Final answer:
The time between successive passes of a given star across the meridian, known as a sidereal day, is 23 hours, 56 minutes. This period is the actual rotation period of Earth and differs from the solar day due to Earth's orbit around the sun.
Step-by-step explanation:
The time between successive passes of any given star across the meridian, known as a sidereal day, is 23 hours, 56 minutes. This period is slightly shorter than a solar day (which is 24 hours) due to the Earth's simultaneous orbit around the sun. While Earth completes one rotation on its axis, it also moves a bit in its orbit, thus requiring approximately an additional 4 minutes for the sun to reach the meridian. However, since stars are so far away, this orbital motion is negligible in their apparent motion, leading to the nearly 4-minute difference between a solar day and a sidereal day.
To calculate the exact length of a sidereal day, one can use the provided information. Since the Earth completes 366.2422 rotations in a year, not 365.2422, the true rotation period of the Earth can be found by dividing the average solar day by the number of Earth rotations per year:
Rotation period = (365.2422 days / 366.2422 rotations) × 86400 seconds
After performing this calculation, we find that the rotation period of the Earth is approximately 86164 seconds or 23 hours, 56 minutes, and 4 seconds, which is the duration of a sidereal day.