# Error in "Efficient Method for Calculating the time of Sunrise and Sunset" by Robin G Stuart

I've been implementing this paper in python. "Efficient Method for Calculating the time of Sunrise and Sunset" by Robin G Stuart.

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?

• Well, they only claim that the method is efficient, not effective! Oct 4 at 16:49

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.)

• Have you attempted to contact the publisher or author to get a correction published? Oct 5 at 19:28
• @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. Oct 6 at 16:07
• I imagine a correction could have been published in Sky and Telescope back in the 90s but it hasn't made its way online. Oct 6 at 16:09