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Resolving Sirius as a stellar disk. Did I calculate this right?

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#1 Zoltan89

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Posted 23 May 2022 - 02:46 PM

I was wondering, just what size of telescope would you need to resolve Sirius as a stellar disk. Lets ignore the effects of seeing for a moment.

Give the formula ( 116/ Aperture ) to get the telescopic resolution, I created a chart with many apertures and googled the angular size of Sirius.

Given Sirius has an angular size of 0.005936″, the smallest telescope to start resolving it is "769 Inches, around 19.5 meters of aperture. And that is only begins to resolve it. This is a lot more than I thought haha.

Could someone confirm if the calculation is correct?

Thanks!


Edited by Zoltan89, 23 May 2022 - 02:49 PM.


#2 bobzeq25

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Posted 23 May 2022 - 03:19 PM

Needless to say, as a practical matter, there is no way to see any star as a disk with any telescope.



#3 haleakala

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Posted 23 May 2022 - 03:23 PM

You piqued my interest since it has been long known that this is out of the reach of modern telescopes along the lines of your calculations. However, in googling this, I realized it has been done with a separated array of large coordinated terrestrial scopes on a few red giants like Betelgeuse. Take the atmosphere out and Hubble could also get to the resolving limit of a few of these. I imagine James Webb will be even better. Still, we are talking several pixels, but we are getting there. Interesting!



#4 John Miele

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Posted 23 May 2022 - 03:28 PM

Should be easy peasy for the Keck...lol.gif

 

The Interferometer allowed the light from both Keck telescopes to be combined into an 85-metre (279 ft) baseline, near infrared, optical interferometer. This long baseline gave the interferometer an effective angular resolution of 5 milliarcseconds (mas) at 2.2 µm, and 24 mas at 10 µm.



#5 John Fitzgerald

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Posted 23 May 2022 - 03:35 PM

I could see a space telescope, constructed in space, from components manufactured on the earth, at 25 to 30 meters diameter.  It could be done with current technology,  given the enormous amount of funding it would take. Segmented mirrors, like the Webb.



#6 TOMDEY

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Posted 23 May 2022 - 04:04 PM

Betelgeuse --- on the cusp of Hubble's theoretical capability (had it been properly built).    Tom


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#7 BQ Octantis

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Posted 23 May 2022 - 04:25 PM

"Resolution" also depends on the wavelength of the camera. A mono camera will have 90% QE at 400nm, so that's probably a better number for wavelength. So to "resolve" that angular separation, I get 16.9 meters. The math looks like this:

 

Screen Shot 2022-05-23 at 4.54.55 PM.png

 

But what does that really mean…to "resolve"?

 

It means that if you observed or took a picture of two point objects of equal brightness separated by the diameter of Sirius, they would not get swallowed into a single Airy disk. Instead, they would form an oblong of two Airy disks.

 

Forming an image of a disk is a very different task than "resolving" two points. For instance, your eye pupil can "resolve" 67 arcseconds in daylight and 27 arcseconds fully dark adapted (at 533 nm). Jupiter is typically in the 40 arcsec range. But can you make out Jupiter's disk? Nope.

 

A better reference is how they got that recent picture of that black hole the size of Mercury's orbit at 27,000 light years distance. They used a resolution 6 times smaller than the target to form an image of 3 blurry blobs on a ring. And to get details on Jupiter, I use an aperture with a "resolution" 50 times smaller than Jupiter's disk.

 

So multiply your estimate by 10 to 100. You'd probably need the better part of 200 meters of aperture. And a good Strehl ratio. Somewhere on the moon.

 

BQ


Edited by BQ Octantis, 23 May 2022 - 06:28 PM.

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