Build Your Own Sidereal Clock

From Wikipedia:
Sidereal time /saɪˈdɪəriəl/ is a time-keeping system astronomers use to keep track of the direction to point their telescopes to view a given star in the night sky. Briefly, a sidereal day is a "time scale that is based on the Earth's rate of rotation measured relative to the fixed stars."[1]

From a given observation point, a star found at one location in the sky will be found at nearly the same location on another night at the same sidereal time. This is similar to how the time kept by a sundial can be used to find the location of the Sun. Just as the Sun and Moon appear to rise in the east and set in the west, so do the stars. Both solar time and sidereal time make use of the regularity of the Earth's rotation about its polar axis, solar time following the Sun while sidereal time roughly follows the stars. More exactly, sidereal time follows the vernal equinox, which is not quite fixed among the stars; Precession and nutation shift the equinox slightly from one day to the next, so sidereal time is not an exact measure of the rotation of the Earth relative to inertial space.[2] Common time on a typical clock measures a slightly longer cycle, accounting not only for the Earth's axial rotation but also for the Earth's annual revolution around the Sun of slightly less than 1 degree per day.

A mean sidereal day is about 23 hours, 56 minutes, 4.091 seconds (23.93447 hours or 0.99726957 mean solar days), the time it takes the Earth to make one rotation relative to the vernal equinox. (Due to nutation, an actual sidereal day is not quite so constant.) The vernal equinox itself precesses slowly westward relative to the fixed stars, completing one revolution in about 26,000 years, so the misnamed sidereal day ("sidereal" is derived from the Latin sidus meaning "star") is some 0.008 seconds shorter than the Earth's period of rotation relative to the fixed stars.

The blog at our favorite open-source company Adafruit has a link to an observatory in Brazil with an article on building your own Sidereal clock:

A clock that displays UT(Universal Time) and LST (Local Sidereal Time) is a useful device to have in an astronomical observatory. Using the Arduino open source platform it is possible to build a sidereal clock for less than $200.