Greenwich mean sidereal time

The Greenwich mean sidereal time is defined by the hour angle between the meridian of Greenwich and mean equinox of date at $0^h$ UT1: [A. B6]:

$$\Theta_{GMST} = 24110^s.54841 + 8640184^s.812866 T_U + 0^s.093104 T_U^2 - 6^s.2 \cdot 10^{-6} T_U^3 ,$$ (18)

in seconds of a day of 86400s UT1, where $T_U$ is the time difference in Julian centuries of Universal Time (UT1) from J2000.0.

From this the hour angle in degree $\theta_{GMST}$ at any instant of time $d_0$ (Julian days from J2000.0) can be calculated by

$$\theta_{GMST} = \Theta_{GMST} (T_U(0^h))\times 360^\circ/86400^s +180^\circ + 360^\circ * d_0$$ (19)

For the precision needed in this paper we may neglect the difference between $T_U$ and $T_0$, such that (Meeus, 2000):

$$\theta_{GMST} \approx 280^\circ.46061837 + 360^\circ.98564736629 d_0 + 0^\circ.0003875 T_0^2 - 2^\circ.6 \cdot 10^{-8} T_0^3 .$$ (20)