What relativistic Doppler shift occurs when source motion is perpendicular to the observer's line of sight?

The relativistic Doppler shift produced when a source moves perpendicular to an observer’s line of sight is the transverse Doppler effect.

Unlike the familiar approaching-or-receding Doppler shift, this effect does not depend on the source moving closer or farther away at that instant. Instead, it arises from special-relativistic time dilation: a moving source’s emission process appears to run more slowly to the observer. The received light is therefore shifted toward lower frequency, or redshifted.

The effect is extremely small at ordinary speeds but becomes measurable for particles, fast ions, precision clocks, and astronomical objects. It is sometimes called a second-order Doppler effect because, at low speeds, its size is proportional to approximately the square of the speed divided by the speed of light. Experiments such as the 1979 Hasselkamp–Mondry–Scharmann measurement and the Ives–Stilwell experiment tested this relativistic prediction. It is not the Zeeman effect, which splits spectral lines in a magnetic field, nor gravitational redshift, which comes from gravity.