Under which specific viewing geometry does the radial velocity method fail to detect a planet's gravitational tug?

Answer

When the system is viewed perfectly face-on.

If the system is viewed perfectly face-on, the star's motion along our line of sight is zero, meaning no measurable redshift or blueshift occurs, rendering the planet undetectable by this technique.

Under which specific viewing geometry does the radial velocity method fail to detect a planet's gravitational tug?
measurementastronomyexoplanetsdetection