NavList:

Pierre B, you wrote:

"I think you got the point. I've got a 3.5x38 telescope. Recently I tried
a lunar distance with Saturn. The ephemeris give for Saturn a semi
diameter of 0.2', that is a whole diameter of 0.4'. But through the
scope, I see only a spot. A bright one, but nevertheless a spot. So the
magnification is too small to get a 0.4' accuracy."

 

They say that the resolution of the unaided human eye, corrected if necessary, is somewhere between 1 and 2 minutes of arc (sources disagree, and I haven't done any serious testing but it's clearly somewhere in that range). Let's call it 1.5 minutes for the sake of discussion. All other things being equal, a magnification of 3.5 should yield an apparent resolution slightly greater than 0.4 minutes. We can't do better than that unless we trade in our eyes for a better model... or acquire a higher powered telescope for our sextants.

 

By the way, for what it's worth, I think it's distinctly easier to see a gap between two images of a given angular size than it is to detect an object's angular diameter of the same size.