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Cosmic Challenge: A Trio of Binaries

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Cosmic Challenge: A Trio of Binaries

September 2021

Phil Harrington

This month's suggested aperture range:

6- to 9.25-inch (15-24 cm) telescopes










STF 3057

Binary star

00h 04.9m

+58° 32.0'




STF 3062

Binary star

00h 06.3m

+58° 26.2'




Lambda Cas

Binary star

00h 31.8m

+54° 31.3'





How close can two stars appear and still be resolvable as two? The single most important factor that influences the result is a telescope's aperture. All other things being equal, the larger the aperture, the finer the level of detail resolved. Of the many observational experiments that have been conducted to determine the resolution limits of telescopes, the two most often cited are the Rayleigh Criterion and the Dawes Limit.  



Above: Late evening star map showing the location of this month's Cosmic Challenge.


Credit: Map adapted from Star Watch by Phil Harrington


Above: Finder chart for this month's Cosmic Challenge.


Credit: Chart adapted from Cosmic Challenge by Phil Harrington
Click on the chart to open a printable PDF version in a new window




The Rayleigh Criterion, devised by John William Strutt, the third Baron Rayleigh, in 1878, predicts how close two stars can be to each other and still be distinguishable as two separate points. Based on empirical data, the Rayleigh Criterion for any telescope can be calculated using the formula: Rayleigh Criterion = 138 ÷ D, where D = aperture in millimeters, and the result is expressed in arc-seconds.


The 19th-century English astronomer William Dawes derived a formula for calculating just how close a pair of 6th-magnitude yellow stars can be to each other, and appear elongated, but not separately resolved (see diagram below). His formula, known as Dawes Limit, is: Dawes Limit = 114 ÷ D.  Again, D = aperture in millimeters and the result is in arc-seconds.


Above: Dawes Limit.  The resolving power of an 8-inch telescope. (a) Not resolved, (b) Barely resolved, or the Dawes Limit for the aperture, © Fully resolved.

Credit: Diagram adapted from Cosmic Challenge by Phil Harrington


Based on these formulas, a 6-inch (15-cm) aperture should be able to discern the duality of a binary star with components separated by 0.91" (Rayleigh) and 0.76" (Dawes).  At the other end of this challenge's aperture range, a 9.25-inch (24-cm) instrument should be able to resolve, at least partially, a pair of stars separated by 0.59" and 0.49", respectively.  These are ideal numbers based a pair of 6th-magnitude yellow stars.  In the case of Dawes Limit, these values predict how close those stars can be to each other, and appear elongated, but not necessarily resolved separately.


Can your telescope meet the Rayleigh and Dawes challenge? Here are three pairs of stars that will prove worthy adversaries for 6- to 9.25-inch telescopes. All lie in fairly close proximity to each other and offer a broad range of separation distances. Let's see how well you do.


First up are Struve 3057 (often abbreviated as Σ 3057 or STF 3057) and Struve 3062 (STF 3062), both discovered by Friedrich Georg Wilhelm von Struve.  Von Struve was the first astronomer to search for and study binary stars.  He compiled those studies into a catalog published in 1827 entitled Catalogus Novus Stellarum Duplicium, or simply the Dorpat Catalogue, for the Tartu Observatory at the Imperial University of Dorpat in Estonia where the discoveries were made.   Both lie 50' southwest of Caph [Beta (β) Cassiopeiae], the westernmost star in the constellation's familiar 5-star W pattern.  Together, Caph and the two doubles form a prominent isosceles triangle that's easy to find through finderscopes.


STF 3057, at the triangle's northwestern corner, presents a challenge not because of its close-set stars -- they are separated by nearly 4 arc-seconds -- but rather by the disparity in their magnitudes.  The primary sun shines at magnitude 6.7, but its companion shines at only magnitude 9.3.


Marking the triangle's southern corner, STF 3062 presents a different sort of test, one more in line with Dawes' original concept.  Here, we find two stars shining at magnitudes 6.4 and 7.3, and separated by 1.3".  Given reasonably good seeing conditions and optical quality, a 6-inch should be able to resolve STF 3062 fairly handily; indeed, STF 3057 might prove more difficult.


Above: Sketch of STF 3062 as seen through the author's 8-inch (20-cm) Newtonian reflector.


Looking for tougher game?  Take aim at Lambda (λ) Cassiopeiae (STT 12, for its listing in Otto Wilhelm von Struve's catalog).  Otto Struve was the son of Friedrich Georg Wilhelm von Struve, and created the Pulkowo Catalog of binary stars as an expansion of Friedrich's earlier work.


Lambda's components shine at magnitudes 5.3 and 5.8, a little brighter than Dawes' ideal test star.  The resulting glare makes this test all the harder.  These two blue-white main sequence stars orbit a common center of mass once every 640 years and are currently separated by only 0.5 arc-seconds.  If you own an 8-inch or larger scope, Lambda Cas is a formidable opponent indeed.


Have a favorite challenge object of your own?  I'd love to hear about it, as well as how you did with this month's test.  Contact me through my website or post to this month's discussion forum.


Until next month, remember that half of the fun is the thrill of the chase.  Game on!

