The system of uniformly accelerating observers

We begin with a scenario that involves point-like observers starting at t=0 from the origin O of an inertial reference frame. They move with all possible proper accelerations in the positive direction of the OX axis. Equipped with light sources the accelerating observers get involved in experiments like Doppler Effect, radar detection and radar echo. We derive formulas accounting for the experiments mentioned above. In the case of the Doppler Effect we take into account the non-locality aspect in the time interval measurement by accelerating observers.