Doppler frequency shift based on the local-ether model of wave propagation

[[abstract]]Consider the Doppler effect between a transmitter and a receiver moving at velocities vs and v_e, respectively. According to classical propagation, the transmitted and received frequencies due to the Doppler effect is given by f_t/f_r=1+dR/cdt, where the propagation range R=R_t( 1+u_e/c) , u_e=v_e\cdot hatR_t, Rt is the directed separation distance from transmitter and receiver, and v_e, v_s, and Rt are all referred at the instant of wave emission [1]. The range modification v _e\cdot R_t/c (=R-R_t) is due to the Sagnac effect associated with the longitudinal movement of the receiver during wave propagation. Due to relative motion between transmitter and receiver, d R_t/dt=v _es=v_e-vs and hence dR_t/dt=u_es=u_e-u_s. Thereby, to second order of normalized speed, the Doppler frequency shift is [ f_t/f_r=1+u_es/c+(v_e\cdot v_es+ a_e\cdot R _t)/c^2. ] For the case of radial relative motion without acceleration, where Newtonian relative velocity v_es is parallel to ± R_t, f_r/f_t=(1-u_e/c)/(1-u_s/c). This is just the well-known classical Doppler formula. According to the local-ether model of wave propagation [2], there emerges one fundamental difference. That is, velocities vs and ve are both referred specifically to a geocentric or a heliocentric frame with respect to which the gravitational potential of the Earth or the Sun is stationary, depending on the propagation being earthbound or interplanetary. However, its effect is merely of second order.[[fileno]]2030130010020[[department]]電機工程學