Resolving bodies at large distances

[mjda]

Homework Statement

If a 6.5m diameter telescope operates at wavelengths between 600nm to 2800nm, and for stellar densities similar to the Solar neighbourhood, what is the range of distances this telescope can resolve individual stars?

Homework Equations

The Attempt at a Solution

My attempts so far have led to calculating the angular resolutions of the telescope at 600nm and 2800nm:

1.12*10^-7 rads && 5.25*10^-7 rads, respectively.

How do I go forward from here? I don't understand how to incorporate the local Solar density into this problem?

 

[phyzguy]

The problem isn't clear to me either. You should ask for clarification. What does it mean to "resolve individual stars"? Individual stars are points of light and not resolved into disks in even the largest telescopes. Are you supposed to calculate an average separation of stars in the solar neighborhood and see how far away you can resolve that separation? It is a very poorly worded question, in my opinion.

 

[mjda]

The problem isn't clear to me either. You should ask for clarification. What does it mean to "resolve individual stars"? Individual stars are points of light and not resolved into disks in even the largest telescopes. Are you supposed to calculate an average separation of stars in the solar neighborhood and see how far away you can resolve that separation? It is a very poorly worded question, in my opinion.

Right?!

I had it in my head that what if it actually means, how far can a body of similar size to the Sun be resolved at these wavelengths by the 6.5m telescope.

My problem is "the stellar densities", and Solar neighbour hood, wording.

If I have the angular resolutions at the respective wavelengths, surely all I need is the size of the body I'm trying to resolve and then I can work out the maximum distance it can be to be resolved?

 

[phyzguy]

If I have the angular resolutions at the respective wavelengths, surely all I need is the size of the body I'm trying to resolve and then I can work out the maximum distance it can be to be resolved?

Yes. But what is the problem asking? Is it asking you to resolve individual stars into disks? In this case the relevant size is the diameter of the star. Or is it asking you to separate nearby stars? In this case the average distance between stars is the relevant size. These are very different length scales. There is no way to know what is being asked without asking for clarification.

 

[vela]

I read the question to refer to the telescope's ability to resolve two stars distinctly. Given some average separation between stars, at some distance, their angular separation will be too small for the telescope to resolve as separate stars because of the diffraction limit.