Celestial Programming : Greenwich Mean Sidereal Time

Greenwich Apparent Sidereal Time (GMST) is essentially the Right Ascention line which is directly above the Greenwich meridian at a specified time. It differs from Greenwich Apparent Sidereal Time (GAST), in that GAST takes nutation into account. GMST is used in place of GAST to save on computational effort at the expense of a loss of accuracy on the order of about 20 arcseconds (or 1 second of Sidereal Time). The propper time to use is UT1, but UTC can be used if an error of .9 seconds is acceptable.

Reference: The IAU Resolutions on Astronomical Reference Systems, Time Scales, and Earth Rotation Models Explanation and Implementation (George H. Kaplan) eqations 2.11 and 2.12.

$$ \begin{align*} \theta &= 0.7790572732640 + 0.00273781191135448D_u + frac(JD(UT1)) \\ T &=\frac{JD_{UT1} - 2451545.0}{36525} \\ GMST &= 2\pi\theta + (0.014506 + 4612.15739966T + 1.39667721T^2 - 0.00009344T^3 + 0.00001882T^4)/60/60*\pi/180 \end{align*} $$ $ D_u $= Number of days of UT1 since J2000 (JD(UT1) - 2451545.0)
$ \theta $ = Earth Rotation Angle (in fractions of full rotations)
T = Centuries of UT1 since J2000
GMST = Greenwich Mean Sidereal Time (in radians)