Abstract
The theory of gravitation allowing variation of the gravitational constant $G$ by means of a scalar field introduced by Brans and Dicke is applied in the case of a fluid sphere in gravitational equilibrium. The departure of the mass-radius relation in this theory from the Einstein theory is investigated for different values of the constant $\ensuremath{\omega}$ and for high central-energy densities in completely degenerate stars (neutron stars).
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