The present work investigates the practical consequences of the recent experimental observations, achieved with the help of the tightly synchronized atomic clocks in orbit, on the current view about the nature of the gravitational fields. While clocks, stationary within gravitational fields, show exactly the gravitational slowing predicted by General Relativity (GR), the GPS clocks, in orbit round earth and moving with earth round the sun, do not show the gravitational slowing of the solar field, predicted by GR. This absence can only mean that the orbital motion of earth cancels this gravitational slowing, which obviously cancels too the spacetime curvature. On the other hand, the Higgs theory introduces the Higgs Quantum Space (HQS) giving mass to the elementary particles by the Higgs mechanism. The HQS thus necessarily governs the inertial motion of matter-energy and is locally their ultimate reference for rest and for motions. Motion with respect to the local HQS and not relative motion is what causes clock slowing, light anisotropy and all the, so-called relativistic effects. Non-uniform motion of the HQS itself necessarily creates inertial dynamics, which, after Einstein’s equivalence of gravitational and inertial effects, is gravitational dynamics. The absence of the gravitational slowing of the GPS clocks by the solar field, together with the null results of the light anisotropy experiments on earth, demonstrates that earth is stationary with respect to the local HQS. This can make sense only if the HQS is moving round the sun according to a Keplerian velocity field, consistent with the planetary motions. This Keplerian velocity field of the HQS is the quintessence of the gravitational fields and is shown to naturally and accurately create the gravitational dynamics, observed on earth, in the solar system, in the galaxy and throughout the universe, as well as all the observed effects of the gravitational fields on light and on clocks.