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A relation between the centripetal acceleration g_obs in galaxies and thegravity due to the baryon distribution g_bar has been found by McGaugh (2016)and Lelli et al.(2017). It also summarizes properties such as the Tully-Fisherand Faber-Jackson relations. Below about g_bar= 10E-10 m s^(-2), the observedrelation deviates from the 1:1 line, g_obs being much larger than g_bar. Theacceleration relation is followed by late and early type galaxies, and also bythe dwarf spheroidals where the deviations from the 1:1 line are the largestones. These deviations are currently attributed to dark matter.  We show that the scale invariant theory, with the assumption of the scaleinvariance of the empty space, correctly predicts the observed deviations inthe acceleration relation. The large deviations (up to a factor 400) and theflattening of the acceleration relation observed for the dwarf spheroidalgalaxies are also well described. The presence of dark matter is no longernecessary in the scale invariant context, which also accounts why dark matterusually appears to dominate in galactic regions with low baryonic gravities.

The acceleration relation in galaxies and scale invariant dynamics: another challenge for dark matter