Aims: The paper explores the hypothesis that the speed of light c is decreasing over time at rate (dc/dt)=-H? c, H being the Hubble constant. This hypothesis differs from the so-called tired light, in which the velocity c is supposed to vary during the journey of photons in the empty space for some frictional mechanism. In the hypothesis of the author the speed c, during this journey, is assumed constant. In this way the problems of the tired hypothesis are overcome. Methods: The paper links the variation dc/dt with the Hubble constant and infers a value of dc/dt from the difference between the value of the variation of the Earth-Moon distance measured by the Lunar Laser Ranging Experiment and the tidal effect. Results: Under the hypothesis c time varying, we explain: 1) The cosmological redshift. 2) The anomalous acceleration ap ≈ -8 × 10-10 m?sec-2, measured for some spacecrafts. 3) The high redshift of supernovae Ia, which seems to evidence an acceleration of the expansion of the universe. 4) The peripheral motion of stars in galaxies around their rotational centre. 5) The dilation of the light curves observed for supernovae Ia.
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