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How much more light does a 102/640 Dob gather when compared to a 76/300?

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#1 Jethro777

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Posted 09 May 2021 - 05:58 PM

I struggle with maths - if someone could show me how to compare the two, that would be amazing.



#2 AstroBrett

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Posted 09 May 2021 - 06:26 PM

The area of a circle is given by the formula pi times the radius squared; which is just pi time radius time radius.  Since the radius is one half of the diameter of the scope, in your two cases the radii would be 51 mm and 38 mm. Thus the two areas would be:

 

     3.1415 x 51 mm x 51 mm = 8,171 square mm

 

     3.1415 x 38 mm x 38 mm = 4,536 square mm  

 

The larger aperture would then collect 8,171 / 4536 = 1.80 times as much light.

 

You should note this is just ratio of the total flux of the light down the tube, and doesn't take into account the different f/ratios of the two optical combinations and the resulting amount of light per unit area of the focal plane. In that case, the 102 mm scope has an f/ratio of 6.27 and the 76 mm scope has an f/ratio of 3.95, so the smaller aperture scope would be faster in the sense of how quickly an image could be gathered, although that would be achieved at the expense of a much smaller plate scale. 

 

I hope that helps.

 

Brett


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#3 Star Geezer

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Posted 09 May 2021 - 06:32 PM

The 102/640 Dob will have better definition (102mm objective) at higher power with better focus (640mm focal length) than a Celestron Firstscope.


Edited by Star Geezer, 09 May 2021 - 08:43 PM.


#4 sevenofnine

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Posted 09 May 2021 - 06:55 PM

By definition: Comparisons of different sized apertures for their light gathering power are calculated by the ratio of their diameters squared. So...

 

([102x102] / [76x76]=1.8)

 

The 102mm scope gathers 1.8 times the amount of light compared to the 76mm. This formula is easier to understand than AstroBrett's but they both arrive at the same answer. scratchhead2.gif



#5 eyeoftexas

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Posted 09 May 2021 - 07:24 PM

This formula is easier to understand than AstroBrett's but they both arrive at the same answer. scratchhead2.gif

Your formula is simply AstroBrett's with the value of pi deleted.  By taking the ratio of the areas, the pi's cancel.  


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#6 Nuages

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Posted 09 May 2021 - 07:26 PM

How big are the secondaries?



#7 TOMDEY

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Posted 09 May 2021 - 11:02 PM

For a single target that fits within the Field of View... the ~amount of light~ is proportional to aperture area.

 

But the generalized answer gets a bit more involved >>>

 

For a statistically-isotropic target region that exceeds the field of view, the ~amount of light~ is proportional to the étendue of the system, which is the product of both the aperture area and the object-space solid angular field of view supported by the system; neither stands alone. So you can increase the effective performance by either increasing aperture, or field, or especially both. Under the extended object-space isotropic assumption, this is consequent of Emmy Noether's Theorem --- no free lunch.

 

This explains why we hoggish amateurs drool over big telescopes with huge fields.   Tom

 

[I worked Patent Examination for Solar Energy Concentrators back in the 1970's and 80's --- which intimately immerses in that kinda stuff. Many many patents violated Emmy's Theorem, so should have been disallowed as surely as Perpetual Motion machines. But many slipped right past most federal examiners... because both the inventors and examiners were pretty ignorant on the nuances of that emerging arena. Frankly --- that is still the case.]


Edited by TOMDEY, 09 May 2021 - 11:04 PM.

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#8 SeattleScott

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Posted 10 May 2021 - 11:45 AM

So yeah 80% brighter views.

But if going from 3” to 4” gives you 80% brighter views, imagine going from 3” to 5”. The 5” tabletop Dobs are around $200 and still very portable. I would say this is the logical upgrade. Unless a 4” came available on Craigslist for cheap.

Scott
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#9 vtornado

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Posted 10 May 2021 - 07:27 PM

Usually the secondary of smaller scope is a larger ratio than a larger one.

This leads to more % light loss in the smaller scope and less contrast.

This puts the 76mm at a larger disadvantage than even the area problems suggest.

 

Any scope under 80mm I would consider a refractor.

No collimation, 97% light transmission vs. 75% for a reflector.

an 80mm refractor delivers about the same light to the eyepiece as a 100mm reflector.

An 80mm f/11 is not to hard to mount and has low enough chromatic abberation for a beginner.


Edited by vtornado, 10 May 2021 - 07:31 PM.


#10 EricSi

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Posted 11 May 2021 - 06:09 AM

As noted above, the light gathering power of a scope increases as the square of the diameter of the primary lens or mirror.

 

It should also be noted that the human eye perceives things on a log scale, so that (unfortunately) the subjective perception of seeing a "better image" increases more slowly than linearly as scope size increases. Many times I've observed the same objects on the same night through my 10" scope and my friend's 24" scope, and the difference is less than you might think.....




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