How to Figure Required Telescope Diameter?

[willgtl]

A awhile ago I wrote a program to calculate various things like maximum resolving power of a given telescope's primary mirror, angular diameter of an object of a given size from a given distance and mirror diameter required to see an object of a given angular diameter.

However, I seem to have completely failed on the last part. I just now looked back at that program and got results of tens of kilometers when I know my result should've been mere dozens of meters. Looking at the code, I appear to have involved the Nyquist-Shannon sampling theorem and photon wavelength, with no recollection as to why.

I have a feeling I'm completely off-base. Could someone enlighten me on how to essentially reverse the Dawes' limit formula, and find the mirror size required for a given angular diameter? Thanks!

 

[Andy Resnick]

From wiki:

"A calculation using Airy discs as point spread function shows that at Dawes' limit there is a 5% dip between the two maxima, whereas at Rayleigh's criterion there is a 26.3% dip."

Does this help? No sampling required, but it is based on diffraction.