in relation to Centripetal Velocity. 



59 



ty _ 



= miles square velocity acquired in falling through 

 one mile. 



r_! L_\r 



5280 "" 13956 3957 J 



5280 



±9 

 \% 



Hence 



G = ^ x 3956 2 = dynamical constant of 



gravitation having reference to the earth's f> . (23) 

 volume and density as unity . 



S = 355000 the sun's mass (earth unity). 



//To 



\f — = c = orbital velocity in circle radius a (miles). (26) 



o\/ — = area described per second in circle. 

 * V 2a 



-a /__ = area described in ellipse. 

 2V 2a * 



v = velocity, and r = radius vector at a point in elliptic 

 orbit. 



S=i Vf'»i' " ^<* e =ZSEF(fi g .l).(27) 



W 



= vsin ie=6 . v / — - - • tan A e 

 V 2a r 



(28) 



Because the product of the per- 

 pendiculars from the two foci of an 

 ellipse to a tangent at any point is 

 equal to the square of the semi- 

 minor axis 



Fig. 1. 



(2a-r)r ax 



b* 



= sec* t e, 



and 

 and 

 Hence 



ta*- v %£-i 



(29) 



. tan I 6= ^g»-(a-r)» = ^ 



w = c tan />. 



(30) 



