the sidereal day is determined by the earth's rotation with respect to the stars
Sidereal time /saɪˈdɪəriəl/ is a time-keeping system that astronomers use to locate celestial objects. Using sidereal time it is possible to easily point a telescope to the proper coordinates in the night sky. Briefly, sidereal time is a ``time scale that is based on Earth's rate of rotation measured relative to the fixed stars'' rather than the Sun.
Sidereal time