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I'm trying to understand the constant 6.697374558 mentioned in this question:

The Astronomical Almanac gives an expression for approximate mean sidereal time, in hours:

$$\mathit{GMST}=6.697374558+0.06570982441908D_{0}+1.00273790935H+0.000026T^{2}$$

I've googled 6.697374558 and found it described here as:

“6.697374558 was the Greenwich hour angle of the Sun at Epoch 2000”.

However, when I input the Sun's RA (18h 45.1m) at 12pm 1 January 2000 into an online RA to hour angle calculator (for the Greenwich meridian) I get 23h 56m 44.55s. Any idea what I'm doing wrong? I'm new to all this, so apologies if I've made any basic errors.

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On any given day, the hour angle of the Sun in Greenwich at 12:00 UTC should be within 20 minutes of 0h. On January 1 the equation of time is about -3 minutes. The solar hour angle you computed is correct.

At epoch J2000.0, D0=-0.5, H=12, and T=0, so $$\begin{align} GMST &= 6.6974 - 0.0329 + 12.0329 \\ &= 6.6974 + 12 \\ &= 18.6974 \end{align}$$ or 18:42:51, about 2 minutes less than the RA of the Sun on that date. The difference between UTC and TT in 2000 accounts for the 1 minute remainder.

Roughly, the constant in question is the sidereal time at mean solar midnight on January 1.

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  • $\begingroup$ Thanks. But does that mean that the online quote I found “6.697374558 was the Greenwich hour angle of the Sun at Epoch 2000” is therefore incorrect? $\endgroup$
    – Peter
    Aug 12, 2021 at 9:50
  • $\begingroup$ @Peter That's right, it fails the sanity check in my first sentence. $\endgroup$
    – Mike G
    Aug 12, 2021 at 17:58
  • $\begingroup$ Which only goes to show that not everything you read on the internet is true. $\endgroup$
    – Peter
    Aug 12, 2021 at 19:22

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