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# Arc Seconds (Resolving Power)

13 replies to this topic

### #1 School Me

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Posted 27 October 2020 - 07:55 PM

Hello CN,

This is my first post as I have been reading up on the pinned items.

If I understand arc seconds properly, it is the ability to split stars and see objects.

How does this relate to to other attributes of the telescope or type of telescope.  Is there a formula that relates this number to aperture or something else? And does the number change based on reflectors, refractors, or other style scopes?

What is a reasonable number to shoot for in a telescope?  I am interested in all space objects.  I do not own a telescope yet, but I hope to purchase one soon once I understand all the aspects of the scope.

Thank you,

SM

### #2 ShaulaB

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Posted 27 October 2020 - 07:59 PM

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### #3 lee14

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Posted 27 October 2020 - 08:04 PM

There is a simple formula known as Dawes' Limit; R (in arc seconds) = 4.56/D (diameter in inches). The larger the aperture, the greater the resolving power, but in practice seeing (atmospheric steadiness) can often be the more significant variable.

Lee

### #4 Jon Isaacs

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Posted 27 October 2020 - 08:05 PM

Hello CN,

This is my first post as I have been reading up on the pinned items.

If I understand arc seconds properly, it is the ability to split stars and see objects.

How does this relate to to other attributes of the telescope or type of telescope.  Is there a formula that relates this number to aperture or something else? And does the number change based on reflectors, refractors, or other style scopes?

What is a reasonable number to shoot for in a telescope?  I am interested in all space objects.  I do not own a telescope yet, but I hope to purchase one soon once I understand all the aspects of the scope.

Thank you,

SM

The resolving power is directly related to aperture. Most if not all simple use what's know as the Dawes limit:

R= (4.56 inch / D ) x arc-seconds.

A 4.56 inch scope will, under ideal conditions, barely split a 1.0 arc-second double.

Jon

### #5 John Fitzgerald

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Posted 27 October 2020 - 08:20 PM

Arc seconds are units of measurement on the sky.  Example: From the horizon to Zenith (straight up), the distance is 90 degrees of arc.  Each degree is divided into 60 minutes of arc.  Each minute of arc is divided into 60 seconds of arc.  A second of arc (arc second) is a very small measurement.  The moon as seen from the earth measures about 1/2 degree, or 30 minutes of arc across.  That's 1,800 seconds of arc across.

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### #6 JamesMStephens

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Posted 27 October 2020 - 08:47 PM

Resolving power is the ability to split stars, or the smallest (angular) size that can be resolved.  For objects in the sky we use seconds of arc, with an arc second being 1/3600-th of a degree (so it's analogous to a temporal second being 1/3600-th of an hour.)

There are several crireria.  One is the Rayleigh criterion, resolving power (in radians) = 1.22(wavelength)/(Diameter of objective lens/mirror).  Wavelength is commonly taken as about 550 nanometer (peak sensitivity of the eye).  (Make sure wavelength and diameter are in the same units!)

The Dawes limit, resolving power (in arc seconds) = 4.56/(Diameter of objective lens/mirror in inches)

You may find another one or two.

Jim

Edited by JamesMStephens, 27 October 2020 - 08:49 PM.

### #7 barbarosa

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Posted 27 October 2020 - 08:47 PM

Some companies, Celestron is one, sometimes give you the resolution specs.

Here it is for the 9.25" Edge HD

Resolution (Rayleigh) 0.68 arc seconds
Resolution (Dawes) 0.57 arc seconds

For my RASA 8 the numbers are,

Resolution (Rayleigh) 0.68 arc seconds
Resolution (Dawes) 0.57 arc seconds

Here is is for my Esprit 120?

Dawes Limit 0.97
Rayleigh Limit 1.16

Other companies, including Televue and Stellarvue do do not give these numbers,  I suspect that these numbers are among the least important to most buyers. In any case while they tell you how well the scope might resolve in perfect conditions they  are calculated values. They do not tell you if one scope is otherwise better than another.

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### #8 litesong

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Posted 27 October 2020 - 09:11 PM

Ahhh, its so fine to know that a cheap mis-produced 100mm single lens is as good as an apo-chromatic Takehashi. You make my heart sing that us poor people can get Hubble quality views for \$9.98.

Edited by litesong, 27 October 2020 - 09:12 PM.

### #9 Migwan

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Posted 27 October 2020 - 09:46 PM

Here's some links I ran into recently that you might be interested in.

http://fisherka.csol...albinaries.html

http://www.jdso.org/...Napier_Munn.pdf

jd

### #10 bobzeq25

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Posted 27 October 2020 - 10:12 PM

Note that, in practice your resolution will often be limited by your "seeing" (atmospheric stability) rather than the Dawes limit, which is a theoretical "best" number applicable to theoretical perfect seeing.

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### #11 starbug

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Posted 28 October 2020 - 02:08 AM

Ahhh, its so fine to know that a cheap mis-produced 100mm single lens is as good as an apo-chromatic Takehashi. You make my heart sing that us poor people can get Hubble quality views for \$9.98.

