havesomeseichel-
“This interval is known as a “sidereal” day, which is 23 hours, 56 minutes, 4.06 seconds.”
Correct!
The (almost) quarter-day that must be compensated for is due to the fact that the earth takes about 365.24 days to circle the sun.
The length of each day is the same, although the amount of daylight differs.
The orbit itself is not a perfect circle – we are closer to the sun during the northern hemisphere’s winter.
The best way I can think of to explain why more than a full rotation is needed in a 24 hour period is:
Let’s imagine the earth as a marble, circling around the outide of a clock. The sun is the center of the clock. Let’s say (for simplicity’s sake) the year is only four days long. If the marble (earth) moves from the 9 o’clock position to the 12 o’clock position (one day), and the marble rotates 360 degrees, the part of the marble which faced the sun is now facing off to the right. It must rotate an extra quarter turn for the part that faced the sun to again face the sun.
This less-the-24-hour rotation equaling a 24-hour day is because the earth rotates counter-clockwise when viewed from a spaceship parked over the north pole. If it rotated clockwise and the day was still 24 hours, a full rotation would be longer than a 24-hour day-night cycle.