Sidereal time is time measured with respect to the stars. If you have looked regularly at the stars through a whole year you will have noticed that the constellations visible at night changes with the seasons.
This part will amongst other things show you why.
Our clocks are based on the solar day, that is the time it takes Earth to rotate and show the same face to the Sun again. This period is 24 hours (This is the mean period, you can learn more about this in the equation of time tutorial).
Lets see what happens from day to day, press the Try it button below to open the planisphere. The step size has been set to 24 hours. Press the forward button 10-20 times and observe the motions of the Sun and the stars.
As you move forward the Sun returns to almost the same location in the sky in 24 hours. But the stars seems to speed ahead of the Sun, or to put it another way: the Sun appears to drift eastward with respect to the stars.
It's easy to assume that the Earth rotates 360° during 24 hours, but as the drawing above illustrates, this is not correct. Because Earth also orbits the Sun it needs to rotate a little bit more than 360 degrees to show the same face to the Sun again.
A sidereal day is the time it takes a star to return to the exact same place in the sky. Because the stars are very distant from us the motion of the Earth in its orbit makes an negligible difference in the direction to the stars. This means the Earth rotates 360° in one sidereal day.
Lets try to figure out how long a sidereal day is. We start with a step size of 1440 minutes, which is equal to 24 hours. Now you need to adjust the step size by adding or substracting minutes until the stars move as little as possible when you step forward, try it now.
You probably found that 1436 minutes was the time when the stars moved the least. This means that the sidereal day is about 4 minutes shorter than the solar day.
As we have seen the Earth must rotate a little more than 360 degrees during one solar day. To be precise the Earth must rotate an extra 0.986°. This makes the correct length of a sidereal day 23 hours 56 minutes and 4 seconds long.