What is the tolerance for astrophysic measurements compared to distance? So I have a fascination with precision.  I collect micrometers, I have a pride in my caliper collection.  That set of precision is for useful systems here on earth.
Maybe for a high end rifle with no stamped parts we shoot for a tolerance of half millionth inch on critical systems.
With astrophysics, what tolerances are they using?   The earth is always moving around the sun that is always moving around a galactic black hole that is moving in a cosmic dance and not always in nice circles or perfect geometric lines.
We use certain super novae to measure distances, but that can only be as accurate as our optics and maybe variables we can’t predict.
This is so exciting to think about in my head.
So what is the system of tolerance used in astrophysics???
 A: There's two ways to look at precision in astrophysics. Crazy precise, or crazy imprecise. It depends on if you look at what's being measured, or what the result is. I'll use measuring cosmic distances as an example.
Distances are calculated using the cosmic distance ladder. This starts with direct measurements using simple geometry like parallax. The more fine these measurements are, the further distances we can measure directly. Parallax angles can be measured, in some cases, to 20 microarcseconds allowing precision measurements out to 10,000 light years. That's 94,610,000,000,000,000 km. Astonishingly precise!
However, this doesn't always result in precise measurements. Stellar objects often don't have sharp edges. Sometimes they change size. Often there's dust in the way. Gravity warps the path of light. And the distances are mind-boggling!
This can result in measurements with breathtaking error bars. For example, Betelgeuse is one of the brightest stars in the sky, yet we have a lot of trouble measuring its distance. 2008 observations gave 643 ±146 ly, huge error bars. Updates measured 724 ly +111/−156 ly and 548 ly +88/−49 ly. These might seem like huge errors, but that's only because the distances involved are so mind-bogglingly enormous. 500 ly is 5,670,000,000,000,000 km.
The actual measurements are +/- less than one milliarcsecond. Imagine the width of a coin in Paris as seen from New York City, that's a milliarcsecond.
After that things start to get fuzzy. Very fuzzy. Beyond the range where parallax is useful, astrophysicists must extrapolate distances and the inaccuracies in the direct measurements compound each other. For example, some events like supernovae are thought to always have the same absolute brightness. If you measure their relative brightness you can calculate their distances. These are called standard candles. These must be calibrated using other distance measuring techniques which themselves have uncertainty.
For these reasons, at galactic scales astrophysicists often work in orders of magnitude rather than precise numbers.
