Unrelated to practical zmanim calculations, it is fascinating to see that with enough work, astronomers were able to pinpoint the exact date and time that Claude Monet painted the Cliff at Etretat, Sunset painting based on the position of the sun at sunset. Researchers from Texas State University published information showing that the masterpiece was painted (or more accurately, visualized in Claude Monet's mind) at 4:53PM on February 5^{th}, 1883.
The picture of the Kosel below was taken by my grandfather Sidney (Nesanel) Siegfried. While I can’t pinpoint the exact time the picture was taken, I do know that it was taken in the early afternoon on Aug 1^{st}, 1932 כ״ח תמוז תרצ״ב. I leave it to the readers of this post to try and calculate the exact time the picture was taken based on the shadows.

5 thoughts on “Forensic Zmanim Calculations”

Very nice picture of the Kosel from the period before the State of Israel.

Hi, I tried contacting you directly from the contact page, but there’s an error, and it doesn’t display the code you have to type in to send the message!
Anyway, here’s what I had wanted to ask you:

I was just wondering if you could tell me which algorithm (USNO/NOAA) provides the more accurate time for sunrise/set? You’ve mentioned the differences before on your blog, and I was wondering if you have reached a definitive conclusion?
Also, you mentioned a while back two calculations for correcting for altitude – have you decided which is the better of the two (you mentioned something about correcting for refraction differences at higher altitudes)?
One last question – have you come across any method for correcting for the altitude of the horizon (quite important for Jerusalem sunrise)?
Thank you!

Yehuda,
Thank you for your persistence. I “fixed” the contact page by getting rid of the contact plugin and just inserting contact details. I am sorry to disappoint with my answers but no, no, no. Hopefully it is something I will get to eventually. The accuracy is almost meaningless given the amount of difference that is caused by changes in refraction due to weather (I have a new post in progress that will hopefully be out in the near future to discuss refraction).

Thanks for the reply.
I did notice that the wikipedia page for the sunrise equation uses a variation of the “other” (not the one you use in the API) equation for correcting for elevation. However, it uses a slightly different constant (after dividing the constant by 60, to compare like with like).
I have no idea where it comes from though (there are no references!).

At one point in the comments to the API you mention a difference between the USNO and NOAA formulas with regard to the apparent solar radius changing at different times of year, but I don’t really understand what you wrote. Are you saying that the NOAA formula is more accurate in that respect?

On a different point, with regard to using sealevel sunrise/set for calculating other times in the day, the most popular luach in Jerusalem (Itim L’binah) does that as well, but not when it comes to calculating the 72min fixed Rabeinu Tam. Then they use the elevation shkiah. I think most other calendars here follow this as well.
It leads to the interesting result that the 72min fixed R”T is almost always LATER then the 16.1deg R”T (in Jerusalem, there’s approximately a 5 min difference in sunset due to elevation, which is greater then the extra time using degrees for most of the year).
And can you clear up one other point for me: extending the logic for using sealevel sunrise/set should lead us to use a sunrise/set without correcting for refraction and sun radius. Why do we not do that?

Very nice picture of the Kosel from the period before the State of Israel.

1:17 pm

Thanks for the fun! Now onto making a zmanim chart for shul.

Hi, I tried contacting you directly from the contact page, but there’s an error, and it doesn’t display the code you have to type in to send the message!

Anyway, here’s what I had wanted to ask you:

I was just wondering if you could tell me which algorithm (USNO/NOAA) provides the more accurate time for sunrise/set? You’ve mentioned the differences before on your blog, and I was wondering if you have reached a definitive conclusion?

Also, you mentioned a while back two calculations for correcting for altitude – have you decided which is the better of the two (you mentioned something about correcting for refraction differences at higher altitudes)?

One last question – have you come across any method for correcting for the altitude of the horizon (quite important for Jerusalem sunrise)?

Thank you!

Yehuda,

Thank you for your persistence. I “fixed” the contact page by getting rid of the contact plugin and just inserting contact details. I am sorry to disappoint with my answers but no, no, no. Hopefully it is something I will get to eventually. The accuracy is almost meaningless given the amount of difference that is caused by changes in refraction due to weather (I have a new post in progress that will hopefully be out in the near future to discuss refraction).

Thanks for the reply.

I did notice that the wikipedia page for the sunrise equation uses a variation of the “other” (not the one you use in the API) equation for correcting for elevation. However, it uses a slightly different constant (after dividing the constant by 60, to compare like with like).

I have no idea where it comes from though (there are no references!).

At one point in the comments to the API you mention a difference between the USNO and NOAA formulas with regard to the apparent solar radius changing at different times of year, but I don’t really understand what you wrote. Are you saying that the NOAA formula is more accurate in that respect?

On a different point, with regard to using sealevel sunrise/set for calculating other times in the day, the most popular luach in Jerusalem (Itim L’binah) does that as well, but not when it comes to calculating the 72min fixed Rabeinu Tam. Then they use the elevation shkiah. I think most other calendars here follow this as well.

It leads to the interesting result that the 72min fixed R”T is almost always LATER then the 16.1deg R”T (in Jerusalem, there’s approximately a 5 min difference in sunset due to elevation, which is greater then the extra time using degrees for most of the year).

And can you clear up one other point for me: extending the logic for using sealevel sunrise/set should lead us to use a sunrise/set without correcting for refraction and sun radius. Why do we not do that?