The correct answer is: C. Mean solar time.
Sidereal time is the time it takes for the Earth to rotate once on its axis, relative to the fixed stars. Apparent solar time is the time it takes for the Sun to appear to move once across the sky, relative to the observer’s meridian. Mean solar time is a measure of time that is based on the average apparent solar time. It is used to keep clocks in sync with the Sun.
The difference in longitude of two places is the difference in the angle between the two lines of longitude that pass through those places. The Earth rotates once on its axis every 24 hours, so the difference in longitude of two places is equal to the difference in their mean solar time.
Sidereal time is not equal to the difference in longitude of two places because it is not synchronized with the Sun. The Earth’s rotation is slowing down very slowly, so sidereal time is getting longer over time. Apparent solar time is also not equal to the difference in longitude of two places because it is affected by the Earth’s orbit around the Sun. The Earth’s orbit is not perfectly circular, so the Sun appears to move slightly faster or slower across the sky at different times of the year.