212 



GRAVITATIONAL METHODS 



[Chap. 7 



with a as equatorial and c as polar radius, while the radius in the prime 

 vertical is 



Py 



s/a^ cos^ (p + c^ sin^ (p 

 Southern Hemisphere Norlhem Hemisphere 



dO° 60* 40' 20' 20' 40" 60' 80' 

 Latitude 



Fig. 7-736. Planetary variation of curvature radii of reference ellipsoid in meridian 



and prime vertical. 



The variation of these radii with latitude is shown in Fig. 7-736. There- 

 fore, with sufl&cient approximation 



{U^\ 



2 2 



g a — c 2 

 5— -cos V?, 



where the second factor is approximately twice the flattening, or 

 2 -(a — c)/a (see eq. 7-14a). By substitution of the numerical value for 

 the equatorial radius, 



(t/A)norm. = 5.15- 10"' (1 + COS 2<p). (7-65) 



