If I want to measure the beam-width of a radio telescope sweeping through a ~ puntual object (the Sun) with a ~ constant flux output when measured:
The value measured sweeping in one frame of reference (and coordinate system), will be the same if it's measured using another frame, right?
If I point to the Sun and sweep in alt-az, I suspect that measurement will be at least roughly similar to a measurement w.r.t e.g., a star on the plane of the Milky Way (using l,b). This because the same principle should be applied for a radio (or any other signal) emitter: a measured angle difference $\Delta \theta$ should be the same in another frame.
What puzzles me is to think that an arbitrary frame could scale any measured quantity but I'm not sure at all.
This could be seen in stellarium as:
I apologize if this is a weird, vague or naive question.