NOTES IOI 



Then the energy taken out is ^ per second. 



4<?p V 2 r 



In one second let the velocity change from v to v% 

 and the distance from r^ to r 2 . 

 The kinetic energy lost is 



v n GM;;/ 



(L - L 



2 2 \, 



really a gain, since r^ > r y 

 The potential energy lost is 



GM;// - 

 The total loss is therefore 



As r^ r^ is very small we may put r^ = r* in the de- 

 nominator and r 2 r^ the diminution of r per second is 



~ dt 



Equating to the loss through resistance 



_ GMw dr _ GMm i S 

 2r* dt r ' ^ap ' v 2 



If we put S in terms of its value S e at the Earth's distance b 

 S = ?^ 



or omitting the suffix and remembering that S is now our 

 terrestrial Solar constant 



2; dt ~ op W 



If in this we put a i as in the text ; p = 5-5 ; r =b 

 ^= 14*8 x io 12 cm. the earth's .distance from the sun; 



