# In the calculation of GMST, what are these constants? [duplicate]

GMST = 6.697374558 + 0.06570982441908 D0 + 1.00273790935 H + 0.000026 T2

From the GMST calculation on the USNO website (and many other places) we encounter these constants:

1. 6.697374558
2. 0.06570982441908
3. 1.00273790935

Can someone enlighten me as to what they represent?

• Number 3 is easy: it's (1 mean solar day) / (1 sidereal day). So (24 hours) / 1.00273790935 is approx 23h 56m 4s. – PM 2Ring Nov 12 '18 at 4:22
• @PM2Ring - As is number 2: It's simply 1.00273790935*24 mod 24, with some extra digits (or rather, the 1.00273790935 is missing a few digits). – David Hammen Nov 12 '18 at 10:09

Aoki et al. 1982 discuss this in more detail and added a $$T^3$$ term (their equation 13, although note the values there are in seconds not hours as in the original USNO version above) for what became the IAU 1984 system. Capitaine et al 2000 added a $$T^4$$ term along with another 32 more terms to the so-called equation of the equinoxes which is added onto the formula for GMST to get GAST (Apparent Sidereal Time). The equation of the equinoxes takes account of the accumulated precession and nutation as the fictitious mean sun is not a very good reflection of reality for precise work. Because of these increased complexities and coupling between the Earth's rotation and the background reference frame of the stars needed for precise work, the IAU did away with sidereal time in 2006 and replaced it with Earth Rotation Angle (ERA) which is a simple linear function of UT1 time.