but how comes a square root in the denominator of eq#1.14wabbit said:
The Relativistic Doppler Shift refers to the change in the frequency of electromagnetic waves (such as light or radio waves) due to the relative motion between the source of the waves and the observer. This effect is described by the theory of relativity, which states that the observed frequency will be different for an observer in motion compared to an observer at rest.
Understanding the Relativistic Doppler Shift is important in various fields, such as astronomy, telecommunications, and satellite communication. It allows us to accurately measure the motion of objects in space, determine the speed of stars and galaxies, and ensure efficient communication between satellites and ground stations.
The Relativistic Doppler Shift is derived using the principles of special relativity, which describe the relationship between space and time in the presence of relative motion. The derivation involves using the Lorentz transformation equations to calculate the change in frequency of the waves due to the relative velocity between the source and the observer.
The formula for the Relativistic Doppler Shift is given by fobs = fsource * √((1+v/c)/(1-v/c)), where fobs is the observed frequency, fsource is the source frequency, v is the relative velocity between the source and the observer, and c is the speed of light.
The Relativistic Doppler Shift takes into account the effects of special relativity, such as time dilation and length contraction, whereas the Classical Doppler Shift assumes that time and space are absolute and do not change with relative motion. Additionally, the Classical Doppler Shift is only accurate for relatively low velocities, while the Relativistic Doppler Shift is applicable for all velocities, including those close to the speed of light.