196 THE REALITIES OF MODERN SCIENCE 



i.e. radial, and the other normal to this, i.e. tangen- 

 tial. Suppose the body, which is instantaneously at p 

 of Fig. 20, follows its tangential path to the point p'. 

 In this position its motion is partly away from the earth, 

 along Op', and partly at right angles to this direction. 



There is now kinetic energy 

 in both degrees of freedom, 

 although in the previous posi- 

 tion the radial k.e. was zero 

 and the motion was entirely 

 tangential. In departing from 

 a circular path it acquires 

 radial kinetic energy, and 

 also increases the potential 

 energy of the system. (The 

 tangential k.e. is decreased.) 

 FlG - 20 - The change in the p.e. is due 



to the increased separation from the earth, but that in 

 the k.e. is due to the new angle which the direction of 

 motion makes with the radial line. The radial k.e. and 

 the p.e. do not necessarily, therefore, increase at the 

 same rate with respect to the space over which the 

 body moves. The radial energy is available for further 

 outward motion and if it increases more rapidly than 

 the potential energy, the body will continue to move 

 away from the earth. Whether or not it does, depends 

 upon the total kinetic energy and hence upon how fast 

 the surface of the earth is rotating about its axis. 



The limiting l case occurs when the increase in radial 



1 Calculations show that for bodies on the surface of our earth 

 this limiting value would be reached if the earth should revolve 

 about 290 times as fast as at present. Bodies on the surface would 



