396 
The Solar System 
[CH. XVI 
the loss by radiation produces very little change of angular momentum while 
the chance of disturbance from outside is negligible. 
Fouché* estimated the total angular momentum of the solar system to be 
28’2 times that of the sun, the latter being supposed to be a homogeneous 
mass rotating uniformly in the period of its outer layers. The effect of con 
centrating all this angular momentum in the sun would be to cause it to. 
rotate 28‘2 times as fast as now. Such a sun would still be rotating less 
rapidly than Jupiter. As the densities of the two masses are about the same 
and the present Jupiter is still very far from breaking up, we may assume the 
primitive sun also would be. This simple calculation needs some adjustment 
both because the sun’s mass is highly concentrated towards its centre, and 
because its inner layers rotate faster than its surface. But no reasonable 
correction can lead to figures which are compatible with the sun having 
broken up by fission f. 
370 . There remains the possibility of the sun having broken up in the 
way originally imagined by Laplace, namely by its shrinkage resulting in a 
shedding of matter in its equatorial plane. There is no limit to the smallness 
of the total angular momentum with which this can happen; indeed, in 
Roche’s model, which we studied in § 229, it can happen when the angular 
momentum is zero, since the whole mass is supposed concentrated at the 
centre. Thus, notwithstanding its present small angular momentum, the sun 
could have broken up in this way if its mass had been sufficiently concentrated 
at its centre. 
A body with high central condensation of mass begins to break up in the 
way we are now considering as soon as 
If r 0 denotes the mean radius, p the mean density, k the radius of gyration, 
M the mass, and M the total angular momentum of the primitive sun before 
the supposed break-up, M = |7rpr 0 s , and M = Mk 2 co, so that 
While about 2000 million years would appear to be the most probable age 
for the earth, various considerations combine to fix its maximum possible age 
at 5000 million years J. Thus when the earth was born, the sun must have 
Laplaces Nebular Hypothesis. 
(370-1). 
* Comptes Rendus, xcix. (1884), p. 903. 
t Problems of Cosmogony and Stellar Dynamics, pp. 15 and 269. 
+ A. Holmes, The Age of the Earth, Chap. vn.