A modified law of gravitation is proposed which takes account of the relative speeds of the moving masses. The law simulates a "supplement" of mass with respect to the standard Newtonian law. Its application to several gravitation problems provides a good order of magnitude for the apparent supplement of mass associated with the motion of the Pioneer satellites, that of stars in galaxies or galaxies in galaxy clusters, for the same value of one additional parameter. The law equally simulates a lack of attraction, for the later stages as compared to the early stages, for a system of expanding masses, imitating a repulsive force. The order of magnitude of the corresponding energy fits with what is found in the literature for the "acceleration" of universe expansion. The conceptual framework in which the law is proposed is sketched out: it is based on the assertion of the fundamental link between the space and time concepts, and on a better symmetry of the physical laws with respect to these parameters. The study is preliminary, it simply establishes orders of magnitude for the expected effects, by an approximate approach of the two-body problem. In the near future it seems interesting to perform quantitative computer simulations so as to check whether the proposed law resists to further confrontations with observational data. If it did, it would avoid in the same time the use of dark matter and dark energy. The present work also gives clues to help reconsider the theory of relativity, in continuity with the modified law of gravitation, and its links with gravitation and electromagnetism.