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# Relationship LP and Telescope magnitude limit

There are established algorithms for calculating the theoretical magnitude limit of a telescope depending on aperture. Do you know of a similar proven formula for light polluted skies based not only on aperture but also on the naked eye magnitude limit?
Wilfried

Used acronyms: NEML=Naked Eye Magnitude Limit, SQM=Sky Quality Meter, TML=Telescope Magnitude Limit, CO=Central Obstruction, delta_m=difference in magnitudes between double star components, RoT=Rule of Thumb, pD_mm=proposed D_mm for resolving a binary (ident with earlier used pA=proposed Aperture), D_mm=Diameter (of scope) in mm, UCAC4=USNO CCD Astrograph Catalog 4th edition

Here's one that might be of interest:

Naked eye limiting magnitude

DreamCatcher Dobservatory/AstroTech 16" dob.

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Thanks, certainly of interest - but what I am looking for exactly would be an extension to the formula for calculating the Telescope Limiting Magnitude like for example "TLM=2,7+5*LOG10(D_mm)-f(NELM)".
Wilfried

Used acronyms: NEML=Naked Eye Magnitude Limit, SQM=Sky Quality Meter, TML=Telescope Magnitude Limit, CO=Central Obstruction, delta_m=difference in magnitudes between double star components, RoT=Rule of Thumb, pD_mm=proposed D_mm for resolving a binary (ident with earlier used pA=proposed Aperture), D_mm=Diameter (of scope) in mm, UCAC4=USNO CCD Astrograph Catalog 4th edition

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NELM is not a useful measurement of light pollution for use in such a formula. It is too dependent on the observer.

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Quote:

Thanks, certainly of interest - but what I am looking for exactly would be an extension to the formula for calculating the Telescope Limiting Magnitude like for example "TLM=2,7+5*LOG10(D_mm)-f(NELM)".
Wilfried

I'd say that a fair approximation for binoculars is:

BLM = NELM + 2.5*LOG10(mm/7 * mag)

However, this isn't really linear with magnification; it's faster than linear for low magnifications, and magnification becomes almost irrelevant at exit pupils smaller than 1 mm.

Binocular vision is worth about 1/4 magnitude. So subtract 1/4 mag for monocular telescopes.

Tony Flanders

First and foremost observing love: naked eye.

Second, binoculars.

Last but not least, telescopes.

And I sometimes dabble with cameras.

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Tony, thanks - I have checked this and found good values with strong light pollution with NELM around 3 but not these good with less light pollution giving values above the standard TLM formula. But this should be resolvable with some adaptions.
Wilfried

Used acronyms: NEML=Naked Eye Magnitude Limit, SQM=Sky Quality Meter, TML=Telescope Magnitude Limit, CO=Central Obstruction, delta_m=difference in magnitudes between double star components, RoT=Rule of Thumb, pD_mm=proposed D_mm for resolving a binary (ident with earlier used pA=proposed Aperture), D_mm=Diameter (of scope) in mm, UCAC4=USNO CCD Astrograph Catalog 4th edition

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Quote:

Here's one that might be of interest:

Naked eye limiting magnitude

Nice chart!

Happy owner of--
A Mag 1, 12.5 inch Porta Ball
A Dual Axis Equatorial Platform
A PST Double Stack

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