4) Say we want to measure whether a star is coming towards us or away from us using the Doppler shift of the lines in its spectra, with an accuracy of 1 km s-1 or better. Assume for simplicity that the star is in the plane of the Earth's orbit around the Sun. (a) Is it important to take into account the Earth's orbital motion around the Sun? How about Earth's rotational motion on its axis (ignore the tilt of the Earth's rotation axis for this problem) ? In other words, if we didn't take these motions into account, could we make an error larger than 1 km s-1? Use figures to show these effects and calculate what are the largest velocity shifts these two effects can introduce, in km s-1? Use the Earth's sidereal year, orbit size, sidereal day, and radius. (b) For the Earth's rotational motion, describe qualitatively how the velocity shift depends on latitude. That is, does it increase, decrease, or stay the same, and why?
