The feasibility of using in physics of relativistically invariant Newtonians of the free inertial rest energyof matter and Keplerians of the ordinary rest energy of matter, respectively, instead of relativistically noninvariantHamiltonians and Lagrangians, has been shown. And this is in good agreement not only withrelativistically invariant thermodynamics, but also with the equations of the dynamic gravitational field ofboth the Solar System and flat galaxies. Newton's law of gravity is obtained directly from the condition ofno change in the flow of the proper time of matter during its inertial motion in a gravitational field. Andthus the presence of complete compensation of the gravitational dilation of time of the matter by itsinertial motion is proved. True relativistic transformations of the increments of spatial coordinates andtime are obtained. The true relativistic transformations of increments of spatial coordinates and time arepresented. These transformations are based on Keplerian (which is alternative to Lagrangian) and differ from Lorentz transformations only in one parameter b. Based on the analysis of the motion of the planets, the compensation by the centrifugal pseudo-force of inertia not only of the gravitational pseudoforce, but also of the pseudo-force of evolutionary self-contraction of the matter to the center of gravity is confirmed.