Effect of a scale-dependent cosmological term on the motion of small test particles in a Schwarzschild background
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It was recently suggested that the gravitational action could contain a scale-dependent cosmological term, depending on the length or momentum scale characteristic of the processes under consideration. In this work we explore a simple possible consequence of this assumption. We compute the field generated in empty space by a static spherical source (the Schwarzschild metric), using the modified action, The resulting static potential turns out to contain a tiny non-Newtonian component which depends on the size of the test particles. The possible relevance of this small correction for the analysis of the recent Pioneers data [J.D, Anderson et al., Phys. Rev. Lett. 81 (1998) 2858] is briefly discussed. (C) 1999 Elsevier Science B.V, All rights reserved.