UPDATE 2014-10-14 (Description only): On Saturday, October 11, 2014, I gave a presentation on this subject to my astronomy club. I convereted my PowerPoint presentation to .jpgs and posted them as a public album on Facebook. You can access this album with or without having a Facebook account at: https://www.facebook.com/media/set/?set=a.10205329095573313.1073741856.1425866703&type=1&l=9730d636f9 . There is also a video version (no sound) of the presentation at: https://www.facebook.com/video.php?v=10205336473997769&set=vb.1425866703&type=3&theater .
UPDATE 2014-10-07: I have added a couple features to this worksheet and restructured the data to make it and the plots more useful.
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"What is the faintest object I can see in my telescope?" is a common question asked by amateur astronomers. The answer depends on many variables. For instance, is the object a star (point source) or a nebula or galaxy (non-point source)? How experienced is the observer and how good are his/her eyes? What are the seeing conditions? Does the telescope have a clear aperture (e.g. refractor) or does it have a central obstruction (e.g. Newtonian, Schmidt-Cassegrain, etc.)? Regardless, with all other things being equal, the visual limiting magnitude of a telescope is most directly related to the size (area) of the objective lens or mirror. Over the years, various professional and amateur astronomers have published simple empirical equations to estimate the visual limiting magnitude for point sources.
The purpose of this worksheet is to compare five of these equations. For the record, the best I have done with my Celestron CPC-800 SCT (8" diameter, f/10, Schmidt-Cassegrain telescope) is detecting magnitude 15.4 stars during three successive nights observing the dwarf planet Pluto (then M13.9) as it slowly traversed a star field in western Sagittarius in 2009. I accomplished this feat under pristine and steady skies at Courtright Reservoir (elevation 8200 feet) in the Sierra Nevada east of Fresno, California. This site is technically Bortle Class 2, but mountain weather sometimes makes it worse.
NOTE: The attached .zip file contains a Mathcad Prime 3.0 worksheet (.mcdx) and—for those of you who are still using earlier verisions of Mathcad—an Adobe Acrobat printout (.pdf) of the worksheet so can see how it is put together.
