250 EXPLORATION GEOPHYSICS 



32 2 



a = g/{6Qy = 7^ = 0.00894 it/ sec." 



where 



Fi = gravitational force of the earth on a mass m at the distance of the moon 

 Fa = gravitational force of the earth on a mass w on the surface of the earth 

 g = acceleration of a body m due to gravity on the earth's surface 

 a = general acceleration of a body m, not on the earth's surface, due to the earth's 

 attraction 

 Me = mass of the earth 



Since the moon stays in its orbit, we can conclude that the centrifugal 

 force due to its movement around the earth just balances the attractional 

 force calculated above. Hence, ma = mU^/R, where U is the velocity of 

 travel of the moon around the earth and R is the radius of the moon's 

 path. R = 240,000 mi. = 1,267,200,000 feet. The period of revolution (T) 

 of the moon around the earth = 27 days, 8 hours = 2,361,600 seconds. 



a = ^ (2) 



„ = ''•(3.14)-M^6y.200,000 ^ ^^^^^ j,/^^^. 



This is in close agreement with 0.00894, considering the approximate values 

 used, and gives evidence of the validity of the law of gravitation. 



Determination of the Gravitational Constant G. — The value of the 

 "universal constant of gravitation" G was determined by H. Cavendish in 

 1798. To find G it is necessary to measure, with extreme accuracy, the 

 force F (as given in Equation 1), in a set-up where mi, m^, and r are 

 known. The Cavendish torsion balance designed for this purpose (Figure 

 123) consisted of a light bar six feet long, (21), with two lead balls, 

 (mi, m^), two inches in diameter, attached to its ends. The bar was sus- 

 pended at its center by a fine wire attached by a short stem to which was 

 fastened a small mirror for observing the deflection of a light beam. By 

 oscillating the moving system comprising the rod and its two balls, the 

 time required for a number of oscillations may be measured accurately. 

 The moment of inertia of the system may be calculated, and from this 

 value and the time of oscillation, the coefficient of torsion of the torsion 

 wire (t) may be readily calculated. 



Two lead spheres Mi and M2, 12 inches in diameter, were placed at an 

 accurately measured distance (r) about 9 inches from the balls on the ends 

 of the bar. The position of the spheres could be changed relative to the 

 small balls, as shown by positions 1 and 2 of the figure. The deflection 

 caused by the spheres was read with the aid of the telescope and scale set 

 at a distance D from the mirror. 



