Summary: Gravity is interpreted as the pressure force exerted on matter at the scale of elementary particles by a perfect fluid, the rest frame of which defines the inertial frame. The first task is thus to extend Newtonian mechanics so that it allows a deformation of the inertial frame. An application to the stability study of an expanding, rigid or contracting universe is given. The pressure of the inertial fluid is equivalent to a mass force, if the elementary particles have the same (average) mass density, depending only on the fluid pressure. Hence stable particles should be permanent flows in the fluid, such as vortices. Gravity should be only the macroscopic part of the pressure force. Newtonian gravity propagates with infinite speed and is interpreted as the incompressible case. In the compressible case, gravitational (pressure) waves are predicted as well as qualitatively correct modifications to planetary motion. In a forthcoming paper (see the following review; Zbl 0853.53076) the theory is reinterpreted so as to describe the relativistic effects.