APPLICATION OF SECTION V TO THE EARTH-MOON SYSTEM. 95 



VI. APPLICATION OF SECTION V TO THE EARTH- 

 MOON SYSTEM. 



This discussion neglects the rotational momentum and energy of the 

 moon, the eccentricity of the moon's orbit, the inclination of the equator 

 of the earth to the moon's orbit, the slight oblateness of the earth, and the 

 disturbing action of the sun. These factors have probably been of slight 

 importance in the series of changes which P and D may have undergone. 

 The observations show that at present, taking for the radius of the earth 

 that which would give it a volume equal to that of the actual oblate earth, 



(40) 



a^ = 3,958.2 miles S = 332,000 w, 



02 = 1,081.5 miles 1) = 0.997270 mean solar day 



r' = 92,897,000 miles P = 27.32166 mean solar days 



??ii =81.7 viz P' = 365.25635 mean solar days 



From the two-body problem we have * 



P'yjS+m. + m, (^1) 



Consequently the second equation of (8) becomes 



27rr'^Wi 



P',(™.+iy(«+™.+iy ^ (42) 



"2 ""2 



With the data of (40) the first equations of (8) and (42) give 



unit of time = mean solar day 0^=0.688303 



unit of length = 1.45285 a^ Wi =0.626311 



unit of mass =1.59665 w^ 



Using (40) and (43), equations (23) and (24) become 



(43) 



M= 3.01187 + 0.62803=3.639901 .... 



£; = -0.34632 + 1.95689 = 1.61057 J ^^ 



It is found from (25) that at the present time the ratio of the rate of 

 the change of the month to that of the day is 



With the value of m^ given above we find 



4 



^m^i =1.56 



^ There is, of course, a corresponding equation for the motion of the moon about the 

 earth, but since the direct perturbing action of the sun increases the period for a given 

 distance of the moon, the k found from this equation would be too small. 



