P.S. Using this has made it clear to me how bad most sunrise/sunset calculators actually are.
That may just be a function of how you define "sunrise" and "sunset". It is never as simple as "when the sun hits the horizon", but something about some number of arc minutes from something something.
And what I meant was you are not seeing "error", it's just a difference in definition.
I've previously used the formulas on this site to calculate the altitude/azimuth of the Sun and all the planets from a given lat/long/time on Earth.
Half these customers can't be bothered by the edge cases that I've been poring over for nights. The other half puts forward edge cases that I've never been aware of. Some of which are critical to their work-flow. Many are implemented in mere minutes. "Wow. That saves us 30 minutes typing over prices, every day!".
As an engineer I love to find solutions. But as an entrepeneur I really must understand the problem and scope. that 0.1% edge cases is hardly ever part of the success.
https://www.citizenwatch-global.com/support/exterior/directi...
https://www.watchaffinity.co.uk/blog/how-to-use-your-watch-a...
This is more prone to errors closer to the equator and in the summer (https://possiblywrong.wordpress.com/2012/01/25/using-a-watch...) but should be good enough for picking a side of the bus.
(This is all in the northern hemisphere; in the southern hemisphere the sun goes the other way, so change the sign on everything.)
> The equation of time describes the discrepancy between two kinds of solar time. The word equation is used in the medieval sense of "reconciliation of a difference". The two times that differ are the apparent solar time, which directly tracks the diurnal motion of the Sun, and mean solar time, which tracks a theoretical mean Sun with uniform motion along the celestial equator. Apparent solar time can be obtained by measurement of the current position (hour angle) of the Sun, as indicated (with limited accuracy) by a sundial. Mean solar time, for the same place, would be the time indicated by a steady clock set so that over the year its differences from apparent solar time would have a mean of zero.
And this gets into a neat part of the Clock of the Long Now and a cam needed to keep track of that over 10,000 years. https://longnow.org/ideas/the-equation-of-time-cam-keeping-g...