224 The Evolution of Star -Clusters [CH. x 



General Stellar Dynamics 



222. After this brief consideration of the possible origin of our own 

 universe, let us proceed to a general discussion of the motions of stars in 

 clusters. In searching for numerical data we may be guided by the figures 

 we have conjecturally obtained for the past history of our own universe. We 

 have a number of stars, or, at first, gaseous condensations, moving in space 

 under their own attractions and possibly also under the attraction of a central 

 nucleus. We require to find as much as possible about the nature of the 

 motion and the evolution of the system. 



The motion of the stars may to some extent be compared to the motion 

 of the molecules of a gas, and certain formulae may be borrowed from the 

 kinetic theory of gases which will give approximately true results when 

 applied to a star-cluster. 



223. Let us begin by considering the frequency of actual material col- 

 lisions in a cluster of stars. 



At first let us regard the stars as being uniformly spheres of diameter o-, 

 and let us treat the problem as a purely geometrical one, the gravitational 

 attractions of the stars being momentarily neglected. By the familiar methods 

 of the kinetic theory of gases, it is readily shewn that the number of collisions 

 experienced by any one star in time dt will be 



where v is the number of stars per unit volume, and F is their mean relative 

 velocity. 



Thus the mean time between successive collisions of a single star will be 



For our universe in its present state we may take v = 10~ 56 ' 5 and 

 V= 40 kms. a sec. = 4 x 10 6 C.G.S. units. Thus formula (545) gives for the 

 mean interval between collisions 10 41 ' 9 /<r 2 years. Even if we assign to the 

 average star a diameter equal to that of Neptune's orbit, say cr = 4'5 x 10 14 cms., 

 this gives a mean interval of 4 x 10 12 years, a period which is so large com- 

 pared with any reasonable estimate of the age of the universe, that it is at 

 once _clear that the chance of material collisions may be disregarded entirely. 



224. This calculation has neglected the effect of gravitational attraction, 

 which naturally increases the chances of collision. Not only this but stars 

 will act on one another gravitational ly, and so influence one another's motion, 

 at distances far beyond those at which material collisions can occur. The 

 event of two stars coming so close to one another that their gravitational 



