# Are there any examples where the transverse doppler effect is applied in astronomy?

Are there any astronomical examples where the transverse doppler effect(Horizontal doppler effect) is applied (Derives a meaningful result)?

Accounting for the transverse Doppler effect (and other relativistic effects) is essential in modelling the X-ray spectral emission lines from the accretion discs around black holes (e.g. Cadaz & Calvani 2005). In this case the transverse Doppler effect is "mixed up" with gravitational redshift and it is treated holistically in the Schwarzschild or Kerr metrics.

The transverse Doppler effect is also essential in interpreting the signals from binary pulsars and even in single pulsars because of the rotation of the Earth and its motion around the Sun.

• One key is that your examples deal with orbiting bodies, so that there is some other source of information about the motion besides the Doppler effect. For a body moving in free space, there is no way to take one input number (Doppler shift) and get two outputs (radial and transverse velocity). Also, the transverse Doppler shift is of order $(v/c)^2$, whereas the radial Doppler shift is of order $v/c$, so to get the transverse effect to be big enough not to be lost in the radial effect, you want big velocities. Hence your examples, which are highly relativistic systems. – Ben Crowell Nov 18 '18 at 15:19
• @BenCrowell - All true, except there are now possibilities with precisely measured proper motions and parallaxes to have an independent measure of transverse velocity. – ProfRob Nov 18 '18 at 16:35
• Can you check my understanding that about 25km/s or more is enough to measure the transverse velocity with the transverse doppler effect? (Source: lm.facebook.com/…) – KYHSGeekCode Nov 20 '18 at 1:28