I wonder what the science of UFO Phenomena would look like.

For instance, in the vastness of space, you are fairly exposed. It's true that a rock the size of a mountain in space at any significant distance from Earth would hard to detect, but it would hard to hide such a rock, assuming someone was to point a telescope in the right direction which had the resolution to see it.

How big would these interstellar vehicles be, and are they making any effort to "cloak" their presence. As we "know" from star trek even a cloaked Romulan ship leaves a ion trail- from it's engines.

Any alien ship entering our solar system at near light speed and slowing down to order to enter into orbit around earth, generally speaking should fairly obvious to see. Or anything traveling at high speed [say 10 million mph- which is not very fast] should be detectable- because the vacuum of space is not a complete vacuum, and therefore at such speeds should cause some kind of wake- one would see lines which radiated high energy- though perhaps are so high it would be in X-ray part of spectrum- though these would cool, so one should see them optically at some point.

Now, if they "warping around" in something the size of Ford Mustang, one is going to have number of problems detecting this. This kind of magic doesn't allow us much room to look at it scientifically. One could ask is their any strange phenomena that could vaguely fit this profile which we have no other explanation- it is influencing Time in any measurable way, strange gravity anamolies, etc. But this pretty vague stuff. And if you assume some creature who vastly more technological capable than our selves and assume there taking measures to avoid our detection- well why not simply try to look for God with scientific instruments- maybe, He wants to be found.

As far as buzzing around our atmosphere, this doesn't make much sense. Are they lost? Why not simply put some high tech satellite in our orbit- replacing one of ours with their own which acts like one of our satellites, but has far better capability- meanwhile they can say land on the moon and have lunch or whatever. Or if they must fly in our atmosphere for some reason, make the spacecraft look like some vehicle that Earthlings use.