Stars near the ______ should show the greatest Doppler shifts due to the earth's revolution. Why?

Would it be stars near the ecliptic because it deals with the earth revolving and having motion.

correct.

Yes, you are correct. Stars near the ecliptic would show the greatest Doppler shifts due to the Earth's revolution.

The Earth's revolution is the motion of the Earth around the Sun in its elliptical orbit. As the Earth moves in its orbit, it creates an apparent change in the position of stars relative to us on Earth. This is known as the parallax effect.

The parallax effect causes the apparent position of nearby stars to shift slightly as the Earth moves around the Sun. This effect is more pronounced for stars near the ecliptic, which is the plane of the Earth's orbit projected onto the celestial sphere.

As the Earth moves towards a star, its motion causes the star's light to be "compressed" or "blueshifted," resulting in a shift towards shorter wavelengths. On the other hand, as the Earth moves away from a star, the star's light is "stretched" or "redshifted," resulting in a shift towards longer wavelengths. This phenomenon is known as the Doppler effect.

Therefore, stars near the ecliptic, which is the path of the Sun through the constellations during a year, will exhibit the greatest Doppler shifts due to the Earth's revolution because their apparent positions change more significantly as the Earth moves in its orbit.