The correct answer is: A. Mean sun
The sidereal day is the time interval between two successive upper transits of the mean sun across the observer’s meridian. It is the time it takes for the Earth to rotate once on its axis relative to the fixed stars. The mean sun is a fictitious sun that moves across the sky at a constant rate, in contrast to the real sun, which moves at a variable rate due to the Earth’s orbit around the Sun.
The first point of Aries is the vernal equinox, the point in the sky where the Sun crosses the equator from south to north. The first point of Libra is the autumnal equinox, the point in the sky where the Sun crosses the equator from north to south. The polar star is the star that appears to be stationary in the sky, due to the Earth’s rotation.
The sidereal day is shorter than the solar day, which is the time interval between two successive noons. This is because the Earth’s orbit around the Sun is not perfectly circular, so the Earth’s speed in its orbit varies. As a result, the Earth’s rotation is slowed down by the Sun’s gravity.
The sidereal day is important in astronomy because it is used to define the sidereal time, which is the time measured by the Earth’s rotation relative to the fixed stars. Sidereal time is used to track the positions of stars and planets in the sky.