275-277] Motion subsequent to Fission 263 



The mean square of the tangential velocity will be equal to twice the 

 mean square of the radial velocity, as required by the Theorem of Equiparti- 

 tion, when 



an equation whose root is 



Thus the general effect of stellar encounters is to decrease the eccentricity 

 of orbits whose eccentricity is greater than '6370, and to increase the eccen- 

 tricity of orbits whose eccentricity is less than '6370. If the constituents of 

 binaries start life by moving in nearly circular orbits, the general effect of 

 stellar encounters must be to increase the eccentricities of these orbits until 

 they are ranged about a median value e = *6370. This, however, is not the 

 arithmetic average of all eccentricities in the final equipartition state ; it can 

 be shewn that in the final state, the eccentricities would be distributed 

 according to the law 2ede, so that the average value of e would be f . 



If (7 2 denote the mean value of u? + v" + w 2 , the second equipartition con- 

 dition will be satisfied if 



In terms of the period P of description of the orbit, this becomes 



If M, M' are fairly equal, the value of (M+M'y/MM' will not differ 

 greatly from 4. Moreover as equation (587) does not depend greatly on e 

 we may suppose e to have its equipartition value "6370. The equation now 

 becomes very approximately 



We notice that for a massive slow-moving star, P will be large; fora light 

 and rapidly- moving star, P will be small. Taking M + M' equal to the sun's 

 mass, 2 x 10 33 grammes, and G equal to 25 kms. a second, the value of the 

 period is found to be almost exactly three months. For a binary star of nine 

 times the sun's mass, say an average .8-type binary star, the equipartition 

 value of G' 2 would be only one-ninth of that just assumed, and the equipartition 

 value of P would be 243 times that just calculated, or about 60 years. 



277. It has now been seen that stellar encounters produce the same 

 general effect as tidal friction, namely increases in the eccentricity, linear 

 dimensions and period of the orbit. But, whereas tidal friction was found 

 competent to produce only small proportional increases in the period and 



