An arbitrarily small positive value of the gravitational aberration slightly increases the angular momentum of a two-body and multiple body system. This could potentially contribute to the accelerated expansion of the whole Universe. We present some geometrical, physical, geophysical, heliophysical, climatological, cosmological, and astronomical observational arguments, and also numerical tests to support this conjecture. We found a remarkable coincidence between the Hubble constant and the increasing distance of the Moon from the Earth, that is not only due to tidal forces. Numerical examples illustrating the expansion caused by the gravitational aberration are given. This will be modeled by a nonautonomous system of ordinary differential equations with delay.