Tony Flanders' Astronomy Site
Telescopic Limiting Magnitude
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I have performed some experiments to determine the faintest stars that I can see through my 70mm refractor and my 178mm Dob at various magnifications, for objects at various heights above the horizon. The table below summarizes the limiting magnitude for stars more than 45 degrees above the horizon. Note that the telescopic limiting magnitude improves very rapidly as I move from low to medium magnification, and much more slowly as I move to high magnification. The improvement above the top magnifications shown is small.

Aperture and MagUrbanSuburban
naked eye4.65.2
Ranger @15X9.610.2
Ranger @20X10.010.6
Ranger @30X10.411.0
Ranger @40X10.611.2
Ranger @60X10.811.4
Dob @30X11.211.8
Dob @40X11.612.2
Dob @60X12.012.6
Dob @80X12.212.8
Dob @120X12.413.0

The table below shows how the limiting magnitude deteriorates for objects less than 45 degrees above the horizon. Note that the deterioration is more rapid at the urban site than at the suburban site.

Limiting magnitude depends on azimuth as well as altitude; it is significantly worse towards the major light source (in this case, downtown Boston) than towards the darker parts of the sky.  At both sites, the worst skies are roughly ESE (towards Boston) and the best skies NW (towards a corridor of wealthy suburbs). These readings were done to the S, the direction that matters most for astronomy, which is neither the worst nor the best part of the sky.

AltitudeUrbanSuburban
35-45subtract 0.2subtract 0.2
30-35subtract 0.4subtract 0.2
25-30subtract 0.6subtract 0.4
20-25subtract 0.8subtract 0.6
15-20subtract 1.2subtract 0.8