GRAVITATIONAL METHODS 249 



66.7 • 10~° cm.^ g~^ sec~- rh 0.005. \F\ means the absolute magnitude 

 of F. 



The law of gravitation is unique in its wide application. It applies alike 

 to the motions of the heavenly bodies and of discrete particles of matter so 

 minute that their dimensions can usually be disregarded. The gravitational 

 force of attraction acts continuously along a direct line connecting the 

 centers of gravity of masses and is independent of the nature of the material 

 involved. According to exhaustive experiments^ it is also independent of 

 the temperature of the material considered. 



It is not possible to screen off the force of gravity by the interposition of 

 material between bodies. If such zvere the case, the portion of the earth's 

 mass away from the sun would be less strongly attracted than that facing 

 it. No such change in gravity appears to exist. A mass in Australia attracts 

 a mass in London as if the earth were not interposed between them. This 

 law of universal gravitational attraction is one of the broadest and most 

 fundamental physical laws. 



In verifying his conclusions concerning gravity, Newton realized that 

 it was not possible for him appreciably to change the distance of a body 

 from the earth's center in relation to the earth's radius of approximately 

 4,000 miles. Further, the attractional force between two bodies of ordinary 

 size on the surface of the earth is very small and difficult to measure. 

 Assuming an attractional force between bodies, according to the law 

 expressed in Equation 1, it has been shown that a sphere which is homo- 

 geneous, or which can be considered as made up of homogeneous shells, 

 such as the earth, will attract an outside body as though its mass were con- 

 centrated at its center. 



Proof of Newton's Law From the Motion of the Moon. — Newton 

 turned for proof of his law to the motion of the moon around the earth. 

 The earth's radius is approximately 4,000 miles. At the surface of the 

 earth a body is attracted as if the mass of the earth were concentrated at 

 its center, and the acceleration of a falling body due to gravity averages 

 32.2 feet per second^, (= g). The average distance of the earth to the 

 moon is about 240,000 miles, or 60 times the earth's radius. 



With the above facts, we can determine the gravitational attraction of 

 the earth on a body at the distance of the moon. 





t J. H. Poynting, and P. Phillips, Proc. Roy. Soc, Vol. 76A, p. 445. 



