CHAPTER THREE 



DETERMINING THE DISTANCES TO THE HEAVENLY 

 BODIES 



These mathematic men have thoughts that march 

 From sphere to sphere and measure out the blue 

 Of infinite space like roods of garden ground. 



BLACKIE 



A BABY reaches for the moon and a dog barks at it. 

 Apparently they think it is near them. Can you tell 

 merely by looking at it whether it is near or far away? 

 Have you ever mistaken a town clock at night or some 

 other artificial light for the moon and are you sure that 

 the moon is farther away than objects on the earth? 

 Doubtless you have read about the great distances of 

 the sun, moon, and other heavenly bodies from the earth, 

 and perhaps you have wondered how it is possible to 

 learn the distance to an object that no one has ever 

 been able to reach. Astronomers and surveyors do 

 this in a rather simple way. 



Determining distances without measuring them. A 

 surveyor can find the distance to a tree on the other 

 side of a river without crossing the river. On his own 

 side of the river he drives two stakes and then carefully 

 measures the distance between them. Then with his 

 instruments he -sights at the tree from each stake, meas- 

 uring the angles that lines from each stake to the tree 

 make with a line connecting the two stakes. The two 

 stakes and the tree form a triangle of which he knows 

 the length of one side and the size of two angles. By his 

 knowledge of trigonometry he is then able to calculate 

 the length of the other sides of the triangle and thus find 

 the distance from either of the stakes to the tree. By ex- 



167 



