252 The Evolution of Binary and Multiple Stars [CH. xi 



263. We have seen that a double-star must be supposed to be born as 

 the result of cataclysmic motion. The pear-shaped figure is unstable, so that 

 as soon as it is formed dynamical motion ensues and fission results. The 

 masses are at first projected away from one another with considerable velocity, 

 but seem likely to settle down finally to describe steady orbits about one 

 another. 



In his researches on this problem, Sir G. Darwin supposed that the initial 

 orbits would be strictly circular, but this was because he believed the process 

 of fission to be a statical process and not a dynamical process, as we have seen 

 it to be. According to Darwin's view, the changes in the star while fission 

 was taking place were, initially at least, of a purely secular nature, and it was 

 natural to suppose that the final result would be two masses rotating in actual 

 contact and at rest relatively to one another. 



We have seen that this cannot be the final result of fission for incompres- 

 sible masses, because such a configuration would be statically unstable, as 

 indeed was ultimately found by Darwin himself (cf. 64, 65). For a com- 

 pressible mass, there is no reason why it should not be the final result of 

 fission (cf. 164) although the intermediate processes would almost certainly 

 be different from those imagined by Darwin, cataclysmic motion probably 

 ensuing immediately the pear-shaped figure is formed, but possibly giving 

 place to steady statical motion before actual fission occurs. 



There being no longer any theoretical justification for supposing that the 

 initial orbits will be strictly circular, we have to consider the possibility of the 

 masses being thrown apart with appreciable radial velocities, and describing 

 elliptic orbits about one another. 



Consider for simplicity the case in which the original star is supposed to 

 divide into equal masses, and suppose that fission occurs when the centre of 

 each mass is at a distance r from the common centre of gravity. Let each 

 star be supposed to have a radial velocity v in addition Jo the tangential 

 velocity cor in space resulting from rotation. Each mass will describe approxi- 

 mately an elliptic orbit in space so that after the orbits are partially described 

 the masses will again each be at a distance r from their common centre of 

 gravity, but are now approaching each other with a radial velocity v. A col- 

 lision of some kind must occur, and since the masses will not be perfectly 

 elastic, their velocity of recession after collision will be some velocity v less 

 than v, while the radial velocity cor must, from the conservation of angular 

 momentum, be the same as before. It follows that the new orbit will be of 

 less eccentricity than the old, and the eccentricity will further diminish at 

 each subsequent collision. We cannot argue that the eccentricity will be 

 finally reduced to zero ; a limiting value will be reached such that the masses 

 just graze one another at periastron. 



