284-286] The Rotational Theory 271 



why our solar system should be expected to have escaped this common fate. 

 Close encounters with other systems are now so rare as to be negligible, but 

 we have been led to suppose that conditions were widely different in the 

 remote past, so that close encounters in a past epoch may have greatly 

 altered the angular momentum of our system. There is also- another pos- 

 sibility to be considered. If a wandering star were to enter into our system 

 and carry off Jupiter by capture the total angular momentum of the system 

 would be reduced to less than half, although the total mass would only be 

 reduced to an insignificant extent. The occurrence of such an event in the 

 past would invalidate entirely the supposition of the total angular momentum 

 remaining constant. 



286. Leaving this objection aside, let us follow Babinet in supposing 

 that the primitive body out of which our system formed had a mass equal to 

 the total mass, and angular momentum equal to the total angular momentum, 

 of the present solar system. Let us proceed to investigate the possibility 

 of the value of ^/^Tryp for such a system having ever been greater than 

 0-18712. 



The mass of the system is TOOlS times that of the sun, and this, to 

 within one per cent., will be 2 x 10 33 grammes. The angular momentum M 

 arises mainly (cf. 14) from the orbital momenta of the four outermost planets, 

 and these are known perfectly. About a sixtieth of the whole arises from 

 the axial rotation of the sun, and this, depending on the sun's interior arrange- 

 ment, is not known with great accuracy. But to within one per cent, we may 

 take the whole moment of momentum of the system to be 



M = 3-3 x 10 50 c.G.s. units. 



Let r be the mean radius and p the mean density of the primitive mass 

 before break-up, so that Jf =f 7rpr 3 . Let k have been the radius of gyration, 

 so that M = M&a). From these relations it follows that, in any configuration 

 whatever, 



or, inserting numerical values for M, M and 7, 



l-34xl0 8 - (590). 



It follows that &> 2 /27T7/5 can only have been as great as 018712 if A; 4 /r 3 

 was less than 716 x 10 8 cms. If r , the mean radius of the original nebula, 

 is supposed to have been n times the present radius of the sun, then k 2 /r 2 

 must have been less than 0101/0*. For instance with r equal to the radius 

 of Neptune's orbit, & 2 /r 2 must have been less than 0'0013. The exact value 

 which ought to be assigned to n can only be a matter of conjecture. It is 



