You are designing a telescope to map far away stars. Given that our galaxy is 10^5 light years across and most stars are ~10 light years apart,
A) What diameter aperture do you need for mapping these stars? (Using visible light)
B) How large would the aperture have to be to distinguish binary stars? (Only 10^-7 ly apart)
Ideas anyone?

Question

You are designing a telescope to map far away stars. Given that our galaxy is 10^5 light years across and most stars are ~10 light years apart,
A) What diameter aperture do you need for mapping these stars? (Using visible light)
B) How large would the aperture have to be to distinguish binary stars? (Only 10^-7 ly apart)
Ideas anyone?

anonymous · Answer

Might be of use: http://openstudy.com/study#/updates/5486455fe4b0c0f1a151b6ca

anonymous · Answer

Thanks, but how do I use the small angle approximation to help find the answer?

anonymous · Answer

The size of the galaxy is giving you a distance. The separation between two stars is giving you a linear size at said distance.

You can use the small-angle approximation to find the angular size of that linear size at the given distance.

Then you can use the airy disk equation. You have the angular size you need to resolve and the wavelength you want to observe it at. That leaves the diameter left to be found.

anonymous · Answer

So it would be that theta= ~10/10^5?

anonymous · Answer

Yes. That gives you angular size in radians.

anonymous · Answer

Okay thanks.  I actually understand it now! : )