One of the things which helps with "how far" is time: if you can wait until something has rotated a bit, then you get sideways distance to do triangulation. (because the path of the earth in orbit defines a wider baseline so two observations at the equinoxes (for instance) give you maximal distance. If you can wait even longer you get other rotational movements but some of those "longers" are very long.)
As a student in the amateur astronomy space (I didn't progress far) I was quite purturbed by the main sequence "colour == size" thing and the parallel lanes of "colour == distance" and "colour == age"
It felt like cheating to put 3 qualities into play, all of which could undermine the others. I'm not even really sure I think you can have two. Maybe there is some unstated principle that all dull things are old and all red dull things are old and far away, but if you also think all old red dull things are huge but all you got was "it's red" then it's feeling shakey.
Triangulation doesn't especially add much (or, in fact anything at all) when the base of the triangle is 2 AU across (the diameter of the Earth's orbit, or roughly 16 light minutes) and the long axis of the triangle is 13.4 billion light years.
What about for discounting the false positives of objects which may be "closer in the mirror than they appear" ?
I would have thought the differential to movement and the accuracy of a 2AU baseline was meaningful there. And occultation, both of which comes from study of other objects of known distance, which are within the limits of resolution for a 2AU baseline. I believe the GAIA mission pushed to 10-6 arcsec. I can't find a more recent limit online, love to know what it is. (copied from https://astronomy.swin.edu.au/cosmos/t/trigonometric+paralla...)
These are fair points .. but not especially so for objects this distant.
Given what you know from your interest already you might like to, say, work out at what distance objects appear to essentially fixed in position when viewed from either end of a 2 AU baseline.
Having a background wallpaper of 'fixed' objects that can be occluded helps to inform us about the closer occluding objects .. but triangulation doesn't assist in depth sorting all the distant objects that appear fixed.
My comment above assumed (perhaps incorrectly) that you were referring to the title topic and implying that our motion about the sun was enough to determine the distance to these far objects as the JWT moved through a few orbits.
No, I did make that assumption. I didn't realize the limits to VLBI inside our own contextual frame(s) of reference. Getting more AU into things would be nice but I suppose there are other, nicer, cheaper things we can do. And if the main sequence and redshift thing is good enough, then in the end "how far away it is" can remain defined by that, rather than by geometry.
I think the solar system moves ~48 AU around the galactic centre every year. And the Milky Way is doing ~117 AU per year. (Using google for calculations)
So maybe that combined with space based telescopes helps to make the parallax method more useful over time. Depending on vectors, etc.
"Colour" is oversimplifying it a bit. We're usually concerned with the distribution of light received with respect to wavelength. In the case of distance, it's not just that "it's red", but that the entire spectrum has been shifted in the direction of red. That means the features that correspond to, say, a specific Hydrogen emission, appear slightly offset from where they would if you were looking at it in a lab. When you look at age and size, you're looking at the distribution of the spectrum irrespective of a shift and seeing if it's heavier in the red, blue, or somewhere else. That tells you a lot about composition and mass, which helps with the age and size questions.
TL;DR: the use of color terms (e.g., "red") is oversimplifying what astronomers actually do which is an analysis of the overall spectrum and its properties.
It's not color == distance though, it is color + brightness. Maybe there is some unknown principle at play but you could say that about anything which is not directly measurable, for example how old the earth is. But, it's the best we've got so far, and it does provide seemingly reasonable results that also align with parallax measurements when parallax is within the usable range.
As a student in the amateur astronomy space (I didn't progress far) I was quite purturbed by the main sequence "colour == size" thing and the parallel lanes of "colour == distance" and "colour == age"
It felt like cheating to put 3 qualities into play, all of which could undermine the others. I'm not even really sure I think you can have two. Maybe there is some unstated principle that all dull things are old and all red dull things are old and far away, but if you also think all old red dull things are huge but all you got was "it's red" then it's feeling shakey.
Pick one.