The calculation of the z coordinate is straightforward, as can be seen in Figure 2. This figure shows a side cutaway of the Earth with North up. To calculate the x and y coordinates, we will also need the value of R from Figure 2. This figure shows a slice through the Earth, parallel to the equatorial plane and through the observer's location. Upon first inspection, these equations would seem straightforward enough.
Sidereal time is simply time measured relative to the stars.
This time scale is referred to as mean solar time . As with any time system, time is defined as the angle between the observer and some reference direction. As seen in Figure 4, the position of the Sun moves with respect to the stars because of the Earth's orbit around it. By definition, that passage is called local noon. However, when that same position relative to the stars crosses our meridian on the following day, the Sun will not yet have reached our meridian.