The presently used formulas for the relativistic Doppler effect can be tested by reference to Pioneer 10 & 11, which are the unique available experimental devices suited for such a purpose. They are the unique objects having kinematics that can be monitored requiring no use of the Doppler effect. The ?simplest' or ?most beautiful' result, which can be expected, is that the correct choice for the Doppler effect is the non-relativistic formula, while ? both on the theoretical ground and consistently with the Pioneer anomaly - the presently preferred relativistic formula is logically inconsistent. The paper discusses both of the present formulas for the Doppler effect, and of its most general formulation. Two rationales for envisaging the correct form of the formula for the Doppler effect are here considered. The first one relies on an already published treatment. A new alternative approach is here proposed.
