Celestial Programming : Greenwich Mean Sidereal Time - IAU 1982

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.

This is the IAU 1982 version, compatible with IAU 1976 Nutation when computing apparent sidereal time.

Jean Meeus - Astronomical Algorithms

\begin{align*} T &= \frac{jd-2451545.0}{36525} \\ \theta_0 &= 280.46061837 + 360.98564736629(jd-2451545.0) + (0.000387933T^2) - T^3/38710000 \end{align*}

2025-07-08 18:32:01 GMST: 19h 07m 50.98s


//Greg Miller (gmiller@gregmiller.net) https://www.celestialprogramming.com/
//Released as public domain 2025

//Result is in radians
function GMST(jd_ut1){
    const T=(jd_ut1-2451545.0)/36525; //12.1
    let θ0=100.46061837 + 36000.770053608*T + (0.000387933*T*T) - T*T*T/38710000; //12.3
    θ0=θ0%360;
    if(θ0<0) θ0+=360;
    return θ0*Math.PI/180;
}