I recently imaged M57. A catalog that I use says that it is magnitude 9.0 and a size of 2.5 arcmin. I took a single 30-second exposure and compared it to a star chart. The nebula is visible but it is rather dim. Not too far away is a 9th magnitude star that is burnt in and bright. In my primitive mind I rationalize this by saying that if I were to add up the number of photons in the larger area of the nebula and compress it into the smaller area of the star then I might say they are equivalent magnitude.

Somewhere in my mind a formula exists that relates star magnitude to DSO magnitude given the size of the DSO. I applied what I learned from undergraduate courses in Astronomy and Physics from 40 years ago, and came up with an equation that produces unsatisfactory results.

You see, this is the question I would like answered: If a single, unstacked, 30-second image shows stars down to the 13th magnitude then what is the magnitude of the faintest DSO that I can see in that image given its size in arc minutes?

Has anyone heard of such a calculator, or is there a rule of thumb?

Thanks so much.

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