INTRODUCTION
The Earth both rotates on its axis and revolves around the Sun. The rotation gives as the day and the revolution gives us the year. However the two motions interact.
The solar day is divided into 24 solar hours or 1440 solar minutes or 86,400 solar seconds. The solar day is the length of time it takes for the Earth to rotate so that a given point on the Earth sees the Sun at (roughly) the same point in the sky as the the previous day. However, fo this to happen the Earth has tp rotate through close to 361 degrees, not 360 degrees as we might first suppose. This is because of the revolution about the Sun. As this takes a little over 360 days the Sun appears to be about one degree displaced against the fixed backgrounf of stars each day. This is fine for out daily activities which are based on the cycle of night and day.
Astronomers however, and anyone else who is concerned with where the stars appear in the sky, use a different measure of time. Their sidereal day is based on a rotatiogn of the Earth through 360 degrees. The sidereal day is also divided into 24 sidereal hours. This day is approximately 4 minutes shorter than the solar day. More exactly the sidereal day is 23 hours 56 minutes and 4 solar seconds. Thus the sidereal day is 3 solar minutes and 56 solar seconds, or 86,164 solar seconds in length.
A sidereal clock immediately gives the right ascension (celestial longitude) of any object currently crossing the observer's meridian. Local sidereal time minus an objects right ascencion gives the stars hour angle .
SIDEREAL CLOCKS
To keep track of sidereal time we need a sideral clock. This clock must run faster than a solar clock. It must run faster by a factor of 86400 / 86164 or 1.002739.
Now our solar clocks run using a number of different priciples. Some are mechanical and some are electronic. For mechanicall clocks we may be able to adjust the regulator by a sufficient factor to get a clock that will keep sidereal time. An electronic clock may be analog or digital. The digital clocks depend on a certain frequency of alternating current input to keep accurate time. Some of these clocks use the 50 Hz or 60 Hz power into our homes to keep accurate time. Most power companies keep this frequency quite accurately when averaged over a 24 hour or longer period.
Of course, mobile clocks or watches cannot use this power. Very accurate sidereal clocks also use a different method. These clocks generally use their own inbuilt frequency generator and these are based on a quartz crystal which is made to oscillate at a closely maintained frequency. For watches this frequency is usually 32.768 kHz. For fixed clocks it may be a number of frequencies. Twelve MHz is one popular frequency. This frequency is then divided down by an electronic counter to give a 1 second pulse which drives the clock. Highly accurate clocks may use a GPS derived 1 second pulse. The most accurate clocks use a Rubidium or Caesium oscillator.
A sidereal clock is most easily made using a readily available digital solar clock but instead of supplying it with a pulse every solar second supplying it with a pulse every 86164/86400 or 0.997269 solar seconds. Many different designs have been devised to convert a solar clock into a sidereal clock.
SIDEREAL CLOCK DESIGN
Several designs for sidereal clocks have appeared in the pages of the journal 'Sky and Telescope'.
The first circuit shown below is from Sky and Telescope July 1976 pages 59 to 62. This keeps sidereal time to an accuracy of two seconds per year.
The second circuit shown below is from Sky and Telescope May 1978 pages 433 to 436. This is a simpler circuit that keeps accuracy to about one minute per year.
Both of these circuits work using clocks that run off the 50 or 60 Hz mains and add extra pulses to convert from solar to sidereal time.
However, if your observatory does not have access to mains power and is solar powered a different approach must be adopted. This is also the case if your mains power (ie not from a statewide grid) is not stable over long time periods.
This approach is actually simpler, but not cheaper than the above systems.
A 24 hour six-digit digital clock kit is now (2025) available from China (through Amazon) very cheaply [YCL-6 multi-function electronic clock suite]. It keeps solar time using a 12 MHz quartz crystal. By replacing this crystal with a high precision crystal one a frequency of 12.03290 MHz the clcok will then keep sidereal time. Such a crystal can be obtained in Australia from HyQ in Melbourne.
The circuit for the clock is shown below.
Although this clock will not have the long term stability of a good mains driven clock it should be accurate enough for most purposes with an appropriate period of resetting. And with a battery backup it will not be subject to power outages which often destroy any advantage to using a mains AC power source.
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SETTING A SIDEREAL CLOCK
There are many web sites that will help you to calculate sidereal time with which to set your sidereal clock. The URL for four of these is given below.
1 Very extensive explanations of sidereal time calculation with comprehensive formule:
https://www.omnicalculator.com/everyday-life/sidereal-time
2 Easy to Use Sidereal Calculator uses your local date, time, time
zone offest and longitude:
https://phpsciencelabs.com/sidereal-time-calculator/
3 Sidereal to Solar and Solar to Sidereal Calculator:
https://akynocalculator.com/time/sidereal-time-calculator
4 From the US Naval Observatory:
https://aa.usno.navy.mil/data/siderealtime
Australian Space Academy