meridian. All these angles are illustrated in Figure E.3. A sidereal day is the duration
between two passes of the vernal equinox through the meridian and it is slightly shorter
than a solar day. We can understand this by realizing that the Earth has to rotate by 360°
and approximately 360°/365.25 between two passes through the meridian. The duration of
mean sidereal day is approximately 23 h, 56 m and 4 s.
Figure E.3: Illustrating the right ascension α, the local hour angle h, the Greenwich mean sidereal time GMST and the
local mean sidereal time θ L .
To calculate θ L we first have to determine the Greenwich mean sidereal time (GMST),
which is (approximately) given by
where D is as defined above and T is the number of centuries past since Greenwich noon,
Terrestrial Time, on 1 January 2000,
For many applications, the quadratic term may be omitted. GMST is given in hours and
has to be normalized to the range [0 h, 24 h). We can then obtain the local mean sidereal
time in degrees with
where λ 0 is the longitude of the observer.
We thus have the following transform about the rotational axis of the earth,