Celestial Programming : Greenwich Mean Sidereal Time - IAU 2000

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). Both UT1 and Terrestrial Time (TT) are required. UTC can be substituted with a maximum loss of accuracy of about 1 second.

This is the IAU 2000 version, compatible with IAU 2000 Nutation when computing apparent sidereal time.

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.

$$ \begin{align*} \theta &= 0.7790572732640 + 0.00273781191135448D_u + frac(JD(TT)) \\ T &=\frac{JD_{TT} - 2451545.0}{36525} \\ GMST &= 2\pi\theta + (0.014506 + 4612.15739966T + 1.39667721T^2 - 0.00009344T^3 + 0.00001882T^4)/60/60*\pi/180 \end{align*} $$ $ 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 Terrestrial Time since J2000
GMST = Greenwich Mean Sidereal Time (in radians)