Sidereal Time and the Lunar Day
The main use of Sidereal Time is in astronomy where it provides an exact timetable of the stars. The sidereal day is divided into 24 sidereal hours with the hours marked continuously from 0 hours to 24 hours (or 0 hours). To a sky observer sidereal time is the hour angle of the vernal equinox measured westward from your meridian, Figure 2. Because the earth rotates around the sun once a year, while it turns on its axis 365 times, the star day is 1/ 365th of a day shorter than 24 hours . .. about 4 minutes shorter. The star or sidereal day is 23 hours, 56 minutes and 4.09 seconds long...so a star will rise about 4 minutes earlier clocktime each night. One rotation of the earth, in reference to any star, rather than in reference to the sun, equals 24 hours of sidereal or star time. The zero hour (0 hour) at which the sidereal and the solar times are the same occurs when the vernal equinox is on your meridian.
The one feature which makes sidereal time somewhat of a puzzle is that the hours are 10 seconds shorter than similar hours of solar time. While this doesn't sound like much, it amounts to 240 seconds or 4 minutes in one day, 2 hours in one month and 24 hours or one whole day in a year. Why the sidereal day is shorter than the solar day can be seen in Figure 3. Because the earth revolves around the sun, it takes four minutes extra per day between two successive upper transits of the sun. The true period of the earth's rotation is actually the transit to transit time of a star on the vernal equinox. The four minute difference per day allows the stars to advance westward by this amount before the solar day is completed, and this small time difference repeated night after night, gives us a constantly changing parade of stars.
The big advantage of sidereal time is that, since it is governed by the apparent motion of the stars, it also keeps exact pace with them.
THE LUNAR DAY
In similar manner, the moon orbits around the earth as the earth, in turn, orbits around the sun. The new moon appears when sun, moon and earth are in a straight line with the moon in between. There are 29 days, 12 hours, 44 minutes and 3 seconds from one new moon to the next new moon.
This is the lunar month, the very word month comes from the word moon. The moon rises and sets about 50 minutes later each day. On your Spilhaus Space Clock the times of the positions of the moon are given in terms of sun or standard time, and not in terms of the lunar days, etc.
More pictures of Spilhaus Space Clock and how to repair it.