f/x?n/c 3 and 
\/ c/c 0 . therefore t=t 0 /£ g . 
Hence 
ioT q ') I" 
a= 2g f 
Differentiating logarithmically 
Also 
since 
a' 2 dn 
a n dt 
7 rff 
' £ dt : 
1 d£\ [2/, . /r f \ 2 
_ U7/U 1+ 1t 
+ 
u = _/L rf fw 2(1+ 
a V- dtjr? 1 “ 
+ 7m 
a=IU 
tC 
(231) 
(232) 
a '- - Gf)(3) m { 2 ( 1+ \T)) +7m 
Then by (121) and (112) 
a 
(233) 
Since fl = f 2 0 /£ 3 , and P is constant (or at least varies so slowly that we may neglect 
its variation), we have 
Now —=\, hence 
n 
Therefore 
MDCCCLXXX. 
3 m 
« — a £ \7v dt Jn 
Tt TV 1 \ 
“ a ~% t \2Xf/ 
/ , /I d^frtW 3m 
“ a V,; dt)\n*/T 2\t 
5 L 
(234) 
