A variant of the usual formulas for gravitational and electrostatic fields, differing from those by a logarithmic term, is introduced in order to solve some questions connected with a possible atomic contraction phenomenon at large time scale and the so-called hidden mass problem in cosmology. This approach is conceptuallly related to the MOND theory of M. Milgrom but allows a reversal of attracting forces when the distance becomes very small. The asymptotic behavior of solutions of a related dissipative ODE is studied, we obtain that all bounded trajectories converge to a point where the field vanishes.