LAW OF INVERSE SQUARE 281 



acting along BA. This force can always be regarded as acting from 

 the fixed point G, for its line of action is always BG. Moreover, 

 its magnitude per unit mass of star B is 



or, from relations (115), 



This is a force ^ acting towards G if we take 



T 



(ra + ra') 2 



Thus the two stars each describe a conic about the center of 

 gravity of the two. It is possible astronomically to observe the 

 values of the periodic time T and the major axes of the orbits of 

 these conies. From these quantities we can determine the values 

 of /*, so that we know the values of 



ra 



(m + ra') 2 ' (m + ra') 2 ' 



and these at once lead to the values of ra, ra'. In this way it has 

 been found possible to determine the masses of some of the stars. 



EXAMPLES 



(Take the gravitation constant to be -y = C6.6 x 1(T 9 in centimeter-gramme-second units.) 



1. Given that the earth attracts as though its mass were concentrated at its 

 center, and that the value of g at the equator, distant 6.378 x 10 8 centimeters from 

 the earth's center, is 978. 1 centimeters per second per second, find the mass of the 

 earth. 



2. Taking the masses of the earth and moon as 6.14 x 10 27 and 7.94 x 10 25 

 grammes respectively, and assuming their distance apart to be always 3.84 x 10 10 

 centimeters, find the periodic time of the moon. 



3. Taking the sun's mass to be 2 x 10 38 grammes, and the year to be 365.24 

 days, find the semi major-axis of the earth's orbit, regarding the sun as a fixed 

 center of force. 



4. If the sun's mass is 324,000 times that of the earth, by how much must 

 the result of question 3 be altered when the sun's motion is taken into account? 



