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?

  • 7
    $\begingroup$ Well, they only claim that the method is efficient, not effective! $\endgroup$
    – Jon Custer
    Commented Oct 4, 2023 at 16:49

1 Answer 1


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.)

  • 1
    $\begingroup$ Have you attempted to contact the publisher or author to get a correction published? $\endgroup$
    – Ian Kemp
    Commented Oct 5, 2023 at 19:28
  • $\begingroup$ @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. $\endgroup$
    – stanri
    Commented Oct 6, 2023 at 16:07
  • $\begingroup$ I imagine a correction could have been published in Sky and Telescope back in the 90s but it hasn't made its way online. $\endgroup$
    – stanri
    Commented Oct 6, 2023 at 16:09

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .