Relativistic limits of observable velocities

Relativistic transformations proposed in [A. Einstein, Zur Elektrodynamik der bewegter Körper. Ann. der Physik, 17 (1905) 891–921] are based on the speed VV of a signal transmitting the information and on the relative speed vv of a frame (k)(k) moving with respect to a still frame (K)(K), which velocities are considered as given constants. These transformations reflect the links that exist between motions and processes observed in one system from another, and with this theory some experimental effects (aberration, Doppler effect, pressure of light) were explained, and some other effects were predicted, and then confirmed experimentally. However, there is no need to postulate relative velocity vv as a known constant since, using the original Einstein’s model of time synchronization and appropriate signals with known speed of propagation VV, the relative velocity vv of a moving frame (spacecrafts, asteroids, particles in accelerators) can be measured. In this paper, the observation method, reverse to that of Einstein, is presented, and the limit of observable   relative velocities is found which is 30% less than the speed of a signal used for the observation. For example, if a radar or rays of light are used for the observation, then relative velocities |v|