The Tide-generating Forces 255 



the common centre of gravity generates centrifugal forces, which counter- 

 balance the centripetal attracting forces giving the system a stable equilibrium. 

 This equilibrium requires that, for instance, for the system earth-moon the 

 resultant of all forces of attraction between the earth and the moon is equal 

 and directly opposite in direction to the resultant of all centrifugal forces. 

 The origin of this resultant is in the centre of the earth. 



How large is the centrifugal force for an element of mass which moves 

 around common centre of gravity ? The motion in question is a simple transla- 

 tion without rotation. In the case of a so-called revolution, each particle of 

 mass of a body travels the same orbit around a central point. Figure 107 



Fig. 107. Centrifugal forces when a body M rotates around M*. 



explains such a motion. The body with its centre in M accomplishes a revolv- 

 ing motion around the central point M*, and all points of M, for instance, 

 A and B, go through the same circle. The centres of these orbits A* and B* 

 are in the same position to each other as the corresponding points in the 

 body M. The arrows then indicate the direction of the centrifugal forces. 

 The magnitude of the force Z is given by V 2 /a, if V is the velocity of the 

 body and a the radius of her orbit. The centrifugal forces of all particles 

 of mass of a body participating in a revolving motion are equal and have 

 the same direction. If T is the time of a revolution of the body on its orbit 

 and a is the radius, then the centrifugal force will be for a unit of mass 

 Z = 47t 2 a/Tl and is directed along the radius towards the outside. 



If M is the mass of the moon concentrated in its centre, and if an element 

 of unit mass of the earth is at a distance q from the centre of the moon, this 

 element of mass is attracted by the moon with the force x(M/q 2 ) where x = coef- 

 ficient of gravitational force distance apart. The stability of the system 

 earth-moon requires that 



