Louis R wrote:I am constantly amused by the way things like this arise constantly in discussions of Honorverse tech: the sublime confidence that 2000 years of technology can erase or overcome fundamental characteristics of the universe. In this case, no possible advance can overcome a fundamental limit of physical optics. Build it in the '70s or build it two millennia from now, a 2m telescope will have the same resolution. And the same light-gathering power, which is a major consideration in this case. [this is minor compared to one proposal i recall being advanced many years ago, which in effect required that 'technical progress' insert new elements in the periodic table. between known elements.]
Yes, an SD wedge subtends an angle of 4 arcsec at 1 lm - I made those calculations as preparation for that post. The problem is that in order to measure that angle you need to identify both edges of the wedge. And, as I said, unless you have maneuvered specifically to do that the odds of having a suitable set of objects in the field of view are negligible. When you do have them, in order to translate angular width into the linear dimension of the wedge you _must_ know its orientation WRT your line of sight and its distance from you. Get either of those off by 10%, and you can't tell the difference between a freighter and a cruiser.
Once you get close enough, yep, it's a trivial exercise, but at that point you're going to be too freaking close for the answer to do you any good anyway.
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These starships are quite large, and it would be plausible to have several four meter optical telescopes even on a DD without taking up too much room.
Another approach would be to use recon drones and very long baseline interferometry which would effectively give you enormous resolving power. Solving the technical challenges with respect to practical visible-light interferometry wouldn't require suspending the laws of physics. Recon drones aren't exactly small either and could easily have a large optical telescope aboard.
With respect to the orientation of the wedge, you do have some additional information -- you know the wedge is square and you also know its velocity. That limits the degrees of freedom quite a bit. If you can look at a given wedge with recon drones from a couple of different directions I'm pretty sure you can figure out the wedge size.
I know I don't write the books or the rules that physics follow in the books. But it is well-known in our universe that gravitational fields can frequency-shift light (I'm not sure if an impeller wedge would red-shift or blue-shift light). If you looked for hydrogen emission lines associated with nearly all stars and looked for the area where those emission lines were dramatically frequency-shifted, given enough time and looking at the wedge in question from enough angles I suspect you could estimate its size even from a few light-minutes away.
Another way to look at it: if your impeller wedge is moving (which they almost always are) once they occult a star all you need to know is how long the star was occulted from your position (and since you know the velocity) you would get at least a rough estimate of the length of its wedge. Since the wedge is square once you know the length you know its size.
Yes, there are some pathological cases (mainly where the wedge in question is coming directly towards or away from you or where the sidewalls are facing directly towards you) where those techniques won't work -- that's why it would help immensely to look at the wedge from several different angles.