Euler’s interpretation of Newton’s gravity (NG) as Archimedes’ thrust in a fluid ether is presented in some detail. Then a semi-heuristic mechanism for gravity, close to Euler’s, is recalled and compared with the latter. None of these two ‘‘gravitational ethers’’ can obey classical mechanics. This is logical since the ether defines the very reference frame, in which mechanics is defined. This concept is used to build a scalar theory of gravity: NG corresponds to an incompressible ether, a compressible ether leads (...) to gravitational waves. In the Lorentz–Poincaré version, special relativity is compatible with the ether, but, with the heterogeneous ether of gravity, it applies only locally. A correspondence between metrical effects of uniform motion and gravitation is assumed, yet in two possible versions (one is new). Dynamics is based on a (non-trivial) extension of Newton’s second law. The observational status for the theory with the older version of the correspondence is summarized. (shrink)

Paths of shortest length, or geodesics, may not appear as straight lines because acceleration creates distortion. For spaces of constant curvature there are only two possibilities: Either rulers get longer as they move away from the origin or they shrink. Because the longitudinal Doppler shift corresponds to the measure of distance, in velocity space, this space is hyperbolic, corresponding to the second of the two possibilities. Transformations from one inertial frame to another are related to geometrical rigid motions. The square (...) root of the Doppler shift is related to transformations of uniformly accelerated frames. Applications to general relativity and cosmology are given including the time-velocity metric of the Friedmann universe of dust at zero pressure, Hubble's law and the exponential red-shift. (shrink)