@edsu The diameter of the event horizon is too small in most instances to be visible from Earth. Most stellar black holes are Earth sized. If not smaller. Their disks simply cannot be imaged. We've only managed to get very fuzzy images of two so far as I'm aware.
It's also typically hidden behind if not the accretion disk itself, then other galactic dust and matter.
Stars orbit Sag A* at ranges of from 12.6 to over 23,000 AU (astronomical unit, the mean distance from Earth to the Sun, about 150 million km). That maximum range is about 1/3 of a lightyear. Orbital periods range from about 10 Earth years to 2,730.
And as far as I understand it, it's not necessary to measure stellar distances or movement with precision, but changes in momentum, that is, gravitational acceleration by the central mass itself, which can be determined very precisely through Dopplar shifts in the stars' emissions. These can be detected in visible, infrared, or radio ranges, the latter of which pass through galactic dust readily.
@edsu I'm mostly a dabbler myself.
Oh: another element: since orbits are defined by gravitational attraction, knowing the orbital period / characteristics also makes possible a pretty accurate assessment of mass.
My understanding is that this is how the mass of the planets of the Solar System was first determined.
Depending on how observable the orbiting stars are, their own characteristics can be determined with some accuracy as well.
We can determine stellar temperature by the blackbody emissions --- spectral frequency at the surface.
We have a pretty good sense of distance (Galactic centre).
The total observed luminosity is then the emissions per unit area * total visible surface area, which gives us diameter.
And models of stellar evolution give us a pretty good idea of mass.
This is based on good visual observations, which for stars near the Galactic core is probably a sketchy proposition (too much dust, gas, and other stuff in the way). But this is more or less how the sizes and rough approximations of masses of many observable stars is determined.
Stellar distances within the Galaxy is actually somewhat challenging, as there are few mileposts, though highly-predictable stars (e.g., cephid variables) tend to be good at determining distance. These have a characteristic luminosity which varies in a predictable manner, and so the brightness translates directly as distance. For nearby stars (say, in a cluster or nebula), or multi-stellar systems) the distance can then be roughed out.
This is even more effective for remote galaxies, where we want to know the overall distance between that galaxy and ours.
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