<p>This is an error in the paper. The equation is based on</p>
<p><span class="math-container">$\nu - M = 2\varepsilon \sin M$</span></p>
<p>Where M is simplified to be <span class="math-container">$M = l + 1.3450$</span> and <span class="math-container">$\varepsilon = 0.0167$</span>, the eccentricity of the Earth's orbit .</p>
<p>However, the paper is off by a power of 10 and incorrectly shows <span class="math-container">$2\varepsilon = 0.3342$</span> instead of <span class="math-container">$2\varepsilon = 0.03342$</span>.</p>
<p>It should be</p>
<p><span class="math-container">$\nu - M = 0.03342 \sin (l + 1.3450)$</span></p>
<p>(I thought I'd post this Q/A here for others to find if they're looking to use this paper as a source for their calculations. It comes up in almost no search results, so I thought I'd record this error here for others to find.)</p>

CC BY-SA 4.0
2023-10-05T19:28:10.413Z
Have you attempted to contact the publisher or author to get a correction published?
Ian Kemp
CC BY-SA 4.0
2023-10-06T16:07:54.753Z
@IanKemp I haven't, simply because it was published so long ago (1996) and I imagine the author already knows. I googled for any corrections or anything about the paper and got no results apart from the download  link itself, so I figured posting here would be the best option instead.
stanri
CC BY-SA 4.0
2023-10-06T16:09:21.247Z
I imagine a correction could have been published in Sky and Telescope back in the 90s but it hasn't made its way online.
stanri
CC BY-SA 4.0
2023-10-04T10:31:53.187Z
2023-10-04T10:31:53.187Z
stanri
<p>I've been implementing this paper in python.
<a href="https://articles.adsabs.harvard.edu/pdf/1996SouSt..36..239S" rel="noreferrer">&quot;Efficient Method for Calculating the time of Sunrise and Sunset&quot; by Robin G Stuart.</a></p>
<p>The sun's equation of centre is incorrect no matter what I try.
it's</p>
<p><span class="math-container">$\nu - M = 0.3342 \sin (l + 1.3450)$</span></p>
<p>where l is the sun's mean longitude.</p>
<p>Where does this equation come from, and is it correct?</p>

CC BY-SA 4.0
2023-10-04T16:49:56.190Z
Well, they only claim that the method is efficient, not effective!
Jon Custer
<the-sun>
Error in "Efficient Method for Calculating the time of Sunrise and Sunset" by Robin G Stuart
stanri
# Error in "Efficient Method for Calculating the time of Sunrise and Sunset" by Robin G Stuart

(Asked by: username_0 on 2023-10-04)

I've been implementing this paper in python.
["Efficient Method for Calculating the time of Sunrise and Sunset" by Robin G Stuart.](https://articles.adsabs.harvard.edu/pdf/1996SouSt..36..239S)

The sun's equation of centre is incorrect no matter what I try.
it's

$\nu - M = 0.3342 \sin (l + 1.3450)$

where l is the sun's mean longitude.

Where does this equation come from, and is it correct?

**Tags:** the-sun

> **Comments:**
> **username_1**: Well, they only claim that the method is efficient, not effective!  

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## 1 answers

### Answer by username_0 on 2023-10-04. Score: 26

This is an error in the paper. The equation is based on

$\nu - M = 2\varepsilon \sin M$

Where M is simplified to be $M = l + 1.3450$ and $\varepsilon = 0.0167$, the eccentricity of the Earth's orbit .

However, the paper is off by a power of 10 and incorrectly shows $2\varepsilon = 0.3342$ instead of $2\varepsilon = 0.03342$.

It should be

$\nu - M = 0.03342 \sin (l + 1.3450)$

(I thought I'd post this Q/A here for others to find if they're looking to use this paper as a source for their calculations. It comes up in almost no search results, so I thought I'd record this error here for others to find.)

> **Comments:**
> **username_2**: Have you attempted to contact the publisher or author to get a correction published?  
> **username_0**: @IanKemp I haven't, simply because it was published so long ago (1996) and I imagine the author already knows. I googled for any corrections or anything about the paper and got no results apart from the download  link itself, so I figured posting here would be the best option instead.  
> **username_0**: I imagine a correction could have been published in Sky and Telescope back in the 90s but it hasn't made its way online.  

---

