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Lightgathering abilities? 
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#1
Oct2007, 03:56 PM

P: 231

If a star is twice as far away, is it true that it will appear to us 4 times dimmer?
If this is true, can we assume that if we wish to view an object twice as far away while maintaining the same clarity, then the primary mirror of a telescope would have to be 4 times larger in diameter? 


#2
Oct2007, 04:15 PM

PF Gold
P: 7,363

With the telescope question, you are missing a couple of things here. One is that lightgathering ability (assuming unobscured, unattenuated light paths) increases as a function of the square of the diameter of the primary. Ignore pi (essential for computing area) for now, and ignore central obstruction etc and look at the relation of a 10" mirror (10x10=100) and a 12" mirror (12x12=144). You're getting a pretty substantial increase in lightgathering ability for a modest increase in diameter. You're also gaining resolving power with that increase, though that does not follow the "squares law". 


#3
Oct2207, 11:27 PM

Sci Advisor
HW Helper
P: 8,953

Just to clarify, you need a telescope twice the diameter.
Twice as far away is 1/4 thr brightness so you need 4x the area, but this is only twice the diameter. 


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