Aperture vs. Limiting magnitude

I currently have a 10" dob and observe from a location with 4.5 magnitude skies. If I took it to a dark sky site with 6.5 mag views would it be similar to looking through a 25" scope back home in 4.5 mag skies? Thanks for your imput.

Regards,

Mark

Great question and the answer is yes. Here is the math.

The 10" dob has a magnitude gain of 7.8 mags above the dark adapted human eye (e.g.7mm).

The equation is 5*Log10 (D1/D0) where D1 is the aperture of the scope and D0 in the entrance pupil of the eye.

For a 10" scope you would have
5*Log 10 (250mm/7mm)=7.8 mags

For a 25" scope you would have
5*Log 10 (635mm/7mm)=9.8 mags

With Mag 4.5 skies, the 10" would let you see stars about at about mag 12.3 and the 25" would allow you to see stars at about mag 14.3

With Mag 6.5 skies the 10" would let you see stars about mag 14.3 and for the 25" about 16.3.

A short cut would be to determine the mag difference in the 25" and 10" apertures for all visual limiting magnitudes:

5*Log10 (25"/10")=1.99

This means the 25" will let you see about 1.99 mags deeper than the 10" for all visual limiting magnitudes.

sorry Mark... i can confirm what the others here have said... i currently have a 10" and observe with it from my 4.5mag backyard... my old 4.5" scope from the dark skies countryside have far better views, especially with galaxies. Light pollution simply wash out objects and theres nothing u can do. But good news... a 10" is still a manageable scope for travelling with it to dark skies.