<p><strong>Update:</strong>
After a bit of narrowing down, I have found that the analemma is comprised of the sun's positions at the same <em>mean</em> solar time, not <em>apparent</em> solar time. Is this the reason why there is a figure of 8 - due to the equation of time? And does this in fact confirm that at solar noon, the azimuthal angle is always 0 (or 180)?</p>
<hr />
<p>My lecture notes seem to be contradicting themselves, and I cannot seem to find a straight answer online. At one point my lectures say that the azimuthal angle is given by:</p>
<p><span class="math-container">$$
sin(z) = \frac{cos(\delta) sin(h)}{ cos(\alpha)}
$$</span></p>
<p>where <span class="math-container">$\delta$</span> is declination, <span class="math-container">$\alpha$</span> is altitude angle and <span class="math-container">$h$</span> is hour angle (which is also defined to be 0 at noon).</p>
<p>Later on, it also discusses the analemma, which shows a figure of 8 of the sun's position in the sky at the same apparent solar time on different days of the year. This would clearly mean that at solar noon the sun is not always at <span class="math-container">$z = 0$</span>...</p>
<p>Note: The lecture notes do not state what co-ordinate system they are using, if this is of relevance.</p>

CC BY-SA 4.0
2024-11-05T00:42:39.350Z
FWIW, I have a script here that draws solar analemmas on the celestial sphere. https://astronomy.stackexchange.com/a/55736/16685
PM 2Ring
CC BY-SA 4.0
2024-11-05T07:39:59.470Z
The Sun is on the meridian at apparent solar noon, so the apparent time analemma is a straight line. It's not a point because the Sun's declination varies over the course of the year, which alters the Sun's altitude at apparent noon.
PM 2Ring
CC BY-SA 4.0
2024-11-07T15:35:57.893Z
The answers to the two questions in your update are "yes" and "yes."
stretch
<positional-astronomy>
Is the azimuthal angle always (exactly) 0 at solar noon?
ThePhysicsOverthinker
# Is the azimuthal angle always (exactly) 0 at solar noon?

(Asked by: username_0 on 2024-11-04)

**Update:**
After a bit of narrowing down, I have found that the analemma is comprised of the sun's positions at the same *mean* solar time, not *apparent* solar time. Is this the reason why there is a figure of 8 - due to the equation of time? And does this in fact confirm that at solar noon, the azimuthal angle is always 0 (or 180)?

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My lecture notes seem to be contradicting themselves, and I cannot seem to find a straight answer online. At one point my lectures say that the azimuthal angle is given by:

$$
sin(z) = \frac{cos(\delta) sin(h)}{ cos(\alpha)}
$$

where $\delta$ is declination, $\alpha$ is altitude angle and $h$ is hour angle (which is also defined to be 0 at noon).

Later on, it also discusses the analemma, which shows a figure of 8 of the sun's position in the sky at the same apparent solar time on different days of the year. This would clearly mean that at solar noon the sun is not always at $z = 0$...

Note: The lecture notes do not state what co-ordinate system they are using, if this is of relevance.

**Tags:** positional-astronomy

> **Comments:**
> **username_1**: FWIW, I have a script here that draws solar analemmas on the celestial sphere. https://astronomy.stackexchange.com/a/55736/16685  
> **username_1**: The Sun is on the meridian at apparent solar noon, so the apparent time analemma is a straight line. It's not a point because the Sun's declination varies over the course of the year, which alters the Sun's altitude at apparent noon.  
> **username_2**: The answers to the two questions in your update are "yes" and "yes."  

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## 0 answers

