Final answer:
Kepler's original laws, particularly the first law, assumed stars to be motionless which would make radial velocity exoplanet detection impossible. In reality, both stars and planets orbit a common center of mass, which makes the stars appear to wobble when observed, enabling the detection of exoplanets.
Step-by-step explanation:
If Kepler's laws were true as Kepler originally stated them, the radial velocity method of exoplanet detection would not be possible. The correct option that explains this is: a) Kepler's laws put the star motionless at one focus of a planet's elliptical orbit. According to Kepler's first law, each planet moves around the Sun in an orbit that is an ellipse, with the Sun at one focus of the ellipse.
However, this law doesn't take into account the gravitational effect the planet has on the star. In reality, both the star and the planet orbit a common center of mass. This movement of the star can be detected as a small but measurable radial velocity change that we observe as a wobbling motion, which is crucial for the detection of exoplanets.
Kepler's second law, which states that each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal areas in equal times, is indicative of the conservation of angular momentum. This conservation causes a planet to speed up as it gets closer to the Sun and slow down as it moves away.
Detecting exoplanets through the radial velocity method relies not only on the motion of the planets but also on the motion of the stars they orbit, which is not described by Kepler's original laws as he considered the stars to be motionless.
Finally, Kepler's third law provides a relationship between the time a planet takes to orbit its star and its distance from the star, but it does not affect the detection of exoplanets through radial velocity.