Expert: Courtney Seligman - 11/29/2008

Question
Hope you had a good Thanksgiving, Professor Seligman.

Thanks for helping me with the angle of setting (rising)sun question. I got out the spherical trigonometry equations, made a PZS sketch and an Excel spreadsheet.

Unless I made a mistake (not unlikely), the answer I am looking for is "S", not "90-S" (referring to the last part of your answer). In my spreadsheet, calculations for "S" made sense, e.g., for latitude 0, on Equator, I got 90 degrees for path of Sun relative to horizon. Comments?

Regards
Bill  

Answer
You are correct. I inadvertently left out a step at the end of my answer. Although it correctly stated how to define the angles in the PZS triangle, it didn't explain how to convert them to the angle of the rising Sun.

To find that angle, you need to imagine a perpendicular to the hour circle through the Sun. This perpendicular is the declination circle the Sun is on, and is also the diurnal path that it follows; and once the declination circle is added to the PZS triangle diagram, it becomes obvious that the angle of the rising Sun with the horizon is S (not 90-S, as I incorrectly stated).

In case this isn't clear (either to you, or someone else reading this answer), I've added a page to my website, at http://cseligman.com/text/sky/pzstriangle.htm which shows a diagram of the situation.

Courtney Seligman