# How to determine Az-El pointing of a telescope spiral scan?

I am writing a simulation of an automated telescope observation program. One part of this is to run a spiral scan pattern on and around objects of interest. I would like to tile this scan pattern so that each image is immediately adjacent to each other (perhaps with a specified level of overlap). The telescopes I'm simulating are Az-El.

My primary objects of interest are GEO satellites, and that combined with the specific simulation framework used makes Az-El a little more natural to work with than celestial coordinates.

Given the Az-El of the object of interest, I'm trying to determine the Az-El pointing directions for all of the images. As I understand it, I can define an image location in pixel coordinates relative to the central image centered on the object of interest and then project this into Az-El (or other spherical) coordinates. I'm not entirely sure how to do this. I see online and in codes lots of spherical projections (gnomonic, arc, orthographic, for example) but I don't know which one is the right one to use for what I'm trying to do. Is my understanding of the procedure correct, and which projection should I use?

• "Given the Az-El of the object of interest..." might be starting off on the wrong foot. To me, the natural way to proceed would be to work in coordinates on the celestial sphere (celestial coordinates, R.A., Dec) and build your spiral pattern there in those coordinates. Since your automated telescope will need to constantly track the motion of the celestial sphere as the Earth rotates, you will already need to be converting from celestial coordinates to Alt. Az. continuously. – uhoh Nov 14 at 0:52
• photo.stackexchange.com/questions/6111/… may or may not be helpful. – barrycarter Nov 14 at 2:56
• @uhoh, my primary objects of interest are GEO satellites, and that combined with the specific simulation framework I have make Az-El a little more natural to work with. But I agree that R.A. and dec are definitely more natural to work with for celestial objects, and with a different framework in my case too (alas I do not have that option). And for this specific work, I do not need to worry about tracking yet (that's handled by a different piece of software). – NeutronStar Nov 14 at 16:29
• Okay great! I've added a bit of that back into your question. It's always best to amend a post for clarification since many people don't read comments before answering. Thanks for the speedy reply! – uhoh Nov 14 at 16:34