Greenwich Apparent Sidereal Time, is Greenwich Mean Sidereal Time adjusted for nutation.
(Mathematically \(GAST = GMST + Equation Of The Equinoxes\) ). GAST should be used in place of
GMST when computing the apparent coordinates of an object. The equation is the same regardless
of which IAU standards are being used, but differ by the data fed into it. Here the 1980
nutation and \(ε_0\) models are used.
$$
\begin{align*}
ε_0 &= 84381".448 - 46".8150T - 0".00059T^2 + 0".001813T^3 \\
ε &= ε_0 + \Delta \epsilon \\
GAST &= GMST + \Delta \psi \cos \epsilon \\
\end{align*}
$$
Both \(\Delta \psi \) and \(\Delta \epsilon\) come from the nutation algorithm.
GMST comes from the sidereal time algorithm.
\(ε_0 + \Delta \epsilon\) is called the Equation of the Equinoxes
T is Terrestrial Time, GMST should be computed using UT1