The sidereal day is the time it takes for the Earth to complete one rotation about its axis with respect to the ‘fixed’ stars. By fixed, we mean that we treat the stars as if they were attached to an imaginary celestial sphere at a very large distance from the Earth.idereal Day. A sidereal day is the time it takes for the Earth to rotate about its axis so that the distant stars appear in the same position in the sky. A solar day is the time it takes for the Earth to rotate about its axis so that the Sun appears in the same position in the sky.