Sure it is und er certain circumstances. Both Dawes and Rayleigh limits are pure theoretical for an ideal lens under ideal seeig conditions. Also not surewhyyou're using Hubbleas Reference - Hubble has poor basic optics corrected wit a lot of additional elements to get it usable. So all your examles are optics in a different measure far from ideal, and none of them will reacs the theoretical limit, just get more ore lessclose to it.

and yes, in a narrow band, whrethe aberrations are as good as not present,a simple lens will get very close to your Takahashi whatever scope.

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### #12 sg6

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Posted 28 October 2020 - 03:06 AM

Ahhh, its so fine to know that a cheap mis-produced 100mm single lens is as good as an apo-chromatic Takehashi. You make my heart sing that us poor people can get Hubble quality views for \$9.98.

What Litesong says is correct. All you read are the theoretical limits if the item were perfect, unfortunately they are all imperfect to some degree.

I have a nice little 80mm apo triplet with FPL-53 glass, presently over \$1300, according to the theory - the ones you no doubt have been sat up all night getting acquainted with - say that a \$200 80mm achro will perform exactly the same.

How much do you want to bet?

Seems everyone has told you the theory, and apparently all equal sized scopes are all the same. One slight problem is that really you know differently, actually so do the people telling you.

You need to take into account more then just a few numbers, especially when it comes to aperture. Some people will get a scope for double stars and find an aperture mask helps them split stars - they are reducing the aperture to get a better result which is directly opposed to the theories.

One establishment I know uses their 8" refractor for double stars measurements, what they do not use is their 12" refractor. Reason is simple - the 8" is better.

### #13 Jon Isaacs

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Posted 28 October 2020 - 06:39 AM

What Litesong says is correct. All you read are the theoretical limits if the item were perfect, unfortunately they are all imperfect to some degree.

I have a nice little 80mm apo triplet with FPL-53 glass, presently over \$1300, according to the theory - the ones you no doubt have been sat up all night getting acquainted with - say that a \$200 80mm achro will perform exactly the same.

How much do you want to bet?

Seems everyone has told you the theory, and apparently all equal sized scopes are all the same. One slight problem is that really you know differently, actually so do the people telling you.

You need to take into account more then just a few numbers, especially when it comes to aperture. Some people will get a scope for double stars and find an aperture mask helps them split stars - they are reducing the aperture to get a better result which is directly opposed to the theories.

One establishment I know uses their 8" refractor for double stars measurements, what they do not use is their 12" refractor. Reason is simple - the 8" is better.

The Dawes limit is not a theoretical number, it's an experimental number based on observations by William Dawes more than a 150 years ago.  It applies to two magnitude 5 stars.

Seeing is probably the biggest factor in resolving close doubles.  In northern latitudes, it's probably unlikely that a 12 inch will outperform an 8 inch on all but the most stable nights.  Around here, the seeing is often stable enough that a 12 inch will do better than an 8 inch.

Dawes limit doubles are possible and with smaller scopes not hampered by seeing, definitely doable, even with a "\$200" achromat.

In 2010, the short period binary Porrima widened from 1.42 arc-seconds March 1 to about 1.52 arc-seconds at the end of August.

What was remarkable about this is that the Dawes limit for an 80mm is 1.45 arc-seconds so over the summer, this fine double spanned the Dawes limit for an 80mm.  I spent a lot of hours that summer observing Porrima with two different 80mm refractors.  The first was an 80mm F/7 FPL-53 doublet with excellent optics, the second was a Meade 80mm F/11.3 achromat from sometime in the 1980s. I bought it used for about \$100.

I was able to split Porrima in both scopes very near the Dawes limit though the ED doublet was slightly cleaner, made the split first using it.

I have split Dawes limit doubles in my 10 inch Dob. Optical quality is important in splitting very close doubles but a 1.0 double that's essentially the Dawes limit in a 120mm refractor will be very difficult whereas in the 10 inch Dob, it will be split wide and clean.

Jon

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### #14 Eddgie

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Posted 28 October 2020 - 07:01 AM

First, there  are two kinds of resolving power, angular, and linear.

Angular resolving power is primarily a function of aperture and is relatively unaffected by optical power or things like a secondary obstruction.  In other words, the larger the aperture, for given wavelengths of light, the smaller the Airy Disk of a star will be, and this is what the formulas you have been given will show you.  Again, this figure is for angular resolution and is typically based on the telescopes ability to separate double stars. Because the Airy Disk of the double star grows smaller with aperture, the larger the aperture, the more space there will be between the stars.

For extended subjects like planets, and the low contrast detail on their surface, linear resolving power and more importantly, contrast transfer function, describe how "Sharp" the view in a given telescope will appear.  Optical engineers use linear resolution or encircled energy to describe how much contrast the telescope will loose due to the aperture, the presence of a secondary obstruction, chromatism (color error), and optical quality.  This means you can have a smaller telescope with more perfect optics, smaller (or no) obstruction, no chromatism (rare) and perfect optics, and it could make very low contrast detail like faint festoons on Jupiter's surface easier to see in a smaller telescope than in a larger telescopes.  This is not always true and generally the larger telescope starts with better contrast transfer, but better contrast transfer is what allow you your eye to resolve low contrast detail on extended targets

So, even poor telescopes can resolve equal brightness double stars as well as the formula predicts (better sometimes in fact because some errors make the Airy disk appear smaller) but for planets, the best telescope to resolve low contrast detail will be the one with the best contrast transfer and that is not always going to be the larger telescope.

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