<p>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.</p>
<p>At epoch J2000.0, <em>D</em><sub>0</sub>=-0.5, <em>H</em>=12, and <em>T</em>=0, so
<span class="math-container">$$\begin{align}
GMST &amp;= 6.6974 - 0.0329 + 12.0329 \\
     &amp;= 6.6974 + 12 \\
     &amp;= 18.6974
\end{align}$$</span>
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.</p>
<p>Roughly, the constant in question is the sidereal time at mean solar midnight on January 1.</p>

CC BY-SA 4.0
2021-08-12T09:50:31.007Z
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?
Peter
CC BY-SA 4.0
2021-08-12T17:58:44.403Z
@Peter That's right, it fails the sanity check in my first sentence.
Mike G
CC BY-SA 4.0
2021-08-12T19:22:59.170Z
Which only goes to show that not everything you read on the internet is true.
Peter
CC BY-SA 4.0
2021-08-12T04:16:27.743Z
2021-08-12T04:16:27.743Z
Mike G
<p>I'm trying to understand the constant 6.697374558 mentioned in <a href="https://astronomy.stackexchange.com/questions/24859/local-sidereal-time/24863#24863">this</a> question:</p>
<blockquote>
<p>The Astronomical Almanac gives an expression for approximate mean
sidereal time, in hours:</p>
<p><span class="math-container">$$\mathit{GMST}=6.697374558+0.06570982441908D_{0}+1.00273790935H+0.000026T^{2}$$</span></p>
</blockquote>
<p>I've googled 6.697374558 and found it described <a href="http://www.precisedirections.co.uk/Sundials/Basic%20Astronomy%20for%20the%20Gnomonist.pdf" rel="nofollow noreferrer">here</a> as:</p>
<p>“6.697374558 was the Greenwich hour angle of the Sun at Epoch 2000”.</p>
<p>However, when I input the Sun's RA (18h 45.1m) at 12pm 1 January 2000 into an <a href="https://clearskytonight.com/projects/astronomycalculator/coordinate/rightascension_hourangle.html" rel="nofollow noreferrer">online</a> 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.</p>

<coordinate><time>
Understanding the constant 6.697374558 when finding GMST
Peter
# Understanding the constant 6.697374558 when finding GMST

(Asked by: username_0 on 2021-08-09)

I'm trying to understand the constant 6.697374558 mentioned in [this](https://astronomy.stackexchange.com/questions/24859/local-sidereal-time/24863#24863) 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](http://www.precisedirections.co.uk/Sundials/Basic%20Astronomy%20for%20the%20Gnomonist.pdf) 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](https://clearskytonight.com/projects/astronomycalculator/coordinate/rightascension_hourangle.html) 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.

**Tags:** coordinate, time


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## 1 answers

### Answer by username_1 on 2021-08-12. Score: 1 | Accepted answer

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, *D*0=-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.

> **Comments:**
> **username_0**: 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?  
> **username_1**: @username_0 That's right, it fails the sanity check in my first sentence.  
> **username_0**: Which only goes to show that not everything you read on the internet is true.  

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