1 1 8 TWO NEW WORLDS 



10 13 cm. (about the distance of the earth from the 

 sun) the potential is 



6-66 x 10-8 x 10 33 



10*3 



= 6-66 x 10 ia . 



The work done by the sun in accelerating any body 

 from infinity may thus be measured by multiplying 

 this number by the mass of the body in grammes. 

 And this work will be embodied in the energy of 

 motion thus acquired. For a mass of m grammes 

 we have therefore 



m x 6'66 x 10 11 

 or v 2 = 2 x 6-66 x 10 11 



Extracting the square root on both sides, we get 

 v = 3-64 x 10 6 , or 36'4 km. per second, or 22J miles 

 per second. This, as might have been expected, is 

 not far from the earth's speed in its orbit. For 

 the speed may be that of motion in any direction, 

 so long as it is the same for a given distance from 

 the sun. To put the whole relation into one formula, 

 we have 



2QM 



/ 



V 



from which we may at once derive a few important 

 rules : 



1. The speed at any given distance is proportional 

 to the square root of the central mass. 



2. It is proportional to the square root of the 

 gravitational constant. 



3. It is inversely proportional to the square root of 

 the distance. The actual force of attraction between 

 two masses M and m at distance D is equal to 



t The force is in dynes, the masses in 



