Okay, I'm thinking about parabolic antennas right now.  I created a spreadsheet that would take care of all the formulas some years back but I can't seem to find it now.  I'm trying to find all the formulas that I need to get the information I need to make my brain figure out the resolution at a distance based on dish size and frequency receiving.  So I don't have to remember this, again, I'm writing it down here.

1. The formula Ψ = 70λ/D creates an estimate for the beamwidth of half the power (to -3dB of the signal).
2. A larger parabolic antenna will yield a smaller beamwidth which should result in a higher resolution.
3. As frequency goes up the beamwidth goes down.

I'll use a 1m [diameter] dish as a reference since that size isn't too large for personal use.

This provides the basis of receiving a signal from a distance.  But the other question to look at is how big is that signal that you are looking for.  If you are trying to communicate with another terrestrial station, or even an orbiting station, then having equal footing is great as there is no waste.  This hardly happens and the antenna usually ends up trying to pull in a weak station and also gathering the surrounding noise.

But what if I'm not trying to communicate with another station but rather trying to hear a tiny "voice" in the middle of trillions of other voices?  I'd want a very tight beam to be able to not only pull out that tiny voice but also not collect the surrounding voices (and not overwhelming my receiver with a high noise floor).  The vocabulary escapes me at this point.  I'm sure there is a word for it but all I can come up with are words that describe optical reception (e.g. pixels and resolution).  When I can figure out the vocabulary and the formulas needed to put these two puzzle pieces together I'll post it here.