Final answer:
The Doppler method for finding exoplanets is effective when emission or absorption lines are present in the spectrum of the parent star, as it measures the star's radial velocity changes to detect planets.
Step-by-step explanation:
The Doppler method for finding exoplanets works if there are emission or absorption lines in the spectrum of the parent star. This method relies on detecting the radial velocity changes of a star caused by the gravitational influence of an orbiting planet.
As the star moves towards us, we observe a blueshift in its spectrum, and as it moves away, we see a redshift. The changes in the speed of the star indicate the presence of a planet, but the magnitude of the Doppler shifts is very small.
This technique does not require the exoplanet to be terrestrial, nor does it require the exoplanet to orbit exactly edge-on or in a retrograde orbit. The parent star's cycle of activity may affect the clarity of the measurements but is not a primary factor for the method to work.