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We give an estimate of the gravitational field of force exerted on a testparticle by the far galaxies, in the frame of the weak field approximation. Invirtue of Hubble's law, the action of the far matter turns out to be nonnegligible, and even the dominant one. An extremely simplified cosmologicalmodel is considered. A nonvanishing contribution is obtained only if thediscrete and fractal nature of the matter distribution is taken into account.The force per unit mass acting on a test particle is found to be of the orderof $0.2 cH_0$, where $c$ is the speed of light and $H_0$ the present value ofHubble's constant.

On the role of the far fields and of cosmology for the theory of gravitation and for the dark matter problem