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I was taking an astronomy test, the following question came up:

The most important function of the astronomical telescope is:

  1. Resolving power
  2. Light gathering power
  3. magnifying power
  4. focal length

The focal length obviously means nothing here, as well as the magnification (that can always be done later). As far as resolving power and light gathering power go though, they both seem to be "equally" important, in that without the first, there is no detail, and without the second, there is no image.

It does seem that exposure time can compensate for a lack of light gathering power (what matters is the product between the two), but nothing can compensate for resolving power.

My professor seems to think the answer is resolving power. Why is this? Is this some well known idea in astronomy?

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I think resolving power is important, as it's the derivative of the others. You won't see any dimmer objects with huge magnification and too little light. You'll get many blurred dots if you gather lots of light but don't make it useful. Only combining the two you achieve a good resolving power - a decent image of distant objects. –  SF. Nov 6 '13 at 15:48
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The most important feature of a telescope is the astronomer using it. –  Keith Thompson Nov 10 '13 at 23:34
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up vote 4 down vote accepted

Well the angular resolution of a telescope depends on two things: 1) The wavelength of light you're looking in, and 2) the diameter of the primary lens/mirror.

$$ \theta = 1.22 \frac{\lambda}{D}$$

where $\lambda$ is the wavelength of light and $D$ is the diameter of the lens.

Light collecting power is simply how many photons you can collect in a particular wavelength in a given amount of time. Essentially, the bigger the bucket (or lens/mirror), the more rain you can catch. You can sort of get around light collecting power by increasing your exposure time. But, if the size of the object you're trying to observe is smaller than your telescope's resolving power, I don't believe there is really much you can do about it. Being limited by the resolution of your telescope is called being diffraction limited, but most telescopes on Earth are usually seeing limited due to the atmosphere's smearing effects.

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Ah, so you are saying its just the more common limiting factor? –  soandos Nov 6 '13 at 4:17
    
Basically - though if you're trying to observe (not take an image of) an object which is really dim, magnifying it will not make it any better. When it comes to observing dim objects there is no substitute for light collecting power. When it comes to the angular size of the object you have to worry about angular resolution. Make sense? –  astromax Nov 6 '13 at 12:59
    
You could also argue that location of the telescope is also one of the most important things about it. If it's above the atmosphere you no longer have to worry about absorption of regions of wavelength due to the atmosphere and also other atmospheric effects. –  astromax Nov 6 '13 at 13:01
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