# Calculating the time interval between sunrises with and without the atmosphere

I have developed a method to calculate the time of sunrise, sun noon and sunset, but it does not take the atmosphere into account. Therefore, in order for my results to be useful in practice, I need to know the time interval between the sunrise with refraction and without refraction.

By using the Stellarium software I have determined that it is about 7-8 minutes (such that the sun rises 7-8 minutes earlier due to the presence of the atmosphere), although it varies depending on latitude, because the angle at which the sun rises is different - though I believe the angle between the incoming light and the final, refracted, light would be enough to calculate the time interval, which may be independent of latitude and which is shown as $$\theta$$ in the image below.

Is there a way to calculate this time interval or the previous angle, or does it need to be experimental?

• This question is on-topic here, but it would probably be better on Astronomy.SE. Actual sunrise / sunset times can vary from even the best predicted times because of the weather. FWIW, using standard refraction formulae I can calculate sunrise / sunset times that differ by less than a minute from the times given by Horizons. Jun 7 at 7:08