Non-Prefered Reference Frames and Anomalous Earth Flybys

Let us consider a reference frame Sigma prime in which the pseudo-Euclidean geometry holds. Einstein assumed that the principle of special relativity is valid, i.e. the reference frame of any uniformly moving observer is also described by the pseudo-Euclidean geometry. The transformation formulae from one reference frame to the other one are therefore given by the well-known Lorentz-transformations. But Einsteins assumption contradicts the observed dipole anisotropy of the cosmic microwave background (CMB) in the universe. The transformation formulae of the prefered reference frame Sigma prime in which the pseudo-Euclidean geometry is valid to a uniformly moving observer in a non-prefered reference frame Sigma are stated. The geomerty in Sigma is anisotropic. The Doppler shift of objects moving in a non-prefered reference frame is calculated. This result is applied to spacecrafts which fly near the Earth. The observed anomalous frequency shift of several spacecrafts during near Earth flybys does not arise in the non-prefered reference frame Sigma