1 The Relativistic Transverse Doppler Effect at Distances from One to Zero Wavelengths

Many experiments intended to either verify or disprove the relativistic transverse Doppler effect are conducted at 90 ° detection angles using high frequency waves at distances of less than one wavelength between the detector and the source. Yet in the utilization of research conducted by this author for previous works involving the transverse Doppler effect it is found that for the frequencies typically used, the special relativity defined transverse Doppler effect is invalid at distances less than approximately 28 wavelengths between the source and detector. Until this present work, even the Millennium Relativity formulas for the transverse Doppler effect were valid only down to a distance of one wavelength between source and detector. In resolution of this limitation, new formulas will now be introduced that are valid from 0 ° to 180 ° for the relativistic transverse Doppler effect down to a distance between source and detector reaching zero