About the Author:

Phil Harrington writes the monthly Binocular Universe column in Astronomy magazine and is the author of 9 books on astronomy.  Visit his web site at www.philharrington.net to learn more.

Phil Harrington's Cosmic Challenge is copyright 2021 by Philip S. Harrington.  All rights reserved.  No reproduction, in whole or in part, beyond single copies for use by an individual, is permitted without written permission of the copyright holder.


  • random, okiestarman56, Sasa and 2 others like this


This is really interesting though I doubt I can tackle any one of these with a 4” frac but, you can bet I’ll try.

    • PhilH likes this

This is really interesting though I doubt I can tackle any one of these with a 4” frac but, you can bet I’ll try.

Sure you have quite a chance.


I was able to split STF3057 back in 2012 in 80mm refractor (AS80/1200). STF3062 was only elongated star in the same telescope.


Over time I tried many pairs. Out of recent ones, 16 Vul (0.8", 5.8+6.2) comes to my mind. Here I was able to see the elongation already in 82mm refractor, it was still only elongated star in 142mm Newton, while 200mm Newton showed a hint of darker separation between the two components.


And for unequal pair, I remember zeta Her (nowadays around 1.4", 3.0+5.4). I was observing it with my friend. While there was no trace of the secondary in my friends Newton 200/1200mm, both of us could see the component in my 82/1670mm refractor. Later my friend told me that he was able to see the component in 200mm Newton as well during another night.


A little bit more easier is nearby 52 Her (2.1", 4.8+8.5). Here I have positive observations in 82mm refractor, 142mm Newton and my friends 200mm Newton.

    • ArizonaScott and Stellar1 like this
Sep 02 2021 01:01 PM

Hi Phil


Where do you have the data on STT 12 (Lambda Cas) from? According to Stelledoppie, the current separation is just 0.1"...!  



Clear skies!

Thomas, Denmark

    • Jon Isaacs and Migwan like this

I checked STF3057 and STF3062 tonight with my 82mm refractor. Transparency was not the best, the air was very humid and the telescope was covered by the thick layer of condensed water. This was probably the reason why I failed to see the second component of STF3057 (I had few short hints of secondary at PA~290deg but too short to be sure that I saw it). I had more luck with STF3062, here I could see at 278x nice clear tail attached to the Airy disc of main component at PA~0deg. Sometimes it looked like a separated star, may be because of slight color contrast. The main component looked slightly yellowish while the tail was slightly bluer. For fun, I checked lambda Cas as well. Not surprisingly, I could not see even the elongation, however the star looked definitely strange at 330x, I had a feeling that the image of the star could not be focused properly.


I had to use hair dryer at this point to get rid of the dew on the lens and after short peek at Saturn I made this sketch of Jupiter



    • Astrojensen and Voyager 3 like this

Hi Phil


Where do you have the data on STT 12 (Lambda Cas) from? According to Stelledoppie, the current separation is just 0.1"...!  



Clear skies!

Thomas, Denmark

The 0.3" separation appears to come from Phil's 2011 book.  As you mentioned, Stelledoppie shows the 2021 separation at 0.10", which makes it quite a challenge!

    • Astrojensen, Migwan and Csbwsb like this

Hello Phil. I'll give this a go with my 82mm Questar and see what happens.

Hi Phil
Where do you have the data on STT 12 (Lambda Cas) from? According to Stelledoppie, the current separation is just 0.1"...!  
Clear skies!
Thomas, Denmark

I just want to thank you for this info. I'm feeling better already. I've made it down to .46" with my C11 and tried for this bugger twice now. Probably invested 1.5 hours it. I do love a challenge, but...
    • Astrojensen and Csbwsb like this

I've heard from a few people about the separation of Lambda Cas.  I pulled it from my book from 11 years ago.  Still looking for my notes, so once I run it down, I'll post an update here.

You can see the separations over a 30 year period and the apparent orbital plot of Lambda Cas on Stelledoppie.


The pair has been slowly decreasing for quite awhile and we're currently pretty close to the minimum separation (under 0.09"), which will be in a couple of years.


I remember being very excited to resolve it back in 1980 using a C-8.  At the time I believe the separation was about 0.5" and it appeared as two tangent airy discs using 444x.

    • Astrojensen likes this

I tried the challenge tonight using a C8 which I just cleaned inside and out and collimated.  The seeing was not good--I gauged it at 4/10 Pickering but the transparency was excellent.  I had more luck with STF 3057 than with STF 3062.  I could see the secondary starting at 167x and  even better at 200 and 250x.  It was very small and dim compared to the primary and appeared to be at ~PA 300 degrees.


I stepped up from 167x all the way to 299x trying to split STF 3062 but only got a hint of elongation.  I think the seeing was the limiting factor.


Since I couldn't get anywhere with 3062 I didn't even try lambda Cas.

    • Sasa likes this

I checked STF3057 tonight with my 82mm refractor under much more favorable conditions - no dew, good transparency and good seeing. As expect, I had no problem to see the companion in 8mm eyepiece (power 210x). It was very faint star visible with strong concentration for most of the time at PA~320 deg. Mu rough estimate of its distance from the main component was about 1.8 times the radius of the first Airy ring, which should be around 4'' (if I did the math correctly).


BTW, Jupiter was also excellent in these conditions



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