Mishra has recently established, using a generic static metric, the relative local proper-time 3-acceleration of a test-particle in one-dimensional free fall relative to a static reference frame in any static spacetime. In this paper, on the grounds of gravitoelectromagnetism we establish, in a covariant spacetime form, the relative 4-acceleration for the general free fall, indicating its canonical representation with its 3-space cinematical content. Then we obtain the relation between this representation and the very known expression for the relative free fall acceleration in Fermi coordinates. Taking this into account, it is shown that an experiment with relativistic beams in a circular accelerator, modelled by Fermi coordinates, recently proposed by Moliner et al, can test the here established covariant result and, therefore, can also verify Mishra's formula. This possibility of experimental verification, besides its intrinsic importance, can answer a recent inquire by Vigier, related to his recent proposal of derivation of inertial forces.
Velocity dependent forces varying as $k(\hat{r}/r)(1 - \mu \dot{r}^2 + \gamma
r \ddot{r})$ (such as Weber force), here called Weber-like forces, are examined
from the point of view of energy conservation and it is proved that they are
conservative if and only if $\gamma=2\mu$. As a consequence, it is shown that
gravitational theories employing Weber-like forces cannot be conservative and
also yield both the precession of the perihelion of Mercury as well as the
gravitational deflection of light.Comment: latex, 11 pages, no figure
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