Figure of the Earth. 

 unit mass at P is 



v-dd' 



The moment of this force about is 



By 



-de 



487 



Now the re- 



action o£ the unit mass on the earth is exactly the opposite 



o£ the earth's action on the unit mass. Consequently the 



moment about of the couple exerted by the unit mass on the 



"dY . 

 earth is ^ in the direction tending to increase the angle 



up to a right angle. If the sun is at P, the couple exerted 

 by the sun, whose mass is S, is 



s!Z = S§K7r^cos0sin0. 

 00 o r 



If n is the angular velocity of the earth in its orbit 



KS 9 



— — = rn\ 



Thus the couple exerted by the sun on the earth becomes 

 § 7rBn 2 sin cos 0. 



Fig. 3. 



Pole of ecl/ptic 



£/i/?ths Pole 



Sun 



Referring to figure 3, by spherical trigonometry, 

 co> = sin a sin </>. 



