The correct answer is A. one sidereal day.
A sidereal day is the time it takes for the Earth to rotate once on its axis relative to the fixed stars. It is about 23 hours, 56 minutes, and 4.09 seconds long. A solar day is the time it takes for the Earth to rotate once on its axis relative to the Sun. It is about 24 hours long.
The difference between a sidereal day and a solar day is due to the Earth’s orbit around the Sun. As the Earth orbits the Sun, it also rotates on its axis. This means that the Sun appears to move across the sky from east to west. The time it takes for the Sun to return to the same position in the sky is one solar day. However, the Earth has also moved a little bit in its orbit around the Sun during that time. This means that the stars have moved a little bit across the sky as well. The time it takes for the stars to return to the same position in the sky is one sidereal day.
In conclusion, the time interval from when the given star passes directly overhead to when it next passed directly overhead is defined as one sidereal day.