Recent new highly precise experimental observations, achieved with the help of the tightly synchronized clocks of the GPS, reveal very clearly that real space, ruling the inertial motion of matter and the propagation of light, is moving round earth and round the sun according to a Keplerian velocity field, consistent with the local main astronomical motions. Such real space is well at hand in the Quantum Field Theory (QFT), underlying the Standard Elementary Particle Model (SEPM). The QFT entails the idea that space is filled up with the Higgs condensate (HC), a Bose-Einstein condensate of the zero spin Higgs bosons and a very powerfull quantum space (QS), stable up to 1015 degrees Kelvin. According to QFT, likewise the superconducting condensate confines magnetic fields by the Meissner effect, making them short-range and giving inertial mass to the photons, the HC confines the matter fields by the Higgs Mechanism, giving mass to the elementary particles, that is, providing them with mechanical properties. This lets clear that the HC rules the inertial motion of matter and the propagation of light and hence is the locally ultimate reference for rest and for motion of matter and light. Moreover, likewise superconductors, develop a macroscopic velocity field of the superconducting condensate (screening currents), expelling magnetic fields, the HC too may develop a macroscopic velocity field of the condensate (screening currents) in the form of a Keplerian velocity field of the QS, consistent with the local main astronomical motions, round each matter body throughout the universe. The present work demonstrates that this Keplerian velocity field of the QS appropriately induces the observed gravitational dynamics on earth, in the solar system as well as the galactic gravitational dynamics without the need of dark matter. This Keplerian velocity field is the quintessence of the gravitational fields. It thrusts and compresses the matter fields into compact bodies. It also provides a dominant antigravitation mechanism accelerating the expansion of the universe. It finally is shown that this QS-dynamics correctly and appropriately gives rise, in terms of simple and genuine physical effects, to all the other observed effects, caused by the gravitational fields on the propagation of light and on the rate of the clocks.