Physics of the Universe question :

Topic : Astrometry

(a) Ignoring proper motion, determine the apparent position of a star as a function of time as observed from Earth, if it is located at (i) the ecliptic pole (ii) the ecliptic plane.

(b) Including proper motion determine the apparent position of a star, located on the ecliptic pole, as a function of time. Take the direction of the proper motion to be your x-axis.