Cosmological change of G and the structure of the earth

The application by Hoyle and Narlikar (Mon. Not. R. Astron. Soc., 155, 305) of their cosmological theory with a decreasing G to determine changes of radius of a two-zone Earth is shown to be invalid by their homology-treatment. The initial model is not a polytropic distribution and the condition of pressure-continuity is breached in their scaled models. In the present paper the accurate solution of the problem has been found by numerical means and gives a rate of change of radius only about one-quarter that of Hoyle and Narlikar. The consequent rifting of the solid surface-layers is much too small for their purposes. That upwelling of lighter magmatic material would lead to an avulsion of the kind they claim is shown by hydrostatic considerations to be inadmissible. The established existence of an accelerative component of the angular velocity of the Earth shows that the moment of inertia is diminishing, and discussions of changes of internal distribution and radius cannot adequately be made merely by taking account of a possibly changing G. (author)