ASTRONOMY. 163 



tan A : tan A' : : a + b cos I : a b cos I* And 

 tan A tan A' 



h 



" "" 



cos I (tan A 4- tan A')" 



This affords a first approximation to the distance of 

 the planet, supposing its orbit to be circular. 



163. The orbits of the superior planets, in- 

 elude both the Sun and the Earth within them j 

 and the Sun is nearly in the centre of each. 



a. The superior planets are seen in opposition to the 

 Sun as well as in conjunction ; and in the latter si- 

 tuation, the angle subtended by the planet is much 

 less than in the former. The angle, for example, 

 under which the diameter of Mars is seen in oppo- 

 sition to the Sun, is 18".972; and in conjunction 

 3".96, only a fifth part of the former. Hence, rea- 

 soning as before, a being the distance of the Earth 

 from the Sun, and b the distance of Mars from the 

 same, b + a : b a::5:l, and 2 b : 2 a : : 6 : 4, 

 or b : a : : 3 : 2. 



b. When the oppositions of Mars are observed in dif- 

 ferent places of the heavens, and when, of conse- 

 quence, Mars is in different points of his orbit, the 

 ratio of b to a is still found nearly the same; hence, 

 as we know that a does not vary much, the varia- 

 tion of b must be inconsiderable, and the Sun must 



therefore 



